Research work on incorporating damping effects on the quantum dynamics of superconductivity driven out of equilibrium by Terahertz lasers. Presented at the sack lunch seminar in the physics department of University of Minnesota.

1. Impact of damping on
superconducting gap oscillations
induced by Terahertz pulses
Tianbai Cui, Rafael M. Fernandes
Iowa State University and Ames Laboratory
Xu Yang, Chirag Vaswani, Jigang Wang, Peter P. Orth
University of Minnesota

2. [1] R. Matsunaga and R. Shimano, Phys. Scr., 92(2), 24003 (2017).
[2]A. F. Kemper, M. A. Sentef, B. Moritz, J. K. Freericks, and T. P. Devereaux, Phys. Rev. B, 92, 224517 (2015).
Equilibrium superconductivity

3. [1] R. Matsunaga and R. Shimano, Phys. Scr., 92(2), 24003 (2017).
[2]A. F. Kemper, M. A. Sentef, B. Moritz, J. K. Freericks, and T. P. Devereaux, Phys. Rev. B, 92, 224517 (2015).
Equilibrium superconductivity
Δ = −U c−k,↓
ck,↑
k
∑

4. [1] R. Matsunaga and R. Shimano, Phys. Scr., 92(2), 24003 (2017).
[2]A. F. Kemper, M. A. Sentef, B. Moritz, J. K. Freericks, and T. P. Devereaux, Phys. Rev. B, 92, 224517 (2015).
Equilibrium superconductivity
Δ = −U c−k,↓
ck,↑
k
∑

5. [1] R. Matsunaga and R. Shimano, Phys. Scr., 92(2), 24003 (2017).
[2]A. F. Kemper, M. A. Sentef, B. Moritz, J. K. Freericks, and T. P. Devereaux, Phys. Rev. B, 92, 224517 (2015).
Equilibrium superconductivity
Δ = −U c−k,↓
ck,↑
k
∑

6. FREERICKS, AND DEVEREAUX PHY
(b) where ¯τ3 is the z Pauli matr
k
¯GC
k(t,t′
), i.e., the local
The equations to be solv
and as such, the parameters
feasibility of the simulatio
binding model at half fill
strength is Vnn = 0.25 eV
coupling are chosen as 0.8
resulting phonon coupling
Non-equilibrium superconductivity
[1] R. Matsunaga and R. Shimano, Phys. Scr., 92(2), 24003 (2017).
[2]A. F. Kemper, M. A. Sentef, B. Moritz, J. K. Freericks, and T. P. Devereaux, Phys. Rev. B, 92, 224517 (2015).

7. t
Δ t( )
0
Δi
?
Typical time scales

8. t
Δ t( )
0
Δi
?
τ ~1 ps
Typical time scales

9. t
Δ t( )
0
Δi
?
τ ~1 ps
Typical time scales
MORITZ, FREERICKS, AND DEVEREAUX
(b) where ¯τ3 is t
k
¯GC
k(t,t′
)
The equa
and as such,
feasibility o
binding mo
strength is
coupling are
resulting phi<latexit sha1_base64="2N1yYanHrnIcuhqqzhhBb4H1FcQ=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0J3rlilt1c5Bl4s1JpXYEOeq98le3H7M04gqZpMZ0PDdBP6MaBZN8UuqmhieUjeiAdyxVNOLGz/J7J+TUKn0SxtqWQpKrvycyGhkzjgLbGVEcmkVvKv7ndVIMr/xMqCRFrthsUZhKgjGZPk/6QnOGcmwJZVrYWwkbUk0Z2ohKNgRv8eVl0jyvem7Vu7+o1K5naUARjuEEzsCDS6jBHdShAQwkPMMrvDmPzovz7nzMWgvOfOYQ/sD5/AFQr5As</latexit><latexit sha1_base64="2N1yYanHrnIcuhqqzhhBb4H1FcQ=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0J3rlilt1c5Bl4s1JpXYEOeq98le3H7M04gqZpMZ0PDdBP6MaBZN8UuqmhieUjeiAdyxVNOLGz/J7J+TUKn0SxtqWQpKrvycyGhkzjgLbGVEcmkVvKv7ndVIMr/xMqCRFrthsUZhKgjGZPk/6QnOGcmwJZVrYWwkbUk0Z2ohKNgRv8eVl0jyvem7Vu7+o1K5naUARjuEEzsCDS6jBHdShAQwkPMMrvDmPzovz7nzMWgvOfOYQ/sD5/AFQr5As</latexit><latexit sha1_base64="2N1yYanHrnIcuhqqzhhBb4H1FcQ=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0J3rlilt1c5Bl4s1JpXYEOeq98le3H7M04gqZpMZ0PDdBP6MaBZN8UuqmhieUjeiAdyxVNOLGz/J7J+TUKn0SxtqWQpKrvycyGhkzjgLbGVEcmkVvKv7ndVIMr/xMqCRFrthsUZhKgjGZPk/6QnOGcmwJZVrYWwkbUk0Z2ohKNgRv8eVl0jyvem7Vu7+o1K5naUARjuEEzsCDS6jBHdShAQwkPMMrvDmPzovz7nzMWgvOfOYQ/sD5/AFQr5As</latexit><latexit sha1_base64="fMsAfk+GptT+f4vGXjw6PP7E2eg=">AAAB73icbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6LGoB48VbC20oWy203bpZhN3J0IJ/RNePCji1b/jzX/jts1BWx8MPN6bYWZemEhhyPO+ncLK6tr6RnGztLW9s7tX3j9omjjVHBs8lrFuhcygFAobJEhiK9HIolDiQzi6nvoPT6iNiNU9jRMMIjZQoi84Iyu1OjcoiXVFt1zxqt4M7jLxc1KBHPVu+avTi3kaoSIumTFt30soyJgmwSVOSp3UYML4iA2wbaliEZogm907cU+s0nP7sbalyJ2pvycyFhkzjkLbGTEamkVvKv7ntVPqXwaZUElKqPh8UT+VLsXu9Hm3JzRykmNLGNfC3uryIdOMk42oZEPwF19eJs2zqu9V/bvzSu0qj6MIR3AMp+DDBdTgFurQAA4SnuEV3pxH58V5dz7mrQUnnzmEP3A+fwDehI/Y</latexit>
f<latexit sha1_base64="1nPYgCmg3zstc2+9qewl+DvN/kk=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0F/bKFbfq5iDLxJuTSu0IctR75a9uP2ZpxBUySY3peG6CfkY1Cib5pNRNDU8oG9EB71iqaMSNn+X3TsipVfokjLUthSRXf09kNDJmHAW2M6I4NIveVPzP66QYXvmZUEmKXLHZojCVBGMyfZ70heYM5dgSyrSwtxI2pJoytBGVbAje4svLpHle9dyqd39RqV3P0oAiHMMJnIEHl1CDO6hDAxhIeIZXeHMenRfn3fmYtRac+cwh/IHz+QNMI5Ap</latexit><latexit sha1_base64="1nPYgCmg3zstc2+9qewl+DvN/kk=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0F/bKFbfq5iDLxJuTSu0IctR75a9uP2ZpxBUySY3peG6CfkY1Cib5pNRNDU8oG9EB71iqaMSNn+X3TsipVfokjLUthSRXf09kNDJmHAW2M6I4NIveVPzP66QYXvmZUEmKXLHZojCVBGMyfZ70heYM5dgSyrSwtxI2pJoytBGVbAje4svLpHle9dyqd39RqV3P0oAiHMMJnIEHl1CDO6hDAxhIeIZXeHMenRfn3fmYtRac+cwh/IHz+QNMI5Ap</latexit><latexit sha1_base64="1nPYgCmg3zstc2+9qewl+DvN/kk=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0F/bKFbfq5iDLxJuTSu0IctR75a9uP2ZpxBUySY3peG6CfkY1Cib5pNRNDU8oG9EB71iqaMSNn+X3TsipVfokjLUthSRXf09kNDJmHAW2M6I4NIveVPzP66QYXvmZUEmKXLHZojCVBGMyfZ70heYM5dgSyrSwtxI2pJoytBGVbAje4svLpHle9dyqd39RqV3P0oAiHMMJnIEHl1CDO6hDAxhIeIZXeHMenRfn3fmYtRac+cwh/IHz+QNMI5Ap</latexit><latexit sha1_base64="yOEy1gBFh1+VEhvpSAouk0nokLE=">AAAB73icbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6LGoB48VbC20pWy2k3bpZhN3J0IJ/RNePCji1b/jzX/jts1BWx8MPN6bYWZekEhhyPO+ncLK6tr6RnGztLW9s7tX3j9omjjVHBs8lrFuBcygFAobJEhiK9HIokDiQzC6nvoPT6iNiNU9jRPsRmygRCg4Iyu1OjcoifXCXrniVb0Z3GXi56QCOeq98lenH/M0QkVcMmPavpdQN2OaBJc4KXVSgwnjIzbAtqWKRWi62ezeiXtilb4bxtqWInem/p7IWGTMOApsZ8RoaBa9qfif104pvOxmQiUpoeLzRWEqXYrd6fNuX2jkJMeWMK6FvdXlQ6YZJxtRyYbgL768TJpnVd+r+nfnldpVHkcRjuAYTsGHC6jBLdShARwkPMMrvDmPzovz7nzMWwtOPnMIf+B8/gDZ+I/V</latexit>

10. t
Δ t( )
0
Δi
Δ f
?
τ ~1 ps
Typical time scales
MORITZ, FREERICKS, AND DEVEREAUX
(b) where ¯τ3 is t
k
¯GC
k(t,t′
)
The equa
and as such,
feasibility o
binding mo
strength is
coupling are
resulting phi<latexit sha1_base64="2N1yYanHrnIcuhqqzhhBb4H1FcQ=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0J3rlilt1c5Bl4s1JpXYEOeq98le3H7M04gqZpMZ0PDdBP6MaBZN8UuqmhieUjeiAdyxVNOLGz/J7J+TUKn0SxtqWQpKrvycyGhkzjgLbGVEcmkVvKv7ndVIMr/xMqCRFrthsUZhKgjGZPk/6QnOGcmwJZVrYWwkbUk0Z2ohKNgRv8eVl0jyvem7Vu7+o1K5naUARjuEEzsCDS6jBHdShAQwkPMMrvDmPzovz7nzMWgvOfOYQ/sD5/AFQr5As</latexit><latexit sha1_base64="2N1yYanHrnIcuhqqzhhBb4H1FcQ=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0J3rlilt1c5Bl4s1JpXYEOeq98le3H7M04gqZpMZ0PDdBP6MaBZN8UuqmhieUjeiAdyxVNOLGz/J7J+TUKn0SxtqWQpKrvycyGhkzjgLbGVEcmkVvKv7ndVIMr/xMqCRFrthsUZhKgjGZPk/6QnOGcmwJZVrYWwkbUk0Z2ohKNgRv8eVl0jyvem7Vu7+o1K5naUARjuEEzsCDS6jBHdShAQwkPMMrvDmPzovz7nzMWgvOfOYQ/sD5/AFQr5As</latexit><latexit sha1_base64="2N1yYanHrnIcuhqqzhhBb4H1FcQ=">AAAB73icbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlAsoTZyWwyZHZ2nekVwpKf8OJBEa/+jjf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt1O7ecom0J3rlilt1c5Bl4s1JpXYEOeq98le3H7M04gqZpMZ0PDdBP6MaBZN8UuqmhieUjeiAdyxVNOLGz/J7J+TUKn0SxtqWQpKrvycyGhkzjgLbGVEcmkVvKv7ndVIMr/xMqCRFrthsUZhKgjGZPk/6QnOGcmwJZVrYWwkbUk0Z2ohKNgRv8eVl0jyvem7Vu7+o1K5naUARjuEEzsCDS6jBHdShAQwkPMMrvDmPzovz7nzMWgvOfOYQ/sD5/AFQr5As</latexit><latexit sha1_base64="fMsAfk+GptT+f4vGXjw6PP7E2eg=">AAAB73icbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6LGoB48VbC20oWy203bpZhN3J0IJ/RNePCji1b/jzX/jts1BWx8MPN6bYWZemEhhyPO+ncLK6tr6RnGztLW9s7tX3j9omjjVHBs8lrFuhcygFAobJEhiK9HIolDiQzi6nvoPT6iNiNU9jRMMIjZQoi84Iyu1OjcoiXVFt1zxqt4M7jLxc1KBHPVu+avTi3kaoSIumTFt30soyJgmwSVOSp3UYML4iA2wbaliEZogm907cU+s0nP7sbalyJ2pvycyFhkzjkLbGTEamkVvKv7ntVPqXwaZUElKqPh8UT+VLsXu9Hm3JzRykmNLGNfC3uryIdOMk42oZEPwF19eJs2zqu9V/bvzSu0qj6MIR3AMp+DDBdTgFurQAA4SnuEV3pxH58V5dz7mrQUnnzmEP3A+fwDehI/Y</latexit>
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11. t
Δ t( )
0
Δi
Δ f
?
τ ~1 ps
Typical time scales

12. Bath
t
Δ t( )
0 tthermal
≫100 ps
Δi
Δ f
?
τ ~1 ps
Typical time scales

13. Bath
t
Δ t( )
0 tthermal
≫100 ps
Δi
Δ f
?
τ ~1 ps
Typical time scales
Δi

14. Bath
t
Δ t( )
0 tthermal
≫100 ps
Δi
Δ f
?
τ ~1 ps
Typical time scales
Δi
t ∼10 ps

15. [1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006)
Bath
t
Δ t( )
0
Δi
Δ f
τ
Transient dynamics
Δi
tthermal
>100 ps
Δi
Δ f
> eπ /2
≈ 4.8

16. [1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006)
Bath
t
Δ t( )
0
Δi
Δ f
τ
Transient dynamics
Δi
tthermal
>100 ps
Δi
Δ f
> eπ /2
≈ 4.8

17. [1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006)
Bath
t
Δ t( )
0
Δi
Δ f
τ
Transient dynamics
Δi
tthermal
>100 ps
Δi
Δ f
> eπ /2
≈ 4.8

18. [1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006)
Bath
t
Δ t( )
0
Δi
Δ f
τ
Transient dynamics
Δi
tthermal
>100 ps
Δi
Δ f
> eπ /2
≈ 4.8

19. [1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006)
Bath
t
Δ t( )
0
Δi
Δ f
τ
Transient dynamics
Δi
tthermal
>100 ps
Δi
Δ f
< e−π /2
≈ 0.2

20. [1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006)
Bath
t
Δ t( )
0
Δi
Δ f
τ
Transient dynamics
Δi
tthermal
>100 ps
Δi
Δ f
< e−π /2
≈ 0.2
Δ+
Δ−
Persistent Oscillation

21. [1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006)
Bath
t
Δ t( )
0
Δi
Δ f
τ
Transient dynamics
Δi
tthermal
>100 ps
Δi
Δ f
< e−π /2
≈ 0.2

22. Bath
t
Δ t( )
0
Δ f
Transient dynamics
Δi
tthermal
>100 ps
e−π /2
<
Δi
Δ f
< eπ /2
Δi
[1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006). [3] A.F. Volkov, S.M. Kogan, Sov. Phys. JETP, 38(5), 1018 (1974).

23. Bath
t
Δ t( )
0
Δ f
Transient dynamics
Δi
tthermal
>100 ps
e−π /2
<
Δi
Δ f
< eπ /2
Δi
[1] E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, V. Z. Enolskii, Phys. Rev. B, 72, 220503 (2005)
[2] R. A. Barankov, L. S. Levitov, Phys. Rev. Lett., 96, 230403 (2006). [3] A.F. Volkov, S.M. Kogan, Sov. Phys. JETP, 38(5), 1018 (1974).
Coherent oscillation
(t) = 1 + a
cos (2 1t + )
( 1t)
1/2
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24. [1] R. Matsunaga et al., Phys. Rev. Lett., 111, 057002 (2013).
THz-pump-probe-experiment
Nb1−xTixN film
Phys. Scr. 92 (2017) 024003
E / 1
(t)
i<latexit sha1_base64="xdAHGQA8KcTdH9lfv3DkplhhvQA=">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</latexit><latexit sha1_base64="xdAHGQA8KcTdH9lfv3DkplhhvQA=">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</latexit><latexit sha1_base64="xdAHGQA8KcTdH9lfv3DkplhhvQA=">AAACIXicbZDPattAEMZHbpu6TpM4bW+9LDEF9xAjhUJ9NEkLPaZQ/wHLmNV6ZC9eacXuqGCEXiWXvEouOaSU3EpfpmvZh9buBwsfv5lhdr4oU9KS7//yak+ePjt4Xn/ROHx5dHzSPH01sDo3AvtCK21GEbeoZIp9kqRwlBnkSaRwGC2v1vXhdzRW6vQbrTKcJHyeylgKTg5Nm91whoo4+xxmRmekg/MwNlwU4ac1DhXG1KbQyPmC3pdbOi1kWU6bLb/jV2L7JtiaVu8NVLqeNh/DmRZ5gikJxa0dB35Gk4IbkkJh2QhzixkXSz7HsbMpT9BOiurCkr1zZMZibdxLiVX074mCJ9auksh1JpwWdre2hv+rjXOKu5NCpllOmIrNojhXjDRbx8Vm0qAgtXKGCyPdX5lYcJcQuVAbLoRg9+R9M7joBH4n+Pqh1bvcpAF1eAtn0IYAPkIPvsA19EHADdzBA/zwbr1776f3uGmteduZ1/CPvN9/ACmLpNI=</latexit><latexit sha1_base64="0CGjQHswXXvFB751qZT0V60qFJQ=">AAACIXicbZBNS8NAEIY3flu/qh69LBZBD5ZEBHsUP8BjBVuFppTNdtIu3WTD7kQoIX/Fi3/FiwdFehP/jNs2B7W+sPDyzAyz8waJFAZd99OZm19YXFpeWS2trW9sbpW3d5pGpZpDgyup9EPADEgRQwMFSnhINLAokHAfDC7H9ftH0Eao+A6HCbQj1otFKDhDizrlmt8FiYxe+4lWCSrv2A8145l/Nca+hBAP0dei18ejvKCdTOR5p1xxq+5EdNZ4hamQQvVOeeR3FU8jiJFLZkzLcxNsZ0yj4BLykp8aSBgfsB60rI1ZBKadTS7M6YElXRoqbV+MdEJ/TmQsMmYYBbYzYtg3f2tj+F+tlWJYa2ciTlKEmE8XhamkqOg4LtoVGjjKoTWMa2H/Snmf2YTQhlqyIXh/T541zZOq51a929PK+UURxwrZI/vkkHjkjJyTG1InDcLJE3khb+TdeXZenQ9nNG2dc4qZXfJLztc3t2Ckfg==</latexit>

25. [1] R. Matsunaga et al., Phys. Rev. Lett., 111, 057002 (2013).
THz-pump-probe-experiment
Nb1−xTixN film
Phys. Scr. 92 (2017) 024003
E / 1
(t)
i<latexit sha1_base64="xdAHGQA8KcTdH9lfv3DkplhhvQA=">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</latexit><latexit sha1_base64="xdAHGQA8KcTdH9lfv3DkplhhvQA=">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</latexit><latexit sha1_base64="xdAHGQA8KcTdH9lfv3DkplhhvQA=">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</latexit><latexit sha1_base64="0CGjQHswXXvFB751qZT0V60qFJQ=">AAACIXicbZBNS8NAEIY3flu/qh69LBZBD5ZEBHsUP8BjBVuFppTNdtIu3WTD7kQoIX/Fi3/FiwdFehP/jNs2B7W+sPDyzAyz8waJFAZd99OZm19YXFpeWS2trW9sbpW3d5pGpZpDgyup9EPADEgRQwMFSnhINLAokHAfDC7H9ftH0Eao+A6HCbQj1otFKDhDizrlmt8FiYxe+4lWCSrv2A8145l/Nca+hBAP0dei18ejvKCdTOR5p1xxq+5EdNZ4hamQQvVOeeR3FU8jiJFLZkzLcxNsZ0yj4BLykp8aSBgfsB60rI1ZBKadTS7M6YElXRoqbV+MdEJ/TmQsMmYYBbYzYtg3f2tj+F+tlWJYa2ciTlKEmE8XhamkqOg4LtoVGjjKoTWMa2H/Snmf2YTQhlqyIXh/T541zZOq51a929PK+UURxwrZI/vkkHjkjJyTG1InDcLJE3khb+TdeXZenQ9nNG2dc4qZXfJLztc3t2Ckfg==</latexit>

26. [1] R. Matsunaga et al., Phys. Rev. Lett., 111, 057002 (2013).
THz-pump-probe-experiment
Nb1−xTixN film
Phys. Scr. 92 (2017) 024003
E / 1
(t)
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27. Resonantly driven amplitude mode

28. Resonantly driven amplitude mode

29. [1] R. Matsunaga et al., Science, 345, 6201 (2014).
quasi-particles (QPs) in one-photon pro-
s at low temperatures. The sample is an
e superconductor NbN thin film with 24-nm
ness grown on an MgO substrate (24) with
conducting critical temperature (Tc) = 15 K.
ltrafast dynamics of the superconducting
parameter driven by the multicycle pump
is then probed through the transmittance
monocycle THz pulse that enters the
le collinearly with the pump pulse with
able time delay. In general, we can detect
emporal waveform of the transmitted
THz electric field, Eprobe, by varying the
changes with temperature, reflecting the change
of the order parameter. Temporal evolution of the
order parameter induced by the THz pump is
sensitively monitored through the change of
Eprobe relative to its value in the absence of the
pump as a function of the pump-probe delay
time, tpp (16, 22); we denote this change as
dEprobe. For details, see (25). In the present case,
we investigated the order parameter dynamics
in the presence of coherently oscillating multi-
cycle pump fields. The temporal waveform of the
pump THz electric field Epump is displayed in
Fig. 1D for the center frequency of w = 0.6 THz
Intensity(arb.units)
ω=0.6 THz
Epump
|Epump
|2
NbN/MgO
Pump
Probe
WGP
WGPBPF
1086420
Delay Time (ps)
0.3 THz
0.6 THz
0.8 THz
onMarch28,2017http://science.sciencemag.org/from
Resonantly driven amplitude mode

30. [1] R. Matsunaga et al., Science, 345, 6201 (2014).
quasi-particles (QPs) in one-photon pro-
s at low temperatures. The sample is an
e superconductor NbN thin film with 24-nm
ness grown on an MgO substrate (24) with
conducting critical temperature (Tc) = 15 K.
ltrafast dynamics of the superconducting
parameter driven by the multicycle pump
is then probed through the transmittance
monocycle THz pulse that enters the
le collinearly with the pump pulse with
able time delay. In general, we can detect
emporal waveform of the transmitted
THz electric field, Eprobe, by varying the
changes with temperature, reflecting the change
of the order parameter. Temporal evolution of the
order parameter induced by the THz pump is
sensitively monitored through the change of
Eprobe relative to its value in the absence of the
pump as a function of the pump-probe delay
time, tpp (16, 22); we denote this change as
dEprobe. For details, see (25). In the present case,
we investigated the order parameter dynamics
in the presence of coherently oscillating multi-
cycle pump fields. The temporal waveform of the
pump THz electric field Epump is displayed in
Fig. 1D for the center frequency of w = 0.6 THz
Intensity(arb.units)
ω=0.6 THz
Epump
|Epump
|2
NbN/MgO
Pump
Probe
WGP
WGPBPF
1086420
Delay Time (ps)
0.3 THz
0.6 THz
0.8 THz
onMarch28,2017http://science.sciencemag.org/from
Phys. Scr. 92 (2017) 024003
Resonantly driven amplitude mode
uestions regarding the Higgs mode
uctors remain unresolved: How
couple to strong electromagnetic
inear regime? Is it possible to dy-
rol the Higgs mode and therefore
ucting order parameter?
nces in the intense THz genera-
(19, 20) open a new avenue for
r phases in nonequilibrium con-
ude- and phase-resolved spectros-
lti-THz pulses has been realized
the study of coherent transients
ystems in low-energy ranges. The
present work is to explore co-
ear interplay between collective
erconductor and THz light field
g the real-time evolution of the
r under the driving field of a mul-
osed to monocycle) THz pulse.
study evolutions on a picosecond
performed THz pump–THz probe
16, 22) (Fig. 1A). To generate an
ycle THz pulse as a coherent driv-
irst created an intense monocycle
he tilted-pulse front method with
al (19, 23). The monocycle pulse
ugh a band-pass filter to produce a
e(arb.units)
(THz)
0.8 THz
Intensity(arb.units)
ω=0.6 THz
ω>2∆(T)
ω<2∆(T)
Epump
|Epump
|2
NbN/MgO
Probe
WGP
WGPBPF
0
14 K
14.5 K
14.8 K
15.5 K
1086420
Delay Time (ps)
210
Frequency (THz)
0.3 THz
0.6 THz
0.8 THz
1
E / 1
(t)
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31. Coherent pseudospin dynamics: 2nd & 4th orders
A new collective mode + nonlinear current
z
1.2
0.8
0.4
0.0
11
1
cm
-1
)
1086420
Photon energy (meV)
0.5THz
1 w 4K)
DC= w
Nb3Sn
Tc =16K
Mode
amplitude
0.2
0.1
0.0
-DE/E
151050
Dtpp (ps)
1.0
0.5
0.0
161284
T (K)
First observation of
4th order mode!Both T2 and T1 processes
∆E/E
tpp(ps)
Resonantly driven amplitude mode
E/E / 1
(t)
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32. Quench vs Resonant driving

33. t
Δ t( )
0 tthermal
≫100 ps
Δi
Transient dynamics
Δi
Bath

34. t
Δ t( )
0 tthermal
≫100 ps
Δi
τ ~10 ps
Transient dynamics
Δi
BathA t( )= A0
e
−
t−τ /2( )2
2σ 2
cos ωpump
t( )

35. t
Δ t( )
0 tthermal
≫100 ps
Δi
?
τ ~10 ps
Transient dynamics
Δi
BathA t( )= A0
e
−
t−τ /2( )2
2σ 2
cos ωpump
t( )

36. HBCS = εkck,σ
†
ck,σ
k,σ
∑ +U ck,↑
†
c−k,↓
†
c−k,↓
ck,↑
k, ′k
∑
Pseudo-spin formalism
Δ = −U c−k,↓
ck,↑
k
∑
[1] PW. Anderson, Phys. Rev., 112, 1900 (1958)

37. HBCS = εkck,σ
†
ck,σ
k,σ
∑ +U ck,↑
†
c−k,↓
†
c−k,↓
ck,↑
k, ′k
∑
Pseudo-spin formalism
Δ = −U c−k,↓
ck,↑
k
∑
[1] PW. Anderson, Phys. Rev., 112, 1900 (1958)
ˆSk
z
=
1
2
ck,↑
†
ck,↑
+ c−k,↓
†
c−k,↓
−1( )
ˆSk
+
= ck,↑
†
c−k,↓
†
ˆSk
−
= c−k,↓
ck,↑

38. HBCS = εkck,σ
†
ck,σ
k,σ
∑ +U ck,↑
†
c−k,↓
†
c−k,↓
ck,↑
k, ′k
∑
Pseudo-spin formalism
Δ = −U c−k,↓
ck,↑
k
∑
[1] PW. Anderson, Phys. Rev., 112, 1900 (1958)
ˆSk
z
=
1
2
ck,↑
†
ck,↑
+ c−k,↓
†
c−k,↓
−1( )
ˆSk
+
= ck,↑
†
c−k,↓
†
ˆSk
−
= c−k,↓
ck,↑
ck,↑
c−k,↓
k,↑−k,↓
x
y
z
k,↑−k,↓
x
y
z
ck,↑
†
c−k,↓
† ˆSk
+ ˆSk
−
=
=

39. HBCS = εkck,σ
†
ck,σ
k,σ
∑ +U ck,↑
†
c−k,↓
†
c−k,↓
ck,↑
k, ′k
∑
Pseudo-spin formalism
Δ = −U Sk
−
k
∑
Δ = −U c−k,↓
ck,↑
k
∑
HBCS = − Bk ⋅ ˆSk
k
∑
Bk
= 2Re Δ( ),−2Im Δ( ),−2εk( )
[1] PW. Anderson, Phys. Rev., 112, 1900 (1958)

40. Couple BCS to Light
Δ = −U Sk
−
k
∑HBCS = − Bk ⋅ ˆSk
k
∑

41. Couple BCS to Light
Δ = −U Sk
−
k
∑HBCS = − Bk ⋅ ˆSk
k
∑

42. Couple BCS to Light
εk
→ εk−eA t( )Peierls Substitution:
Δ = −U Sk
−
k
∑HBCS = − Bk ⋅ ˆSk
k
∑

43. Couple BCS to Light
Bk
= 2 Re Δ( ),−Im Δ( ),−
εk−eA t( ) + εk+eA t( )
2
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
εk
→ εk−eA t( )Peierls Substitution:
Δ = −U Sk
−
k
∑HBCS = − Bk ⋅ ˆSk
k
∑

44. Bk ! Sk Sk
x
0−
( )=
Δi
2 εk
2
+ Δi
2
Sk
y
0−
( )= 0
Sk
z
0−
( )=
−εk
2 εk
2
+ Δi
2
Initial conditions:
Bk
= 2 Δi
,0,−εk( )
HBCS = − Bk ⋅ ˆSk
k
∑
x
y
z
Pseudo-spin dynamics

45. Bk ! Sk Sk
x
0−
( )=
Δi
2 εk
2
+ Δi
2
Sk
y
0−
( )= 0
Sk
z
0−
( )=
−εk
2 εk
2
+ Δi
2
Initial conditions:
Bk
= 2 Δi
,0,−εk( )
HBCS = − Bk ⋅ ˆSk
k
∑
x
y
z
−
εk−eA t( ) + εk+eA t( )
2
Pseudo-spin dynamics

46. Bk
Pseudo-spin dynamics
x
y
z
Sk
d
dt
Sk
= i HBCS
, ˆSk
⎡
⎣
⎤
⎦ = −Bk
× Sk
Equations of motion:
Δ t( )= −U Sk
−
k
∑

47. Bk
Pseudo-spin dynamics
x
y
z
Sk
d
dt
Sk
= i HBCS
, ˆSk
⎡
⎣
⎤
⎦ = −Bk
× Sk
Equations of motion:
Δ t( )= −U Sk
−
k
∑

48. Bk
Pseudo-spin dynamics
x
y
z
Sk
d
dt
Sk
= i HBCS
, ˆSk
⎡
⎣
⎤
⎦ = −Bk
× Sk
Equations of motion:
Δ t( )= −U Sk
−
k
∑

49. Results
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1 (t) / i<latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XY8kYqCbJF9yPaUJu0mgoFNBOQU=">AAACCHicbVDJSgNBEO1xjXEb9ejBwSDEg3FGBD0G9eAxglkgMww9nZqkSc9Cd40Qhhy9+CtePCji1U/w5t/YWQ6a+KDg8V4VVfWCVHCFtv1tLCwuLa+sFtaK6xubW9vmzm5DJZlkUGeJSGQroAoEj6GOHAW0Ugk0CgQ0g/71yG8+gFQ8ie9xkIIX0W7MQ84oask3D5wT9wYEUldAiGV0Je/28Ph0IvrcN0t2xR7DmifOlJTIFDXf/HI7CcsiiJEJqlTbsVP0ciqRMwHDopspSCnr0y60NY1pBMrLx48MrSOtdKwwkbpitMbq74mcRkoNokB3RhR7atYbif957QzDSy/ncZohxGyyKMyEhYk1SsXqcAkMxUATyiTXt1qsRyVlqLMr6hCc2ZfnSeOs4tgV5+68VL2axlEg++SQlIlDLkiV3JIaqRNGHskzeSVvxpPxYrwbH5PWBWM6s0f+wPj8AYs4mQg=</latexit>

50. Results
tpp (ps)<latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="aeZd1WGoei1mmQ6vjXEuRhhJVXw=">AAACDHicbVDLSsNAFJ3UV62vqks3wSLUTUlE0GXRjcsK9gFNKZPpTTt0MgkzN2IJ+QA3/oobF4q49QPc+TdO2yy09cDAmXPOZeYePxZco+N8W4WV1bX1jeJmaWt7Z3evvH/Q0lGiGDRZJCLV8akGwSU0kaOATqyAhr6Atj++nvrte1CaR/IOJzH0QjqUPOCMopH65Qr2Uw/hAdM4zjJPQIDV/K4zT/HhCE9Nyqk5M9jLxM1JheRo9Mtf3iBiSQgSmaBad10nxl5KFXImICt5iYaYsjEdQtdQSUPQvXS2TGafGGVgB5EyR6I9U39PpDTUehL6JhlSHOlFbyr+53UTDC57KZdxgiDZ/KEgETZG9rQZe8AVMBQTQyhT3PzVZiOqKEPTX8mU4C6uvExaZzXXqbm355X6VV5HkRyRY1IlLrkgdXJDGqRJGHkkz+SVvFlP1ov1bn3MowUrnzkkf2B9/gCpG5yb</latexit>
1 (t) / i<latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XY8kYqCbJF9yPaUJu0mgoFNBOQU=">AAACCHicbVDJSgNBEO1xjXEb9ejBwSDEg3FGBD0G9eAxglkgMww9nZqkSc9Cd40Qhhy9+CtePCji1U/w5t/YWQ6a+KDg8V4VVfWCVHCFtv1tLCwuLa+sFtaK6xubW9vmzm5DJZlkUGeJSGQroAoEj6GOHAW0Ugk0CgQ0g/71yG8+gFQ8ie9xkIIX0W7MQ84oask3D5wT9wYEUldAiGV0Je/28Ph0IvrcN0t2xR7DmifOlJTIFDXf/HI7CcsiiJEJqlTbsVP0ciqRMwHDopspSCnr0y60NY1pBMrLx48MrSOtdKwwkbpitMbq74mcRkoNokB3RhR7atYbif957QzDSy/ncZohxGyyKMyEhYk1SsXqcAkMxUATyiTXt1qsRyVlqLMr6hCc2ZfnSeOs4tgV5+68VL2axlEg++SQlIlDLkiV3JIaqRNGHskzeSVvxpPxYrwbH5PWBWM6s0f+wPj8AYs4mQg=</latexit>

51. Reality vs BCS
tpp (ps)<latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="aeZd1WGoei1mmQ6vjXEuRhhJVXw=">AAACDHicbVDLSsNAFJ3UV62vqks3wSLUTUlE0GXRjcsK9gFNKZPpTTt0MgkzN2IJ+QA3/oobF4q49QPc+TdO2yy09cDAmXPOZeYePxZco+N8W4WV1bX1jeJmaWt7Z3evvH/Q0lGiGDRZJCLV8akGwSU0kaOATqyAhr6Atj++nvrte1CaR/IOJzH0QjqUPOCMopH65Qr2Uw/hAdM4zjJPQIDV/K4zT/HhCE9Nyqk5M9jLxM1JheRo9Mtf3iBiSQgSmaBad10nxl5KFXImICt5iYaYsjEdQtdQSUPQvXS2TGafGGVgB5EyR6I9U39PpDTUehL6JhlSHOlFbyr+53UTDC57KZdxgiDZ/KEgETZG9rQZe8AVMBQTQyhT3PzVZiOqKEPTX8mU4C6uvExaZzXXqbm355X6VV5HkRyRY1IlLrkgdXJDGqRJGHkkz+SVvFlP1ov1bn3MowUrnzkkf2B9/gCpG5yb</latexit>
1 (t) / i<latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XY8kYqCbJF9yPaUJu0mgoFNBOQU=">AAACCHicbVDJSgNBEO1xjXEb9ejBwSDEg3FGBD0G9eAxglkgMww9nZqkSc9Cd40Qhhy9+CtePCji1U/w5t/YWQ6a+KDg8V4VVfWCVHCFtv1tLCwuLa+sFtaK6xubW9vmzm5DJZlkUGeJSGQroAoEj6GOHAW0Ugk0CgQ0g/71yG8+gFQ8ie9xkIIX0W7MQ84oask3D5wT9wYEUldAiGV0Je/28Ph0IvrcN0t2xR7DmifOlJTIFDXf/HI7CcsiiJEJqlTbsVP0ciqRMwHDopspSCnr0y60NY1pBMrLx48MrSOtdKwwkbpitMbq74mcRkoNokB3RhR7atYbif957QzDSy/ncZohxGyyKMyEhYk1SsXqcAkMxUATyiTXt1qsRyVlqLMr6hCc2ZfnSeOs4tgV5+68VL2axlEg++SQlIlDLkiV3JIaqRNGHskzeSVvxpPxYrwbH5PWBWM6s0f+wPj8AYs4mQg=</latexit>

52. • Integrable
• Collisionless
Reality vs BCS
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1 (t) / i<latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XY8kYqCbJF9yPaUJu0mgoFNBOQU=">AAACCHicbVDJSgNBEO1xjXEb9ejBwSDEg3FGBD0G9eAxglkgMww9nZqkSc9Cd40Qhhy9+CtePCji1U/w5t/YWQ6a+KDg8V4VVfWCVHCFtv1tLCwuLa+sFtaK6xubW9vmzm5DJZlkUGeJSGQroAoEj6GOHAW0Ugk0CgQ0g/71yG8+gFQ8ie9xkIIX0W7MQ84oask3D5wT9wYEUldAiGV0Je/28Ph0IvrcN0t2xR7DmifOlJTIFDXf/HI7CcsiiJEJqlTbsVP0ciqRMwHDopspSCnr0y60NY1pBMrLx48MrSOtdKwwkbpitMbq74mcRkoNokB3RhR7atYbif957QzDSy/ncZohxGyyKMyEhYk1SsXqcAkMxUATyiTXt1qsRyVlqLMr6hCc2ZfnSeOs4tgV5+68VL2axlEg++SQlIlDLkiV3JIaqRNGHskzeSVvxpPxYrwbH5PWBWM6s0f+wPj8AYs4mQg=</latexit>

53. • Non-integrable
• Collision
• Integrable
• Collisionless
Reality vs BCS
tpp (ps)<latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="aeZd1WGoei1mmQ6vjXEuRhhJVXw=">AAACDHicbVDLSsNAFJ3UV62vqks3wSLUTUlE0GXRjcsK9gFNKZPpTTt0MgkzN2IJ+QA3/oobF4q49QPc+TdO2yy09cDAmXPOZeYePxZco+N8W4WV1bX1jeJmaWt7Z3evvH/Q0lGiGDRZJCLV8akGwSU0kaOATqyAhr6Atj++nvrte1CaR/IOJzH0QjqUPOCMopH65Qr2Uw/hAdM4zjJPQIDV/K4zT/HhCE9Nyqk5M9jLxM1JheRo9Mtf3iBiSQgSmaBad10nxl5KFXImICt5iYaYsjEdQtdQSUPQvXS2TGafGGVgB5EyR6I9U39PpDTUehL6JhlSHOlFbyr+53UTDC57KZdxgiDZ/KEgETZG9rQZe8AVMBQTQyhT3PzVZiOqKEPTX8mU4C6uvExaZzXXqbm355X6VV5HkRyRY1IlLrkgdXJDGqRJGHkkz+SVvFlP1ov1bn3MowUrnzkkf2B9/gCpG5yb</latexit>
1 (t) / i<latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XY8kYqCbJF9yPaUJu0mgoFNBOQU=">AAACCHicbVDJSgNBEO1xjXEb9ejBwSDEg3FGBD0G9eAxglkgMww9nZqkSc9Cd40Qhhy9+CtePCji1U/w5t/YWQ6a+KDg8V4VVfWCVHCFtv1tLCwuLa+sFtaK6xubW9vmzm5DJZlkUGeJSGQroAoEj6GOHAW0Ugk0CgQ0g/71yG8+gFQ8ie9xkIIX0W7MQ84oask3D5wT9wYEUldAiGV0Je/28Ph0IvrcN0t2xR7DmifOlJTIFDXf/HI7CcsiiJEJqlTbsVP0ciqRMwHDopspSCnr0y60NY1pBMrLx48MrSOtdKwwkbpitMbq74mcRkoNokB3RhR7atYbif957QzDSy/ncZohxGyyKMyEhYk1SsXqcAkMxUATyiTXt1qsRyVlqLMr6hCc2ZfnSeOs4tgV5+68VL2axlEg++SQlIlDLkiV3JIaqRNGHskzeSVvxpPxYrwbH5PWBWM6s0f+wPj8AYs4mQg=</latexit>

54. • Non-integrable
• Collision
• Integrable
• Collisionless
Reality vs BCS
tpp (ps)<latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="6bpKXt7YGY2Bcm9X9VmSytkM7pw=">AAACDHicbVC7SgNBFL3rM8ZXfHQ2i0GITdgVQcugjWUEE4VsCLOTu8mQ2Qczd8Ww7AfY+Cs2ForY+gF2/o2TR6GJBwbOnHMuM/f4iRSaHOfbWlhcWl5ZLawV1zc2t7ZLO7tNHaeKY4PHMlZ3PtMoRYQNEiTxLlHIQl/irT+4HPm396i0iKMbGibYDlkvEoHgjIzUKZWpk3mED5QlSZ57EgOqTO8695To9enYpJyqM4Y9T9wpKdf2YYx6p/TldWOehhgRl0zrlusk1M6YIsEl5kUv1ZgwPmA9bBkasRB1Oxsvk9tHRunaQazMicgeq78nMhZqPQx9kwwZ9fWsNxL/81opBeftTERJShjxyUNBKm2K7VEzdlco5CSHhjCuhPmrzftMMU6mv6IpwZ1deZ40T6quU3WvT8u1i0kbUIADOIQKuHAGNbiCOjSAwyM8wyu8WU/Wi/VufUyiC9Z0Zg/+wPr8ARtGnO8=</latexit><latexit sha1_base64="aeZd1WGoei1mmQ6vjXEuRhhJVXw=">AAACDHicbVDLSsNAFJ3UV62vqks3wSLUTUlE0GXRjcsK9gFNKZPpTTt0MgkzN2IJ+QA3/oobF4q49QPc+TdO2yy09cDAmXPOZeYePxZco+N8W4WV1bX1jeJmaWt7Z3evvH/Q0lGiGDRZJCLV8akGwSU0kaOATqyAhr6Atj++nvrte1CaR/IOJzH0QjqUPOCMopH65Qr2Uw/hAdM4zjJPQIDV/K4zT/HhCE9Nyqk5M9jLxM1JheRo9Mtf3iBiSQgSmaBad10nxl5KFXImICt5iYaYsjEdQtdQSUPQvXS2TGafGGVgB5EyR6I9U39PpDTUehL6JhlSHOlFbyr+53UTDC57KZdxgiDZ/KEgETZG9rQZe8AVMBQTQyhT3PzVZiOqKEPTX8mU4C6uvExaZzXXqbm355X6VV5HkRyRY1IlLrkgdXJDGqRJGHkkz+SVvFlP1ov1bn3MowUrnzkkf2B9/gCpG5yb</latexit>
1 (t) / i<latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XTOmfYCLnb00JfZVG1o+u2lwH1c=">AAACCHicbVC7SgNREJ2Nrxhf66OzcDEIWhh3RdAyqIVlBBOFbAh3b2aTS+4+uHdWCCGljb9iY6GIrZ9g59948yjUeGDgcM4MM3OCVApNrvtl5WZm5+YX8ouFpeWV1TV7faOmk0xxrPJEJuouYBqliLFKgiTepQpZFEi8DboXQ//2HpUWSXxDvRQbEWvHIhSckZGa9o536F+iJOZLDGmffCXaHTo4GotN0bSLbskdwZkm3oQUy1swQqVpf/qthGcRxsQl07ruuSk1+kyR4BIHBT/TmDLeZW2sGxqzCHWjP3pk4OwZpeWEiTIVkzNSf070WaR1LwpMZ8Soo/96Q/E/r55ReNboizjNCGM+XhRm0qHEGabitIRCTrJnCONKmFsd3mGKcTLZFUwI3t+Xp0ntuOS5Je/6pFg+H6cBediGXdgHD06hDFdQgSpweIAneIFX69F6tt6s93FrzprMbMIvWB/f/VSZXA==</latexit><latexit sha1_base64="XY8kYqCbJF9yPaUJu0mgoFNBOQU=">AAACCHicbVDJSgNBEO1xjXEb9ejBwSDEg3FGBD0G9eAxglkgMww9nZqkSc9Cd40Qhhy9+CtePCji1U/w5t/YWQ6a+KDg8V4VVfWCVHCFtv1tLCwuLa+sFtaK6xubW9vmzm5DJZlkUGeJSGQroAoEj6GOHAW0Ugk0CgQ0g/71yG8+gFQ8ie9xkIIX0W7MQ84oask3D5wT9wYEUldAiGV0Je/28Ph0IvrcN0t2xR7DmifOlJTIFDXf/HI7CcsiiJEJqlTbsVP0ciqRMwHDopspSCnr0y60NY1pBMrLx48MrSOtdKwwkbpitMbq74mcRkoNokB3RhR7atYbif957QzDSy/ncZohxGyyKMyEhYk1SsXqcAkMxUATyiTXt1qsRyVlqLMr6hCc2ZfnSeOs4tgV5+68VL2axlEg++SQlIlDLkiV3JIaqRNGHskzeSVvxpPxYrwbH5PWBWM6s0f+wPj8AYs4mQg=</latexit>

55. d
dt
Sk
t( )= −Bk
t( )× Sk
t( ){
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥
⎫
⎬
⎪
⎭⎪
Bk
t( )
Sk
Relaxation of the pseudo-spins
x
y
z

56. d
dt
Sk
t( )= −Bk
t( )× Sk
t( ){
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥
⎫
⎬
⎪
⎭⎪
Bk
t( )
Sk
Relaxation of the pseudo-spins
x
y
z

57. d
dt
Sk
t( )= −Bk
t( )× Sk
t( ){
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥
⎫
⎬
⎪
⎭⎪
Bk
t( )
Sk
Relaxation of the pseudo-spins
E (t) Ei
N0
2
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t (ps)<latexit sha1_base64="Y6hwSdv3YK7pGKsrjs1Ig8A8/AQ=">AAACAHicbVDJSgNBEK1xjXGLC3jwMhiEeAkzIugx6MVjBLNAJoSeTk3SpGehu0YMQy7+ihcPinj1M7z5N3aWgyY+KHi8V0VVPT+RQpPjfFtLyyura+u5jfzm1vbObmFvv67jVHGs8VjGqukzjVJEWCNBEpuJQhb6Ehv+4GbsNx5QaRFH9zRMsB2yXiQCwRkZqVM4Ik9iQCWP8JGyRI88JXp9OusUik7ZmcBeJO6MFCuHMEG1U/jyujFPQ4yIS6Z1y3USamdMkeASR3kv1ZgwPmA9bBkasRB1O5s8MLJPjdK1g1iZisieqL8nMhZqPQx90xky6ut5byz+57VSCq7amYiSlDDi00VBKm2K7XEadlco5CSHhjCuhLnV5n2mGCeTWd6E4M6/vEjq52XXKbt3F8XK9TQNyMExnEAJXLiECtxCFWrAYQTP8Apv1pP1Yr1bH9PWJWs2cwB/YH3+ALgqlyc=</latexit><latexit sha1_base64="Y6hwSdv3YK7pGKsrjs1Ig8A8/AQ=">AAACAHicbVDJSgNBEK1xjXGLC3jwMhiEeAkzIugx6MVjBLNAJoSeTk3SpGehu0YMQy7+ihcPinj1M7z5N3aWgyY+KHi8V0VVPT+RQpPjfFtLyyura+u5jfzm1vbObmFvv67jVHGs8VjGqukzjVJEWCNBEpuJQhb6Ehv+4GbsNx5QaRFH9zRMsB2yXiQCwRkZqVM4Ik9iQCWP8JGyRI88JXp9OusUik7ZmcBeJO6MFCuHMEG1U/jyujFPQ4yIS6Z1y3USamdMkeASR3kv1ZgwPmA9bBkasRB1O5s8MLJPjdK1g1iZisieqL8nMhZqPQx90xky6ut5byz+57VSCq7amYiSlDDi00VBKm2K7XEadlco5CSHhjCuhLnV5n2mGCeTWd6E4M6/vEjq52XXKbt3F8XK9TQNyMExnEAJXLiECtxCFWrAYQTP8Apv1pP1Yr1bH9PWJWs2cwB/YH3+ALgqlyc=</latexit><latexit sha1_base64="Y6hwSdv3YK7pGKsrjs1Ig8A8/AQ=">AAACAHicbVDJSgNBEK1xjXGLC3jwMhiEeAkzIugx6MVjBLNAJoSeTk3SpGehu0YMQy7+ihcPinj1M7z5N3aWgyY+KHi8V0VVPT+RQpPjfFtLyyura+u5jfzm1vbObmFvv67jVHGs8VjGqukzjVJEWCNBEpuJQhb6Ehv+4GbsNx5QaRFH9zRMsB2yXiQCwRkZqVM4Ik9iQCWP8JGyRI88JXp9OusUik7ZmcBeJO6MFCuHMEG1U/jyujFPQ4yIS6Z1y3USamdMkeASR3kv1ZgwPmA9bBkasRB1O5s8MLJPjdK1g1iZisieqL8nMhZqPQx90xky6ut5byz+57VSCq7amYiSlDDi00VBKm2K7XEadlco5CSHhjCuhLnV5n2mGCeTWd6E4M6/vEjq52XXKbt3F8XK9TQNyMExnEAJXLiECtxCFWrAYQTP8Apv1pP1Yr1bH9PWJWs2cwB/YH3+ALgqlyc=</latexit><latexit sha1_base64="p2aIlUCx2PVVUDn36M0nZCv4Ryc=">AAACAHicbVBNS8NAEN3Ur1q/oh48eAkWoV5KIoIei148VrAf0ISy2U7apZsPdidiCbn4V7x4UMSrP8Ob/8Ztm4O2Phh4vDfDzDw/EVyhbX8bpZXVtfWN8mZla3tnd8/cP2irOJUMWiwWsez6VIHgEbSQo4BuIoGGvoCOP76Z+p0HkIrH0T1OEvBCOox4wBlFLfXNI3QFBFhzER4xS1TuSj4c4VnfrNp1ewZrmTgFqZICzb755Q5iloYQIRNUqZ5jJ+hlVCJnAvKKmypIKBvTIfQ0jWgIystmD+TWqVYGVhBLXRFaM/X3REZDpSahrztDiiO16E3F/7xeisGVl/EoSREiNl8UpMLC2JqmYQ24BIZiogllkutbLTaikjLUmVV0CM7iy8ukfV537Lpzd1FtXBdxlMkxOSE14pBL0iC3pElahJGcPJNX8mY8GS/Gu/Exby0Zxcwh+QPj8wdGDpbT</latexit>
x
y
z

58. d
dt
Sk
t( )= −Bk
t( )× Sk
t( ){
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥
⎫
⎬
⎪
⎭⎪
Bk
t( )
Sk
Relaxation of the pseudo-spins
Sk
*
=
ˆsk
*
2
tanh
εk
2
+ Δ*
2
2T*
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
E (t) Ei
N0
2
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t (ps)<latexit sha1_base64="Y6hwSdv3YK7pGKsrjs1Ig8A8/AQ=">AAACAHicbVDJSgNBEK1xjXGLC3jwMhiEeAkzIugx6MVjBLNAJoSeTk3SpGehu0YMQy7+ihcPinj1M7z5N3aWgyY+KHi8V0VVPT+RQpPjfFtLyyura+u5jfzm1vbObmFvv67jVHGs8VjGqukzjVJEWCNBEpuJQhb6Ehv+4GbsNx5QaRFH9zRMsB2yXiQCwRkZqVM4Ik9iQCWP8JGyRI88JXp9OusUik7ZmcBeJO6MFCuHMEG1U/jyujFPQ4yIS6Z1y3USamdMkeASR3kv1ZgwPmA9bBkasRB1O5s8MLJPjdK1g1iZisieqL8nMhZqPQx90xky6ut5byz+57VSCq7amYiSlDDi00VBKm2K7XEadlco5CSHhjCuhLnV5n2mGCeTWd6E4M6/vEjq52XXKbt3F8XK9TQNyMExnEAJXLiECtxCFWrAYQTP8Apv1pP1Yr1bH9PWJWs2cwB/YH3+ALgqlyc=</latexit><latexit sha1_base64="Y6hwSdv3YK7pGKsrjs1Ig8A8/AQ=">AAACAHicbVDJSgNBEK1xjXGLC3jwMhiEeAkzIugx6MVjBLNAJoSeTk3SpGehu0YMQy7+ihcPinj1M7z5N3aWgyY+KHi8V0VVPT+RQpPjfFtLyyura+u5jfzm1vbObmFvv67jVHGs8VjGqukzjVJEWCNBEpuJQhb6Ehv+4GbsNx5QaRFH9zRMsB2yXiQCwRkZqVM4Ik9iQCWP8JGyRI88JXp9OusUik7ZmcBeJO6MFCuHMEG1U/jyujFPQ4yIS6Z1y3USamdMkeASR3kv1ZgwPmA9bBkasRB1O5s8MLJPjdK1g1iZisieqL8nMhZqPQx90xky6ut5byz+57VSCq7amYiSlDDi00VBKm2K7XEadlco5CSHhjCuhLnV5n2mGCeTWd6E4M6/vEjq52XXKbt3F8XK9TQNyMExnEAJXLiECtxCFWrAYQTP8Apv1pP1Yr1bH9PWJWs2cwB/YH3+ALgqlyc=</latexit><latexit sha1_base64="Y6hwSdv3YK7pGKsrjs1Ig8A8/AQ=">AAACAHicbVDJSgNBEK1xjXGLC3jwMhiEeAkzIugx6MVjBLNAJoSeTk3SpGehu0YMQy7+ihcPinj1M7z5N3aWgyY+KHi8V0VVPT+RQpPjfFtLyyura+u5jfzm1vbObmFvv67jVHGs8VjGqukzjVJEWCNBEpuJQhb6Ehv+4GbsNx5QaRFH9zRMsB2yXiQCwRkZqVM4Ik9iQCWP8JGyRI88JXp9OusUik7ZmcBeJO6MFCuHMEG1U/jyujFPQ4yIS6Z1y3USamdMkeASR3kv1ZgwPmA9bBkasRB1O5s8MLJPjdK1g1iZisieqL8nMhZqPQx90xky6ut5byz+57VSCq7amYiSlDDi00VBKm2K7XEadlco5CSHhjCuhLnV5n2mGCeTWd6E4M6/vEjq52XXKbt3F8XK9TQNyMExnEAJXLiECtxCFWrAYQTP8Apv1pP1Yr1bH9PWJWs2cwB/YH3+ALgqlyc=</latexit><latexit sha1_base64="p2aIlUCx2PVVUDn36M0nZCv4Ryc=">AAACAHicbVBNS8NAEN3Ur1q/oh48eAkWoV5KIoIei148VrAf0ISy2U7apZsPdidiCbn4V7x4UMSrP8Ob/8Ztm4O2Phh4vDfDzDw/EVyhbX8bpZXVtfWN8mZla3tnd8/cP2irOJUMWiwWsez6VIHgEbSQo4BuIoGGvoCOP76Z+p0HkIrH0T1OEvBCOox4wBlFLfXNI3QFBFhzER4xS1TuSj4c4VnfrNp1ewZrmTgFqZICzb755Q5iloYQIRNUqZ5jJ+hlVCJnAvKKmypIKBvTIfQ0jWgIystmD+TWqVYGVhBLXRFaM/X3REZDpSahrztDiiO16E3F/7xeisGVl/EoSREiNl8UpMLC2JqmYQ24BIZiogllkutbLTaikjLUmVV0CM7iy8ukfV537Lpzd1FtXBdxlMkxOSE14pBL0iC3pElahJGcPJNX8mY8GS/Gu/Exby0Zxcwh+QPj8wdGDpbT</latexit>
x
y
z

59. d
dt
Sk
t( )= −Bk
t( )× Sk
t( ){
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥
⎫
⎬
⎪
⎭⎪
Sk
Relaxation of the pseudo-spins
Sk
*
=
ˆsk
*
2
tanh
εk
2
+ Δ*
2
2T*
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
x
y
z

60. d
dt
Sk
t( )= −Bk
t( )× Sk
t( ){
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥
⎫
⎬
⎪
⎭⎪
Sk
Relaxation of the pseudo-spins
Sk
*
=
ˆsk
*
2
tanh
εk
2
+ Δ*
2
2T*
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
x
y
z

61. d
dt
Sk
t( )= −Bk
t( )× Sk
t( ){
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥
⎫
⎬
⎪
⎭⎪
Sk
Relaxation of the pseudo-spins
Sk
*
=
ˆsk
*
2
tanh
εk
2
+ Δ*
2
2T*
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
x
y
z

62. Damped quench dynamics
τ
(t)/i<latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="pHH9dppuOcuIUpmDMwCwA6MtJeI=">AAACBnicbVBNS8NAEN3Ur1q/oh5FCBahXmoigh6LevBYwX5AE8JmO2mXbj7YnQil9OTFv+LFgyJe/Q3e/Ddu2xy09cHA470ZZuYFqeAKbfvbKCwtr6yuFddLG5tb2zvm7l5TJZlk0GCJSGQ7oAoEj6GBHAW0Uwk0CgS0gsH1xG89gFQ8ie9xmIIX0V7MQ84oask3D90bEEhdASFW0JW818eT05noc98s21V7CmuRODkpkxx13/xyuwnLIoiRCapUx7FT9EZUImcCxiU3U5BSNqA96Gga0wiUN5q+MbaOtdK1wkTqitGaqr8nRjRSahgFujOi2Ffz3kT8z+tkGF56Ix6nGULMZovCTFiYWJNMrC6XwFAMNaFMcn2rxfpUUoY6uZIOwZl/eZE0z6qOXXXuzsu1qzyOIjkgR6RCHHJBauSW1EmDMPJInskreTOejBfj3fiYtRaMfGaf/IHx+QOnYpiW</latexit>
it<latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="Uy9gwcf3x8Bt/f8EeYQsDvonZ58=">AAAB8XicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DKohWUEE4NJCHubSbJkb+/YnRNCyL+wsVDE1n9j579xk1yhiQ8GHu/NMDMvTJS05PvfXm5ldW19I79Z2Nre2d0r7h/UbZwagTURq9g0Qm5RSY01kqSwkRjkUajwIRxeT/2HJzRWxvqeRgm2I97XsicFJyc9tm5QEe9IRp1iyS/7M7BlEmSkBBmqneJXqxuLNEJNQnFrm4GfUHvMDUmhcFJopRYTLoa8j01HNY/QtseziyfsxCld1ouNK01spv6eGPPI2lEUus6I08AuelPxP6+ZUu+yPZY6SQm1mC/qpYpRzKbvs640KEiNHOHCSHcrEwNuuCAXUsGFECy+vEzqZ+XALwd356XKVRZHHo7gGE4hgAuowC1UoQYCNDzDK7x51nvx3r2PeWvOy2YO4Q+8zx8PFJCA</latexit>
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥

63. τ
(t)/i<latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="pHH9dppuOcuIUpmDMwCwA6MtJeI=">AAACBnicbVBNS8NAEN3Ur1q/oh5FCBahXmoigh6LevBYwX5AE8JmO2mXbj7YnQil9OTFv+LFgyJe/Q3e/Ddu2xy09cHA470ZZuYFqeAKbfvbKCwtr6yuFddLG5tb2zvm7l5TJZlk0GCJSGQ7oAoEj6GBHAW0Uwk0CgS0gsH1xG89gFQ8ie9xmIIX0V7MQ84oask3D90bEEhdASFW0JW818eT05noc98s21V7CmuRODkpkxx13/xyuwnLIoiRCapUx7FT9EZUImcCxiU3U5BSNqA96Gga0wiUN5q+MbaOtdK1wkTqitGaqr8nRjRSahgFujOi2Ffz3kT8z+tkGF56Ix6nGULMZovCTFiYWJNMrC6XwFAMNaFMcn2rxfpUUoY6uZIOwZl/eZE0z6qOXXXuzsu1qzyOIjkgR6RCHHJBauSW1EmDMPJInskreTOejBfj3fiYtRaMfGaf/IHx+QOnYpiW</latexit>
it<latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="Uy9gwcf3x8Bt/f8EeYQsDvonZ58=">AAAB8XicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DKohWUEE4NJCHubSbJkb+/YnRNCyL+wsVDE1n9j579xk1yhiQ8GHu/NMDMvTJS05PvfXm5ldW19I79Z2Nre2d0r7h/UbZwagTURq9g0Qm5RSY01kqSwkRjkUajwIRxeT/2HJzRWxvqeRgm2I97XsicFJyc9tm5QEe9IRp1iyS/7M7BlEmSkBBmqneJXqxuLNEJNQnFrm4GfUHvMDUmhcFJopRYTLoa8j01HNY/QtseziyfsxCld1ouNK01spv6eGPPI2lEUus6I08AuelPxP6+ZUu+yPZY6SQm1mC/qpYpRzKbvs640KEiNHOHCSHcrEwNuuCAXUsGFECy+vEzqZ+XALwd356XKVRZHHo7gGE4hgAuowC1UoQYCNDzDK7x51nvx3r2PeWvOy2YO4Q+8zx8PFJCA</latexit>
Damped quench dynamics
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥

64. τ
(t)/i<latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="pHH9dppuOcuIUpmDMwCwA6MtJeI=">AAACBnicbVBNS8NAEN3Ur1q/oh5FCBahXmoigh6LevBYwX5AE8JmO2mXbj7YnQil9OTFv+LFgyJe/Q3e/Ddu2xy09cHA470ZZuYFqeAKbfvbKCwtr6yuFddLG5tb2zvm7l5TJZlk0GCJSGQ7oAoEj6GBHAW0Uwk0CgS0gsH1xG89gFQ8ie9xmIIX0V7MQ84oask3D90bEEhdASFW0JW818eT05noc98s21V7CmuRODkpkxx13/xyuwnLIoiRCapUx7FT9EZUImcCxiU3U5BSNqA96Gga0wiUN5q+MbaOtdK1wkTqitGaqr8nRjRSahgFujOi2Ffz3kT8z+tkGF56Ix6nGULMZovCTFiYWJNMrC6XwFAMNaFMcn2rxfpUUoY6uZIOwZl/eZE0z6qOXXXuzsu1qzyOIjkgR6RCHHJBauSW1EmDMPJInskreTOejBfj3fiYtRaMfGaf/IHx+QOnYpiW</latexit>
it<latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="Uy9gwcf3x8Bt/f8EeYQsDvonZ58=">AAAB8XicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DKohWUEE4NJCHubSbJkb+/YnRNCyL+wsVDE1n9j579xk1yhiQ8GHu/NMDMvTJS05PvfXm5ldW19I79Z2Nre2d0r7h/UbZwagTURq9g0Qm5RSY01kqSwkRjkUajwIRxeT/2HJzRWxvqeRgm2I97XsicFJyc9tm5QEe9IRp1iyS/7M7BlEmSkBBmqneJXqxuLNEJNQnFrm4GfUHvMDUmhcFJopRYTLoa8j01HNY/QtseziyfsxCld1ouNK01spv6eGPPI2lEUus6I08AuelPxP6+ZUu+yPZY6SQm1mC/qpYpRzKbvs640KEiNHOHCSHcrEwNuuCAXUsGFECy+vEzqZ+XALwd356XKVRZHHo7gGE4hgAuowC1UoQYCNDzDK7x51nvx3r2PeWvOy2YO4Q+8zx8PFJCA</latexit>
Damped quench dynamics
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥

65. τ
(t)/i<latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="pHH9dppuOcuIUpmDMwCwA6MtJeI=">AAACBnicbVBNS8NAEN3Ur1q/oh5FCBahXmoigh6LevBYwX5AE8JmO2mXbj7YnQil9OTFv+LFgyJe/Q3e/Ddu2xy09cHA470ZZuYFqeAKbfvbKCwtr6yuFddLG5tb2zvm7l5TJZlk0GCJSGQ7oAoEj6GBHAW0Uwk0CgS0gsH1xG89gFQ8ie9xmIIX0V7MQ84oask3D90bEEhdASFW0JW818eT05noc98s21V7CmuRODkpkxx13/xyuwnLIoiRCapUx7FT9EZUImcCxiU3U5BSNqA96Gga0wiUN5q+MbaOtdK1wkTqitGaqr8nRjRSahgFujOi2Ffz3kT8z+tkGF56Ix6nGULMZovCTFiYWJNMrC6XwFAMNaFMcn2rxfpUUoY6uZIOwZl/eZE0z6qOXXXuzsu1qzyOIjkgR6RCHHJBauSW1EmDMPJInskreTOejBfj3fiYtRaMfGaf/IHx+QOnYpiW</latexit>
it<latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="Uy9gwcf3x8Bt/f8EeYQsDvonZ58=">AAAB8XicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DKohWUEE4NJCHubSbJkb+/YnRNCyL+wsVDE1n9j579xk1yhiQ8GHu/NMDMvTJS05PvfXm5ldW19I79Z2Nre2d0r7h/UbZwagTURq9g0Qm5RSY01kqSwkRjkUajwIRxeT/2HJzRWxvqeRgm2I97XsicFJyc9tm5QEe9IRp1iyS/7M7BlEmSkBBmqneJXqxuLNEJNQnFrm4GfUHvMDUmhcFJopRYTLoa8j01HNY/QtseziyfsxCld1ouNK01spv6eGPPI2lEUus6I08AuelPxP6+ZUu+yPZY6SQm1mC/qpYpRzKbvs640KEiNHOHCSHcrEwNuuCAXUsGFECy+vEzqZ+XALwd356XKVRZHHo7gGE4hgAuowC1UoQYCNDzDK7x51nvx3r2PeWvOy2YO4Q+8zx8PFJCA</latexit>
Damped quench dynamics
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥

66. τ
(t)/i<latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="1K1P3hRscW/UcNS6rapcHs7VJrM=">AAACBnicbVDJSgNBEK2JW4xbXG4iDAYhXuKMCHoM6sFjBLNAJoSeTk3SpGehu0YIIScv/ooXD4p49Ru8+Td2loNGHxQ83quiqp6fSKHJcb6szMLi0vJKdjW3tr6xuZXf3qnpOFUcqzyWsWr4TKMUEVZJkMRGopCFvsS6378a+/V7VFrE0R0NEmyFrBuJQHBGRmrnD7xrlMQ8iQEVyVOi26Pjk6nYFu18wSk5E9h/iTsjhfIeTFBp5z+9TszTECPikmnddJ2EWkOmSHCJo5yXakwY77MuNg2NWIi6NZy8MbKPjNKxg1iZisieqD8nhizUehD6pjNk1NPz3lj8z2umFFy0hiJKUsKITxcFqbQptseZ2B2hkJMcGMK4EuZWm/eYYpxMcjkTgjv/8l9SOy25Tsm9PSuUL6dpQBb24RCK4MI5lOEGKlAFDg/wBC/waj1az9ab9T5tzVizmV34BevjGxmNmOo=</latexit><latexitsha1_base64="pHH9dppuOcuIUpmDMwCwA6MtJeI=">AAACBnicbVBNS8NAEN3Ur1q/oh5FCBahXmoigh6LevBYwX5AE8JmO2mXbj7YnQil9OTFv+LFgyJe/Q3e/Ddu2xy09cHA470ZZuYFqeAKbfvbKCwtr6yuFddLG5tb2zvm7l5TJZlk0GCJSGQ7oAoEj6GBHAW0Uwk0CgS0gsH1xG89gFQ8ie9xmIIX0V7MQ84oask3D90bEEhdASFW0JW818eT05noc98s21V7CmuRODkpkxx13/xyuwnLIoiRCapUx7FT9EZUImcCxiU3U5BSNqA96Gga0wiUN5q+MbaOtdK1wkTqitGaqr8nRjRSahgFujOi2Ffz3kT8z+tkGF56Ix6nGULMZovCTFiYWJNMrC6XwFAMNaFMcn2rxfpUUoY6uZIOwZl/eZE0z6qOXXXuzsu1qzyOIjkgR6RCHHJBauSW1EmDMPJInskreTOejBfj3fiYtRaMfGaf/IHx+QOnYpiW</latexit>
it<latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="oH7v76e9QnC/lAlp2t79XNFsbVA=">AAAB8XicbVDLSgNBEOyNrxhf8XHzMhgET2FXBD0G9eAxgnlgsoTZyWwyZHZ2mekVwpK/8OJBEa/+jTf/xskmB00saCiquunuChIpDLrut1NYWV1b3yhulra2d3b3yvsHTROnmvEGi2Ws2wE1XArFGyhQ8naiOY0CyVvB6Gbqt564NiJWDzhOuB/RgRKhYBSt9Ni95RJpTxDslStu1c1Blok3J5XaEeSo98pf3X7M0ogrZJIa0/HcBP2MahRM8kmpmxqeUDaiA96xVNGIGz/LL56QU6v0SRhrWwpJrv6eyGhkzDgKbGdEcWgWvan4n9dJMbzyM6GSFLlis0VhKgnGZPo+6QvNGcqxJZRpYW8lbEg1ZWhDKtkQvMWXl0nzvOq5Ve/+olK7nqUBRTiGEzgDDy6hBndQhwYwUPAMr/DmGOfFeXc+Zq0FZz5zCH/gfP4AgTCQ1A==</latexit><latexit sha1_base64="Uy9gwcf3x8Bt/f8EeYQsDvonZ58=">AAAB8XicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E0DKohWUEE4NJCHubSbJkb+/YnRNCyL+wsVDE1n9j579xk1yhiQ8GHu/NMDMvTJS05PvfXm5ldW19I79Z2Nre2d0r7h/UbZwagTURq9g0Qm5RSY01kqSwkRjkUajwIRxeT/2HJzRWxvqeRgm2I97XsicFJyc9tm5QEe9IRp1iyS/7M7BlEmSkBBmqneJXqxuLNEJNQnFrm4GfUHvMDUmhcFJopRYTLoa8j01HNY/QtseziyfsxCld1ouNK01spv6eGPPI2lEUus6I08AuelPxP6+ZUu+yPZY6SQm1mC/qpYpRzKbvs640KEiNHOHCSHcrEwNuuCAXUsGFECy+vEzqZ+XALwd356XKVRZHHo7gGE4hgAuowC1UoQYCNDzDK7x51nvx3r2PeWvOy2YO4Q+8zx8PFJCA</latexit>
−
Sk
t( )⋅ ˆsk
*!
− Sk
*
T1
ˆsk
*!
−
Sk
t( )⋅ ˆsk
*⊥
T2
ˆsk
*⊥
Impact of T1 relaxation process