The document describes a Hamiltonian with terms including Ji,j|ωiωj| and Ei|ωiωi| that depends on parameters ∆/J and ω. It studies the behavior of the system as ∆/J increases from 0 to greater than 6, including plots of the momentum distribution |P(k)|2 that show it spreading out over more values of k/k1. The dependence of the system on other parameters like α, s1, and s2 is also examined through additional plots.
Cosmin Crucean: Perturbative QED on de Sitter Universe.SEENET-MTP
Lecture by dr Cosmin Crucean (Theoretical and Applied Physics, West University of Timisoara, Romania) on July 9, 2010 at the Faculty of Science and Mathematics, Nis, Serbia.
Cosmin Crucean: Perturbative QED on de Sitter Universe.SEENET-MTP
Lecture by dr Cosmin Crucean (Theoretical and Applied Physics, West University of Timisoara, Romania) on July 9, 2010 at the Faculty of Science and Mathematics, Nis, Serbia.
In many applications one observes rapid change of the solution in the boundary region. Accurate and numerically efficient resolution of the solution close to the moving boundaries is considered to be an important problem. We develop an approach to the optimization of the discretization grids for finite-difference scheme. Using the suggested approach we are able to achieve the exponential convergence of the boundary Neumann- to-Dirichlet maps. It increases the convergence order without increasing the stencil size of the finite-difference scheme and preserves stability.
In many applications one observes rapid change of the solution in the boundary region. Accurate and numerically efficient resolution of the solution close to the moving boundaries is considered to be an important problem. We develop an approach to the optimization of the discretization grids for finite-difference scheme. Using the suggested approach we are able to achieve the exponential convergence of the boundary Neumann- to-Dirichlet maps. It increases the convergence order without increasing the stencil size of the finite-difference scheme and preserves stability.
Dual Gravitons in AdS4/CFT3 and the Holographic Cotton TensorSebastian De Haro
Talk given at the workshop "Gravity in Three Dimensions" at the Erwin Schrödinger Institute, Vienna, April 14-24, 2009. I argue that gravity theories in AdS4 are holographically dual to either of two three-dimensional CFT's: the usual Dirichlet CFT1 where the fixed graviton acts as a source for the stress-energy tensor, or a dual CFT2 with a fixed dual graviton which acts as a source for a dual stress-energy tensor. The dual stress-energy tensor is shown to be the Cotton tensor of the Dirichlet CFT. The two CFT's are related by a Legendre transformation generated by a gravitational Chern-Simons coupling. This duality is a gravitational version of electric-magnetic duality valid at any radius r, where the renormalized stress-energy tensor is the electric field and the Cotton tensor is the magnetic field. Generic Robin boundary conditions lead to CFT's coupled to Cotton gravity or topologically massive gravity. Interaction terms with CFT1 lead to a non-zero vev of the stress-energy tensor in CFT2 coupled to gravity even after the source is removed.
"The Metropolis adjusted Langevin Algorithm
for log-concave probability measures in high
dimensions", talk by Andreas Elberle at the BigMC seminar, 9th June 2011, Paris
Likelihood is sometimes difficult to compute because of the complexity of the model. Approximate Bayesian computation (ABC) makes it easy to sample parameters generating approximation of observed data.
3. H= Ji,j |ωi ωj | + Ei |ωi ωi |
i,j=i i
Ei ∆
∆/J = 0 ∆/J > 0
−|x/L|α
e
4. H= Ji,j |ωi ωj | + Ei |ωi ωi |
i,j=i i
Ei ∆
∆/J = 0 ∆/J > 0
−|x/L|α
e
5. H= Ji,j |ωi ωj | + Ei |ωi ωi |
i,j=i i
T < Tc 1
N + U ni (ˆ i − 1)
ˆ n
ψ(r1 , r2 , · · · , rN , ) = φ0 (ri ) 2 i
i=1
V (x) = s1 Er1 sin2 (k1 x) + s2 Er2 sin2 (k2 x)
si i
β = k2 /k1
Ei
6. H= Ji,j |ωi ωj | + Ei |ωi ωi |
i,j=i i
T < Tc 1
N + U ni (ˆ i − 1)
ˆ n
ψ(r1 , r2 , · · · , rN , ) = φ0 (ri ) 2 i
i=1
V (x) = s1 Er1 sin2 (k1 x) + s2 Er2 sin2 (k2 x)
si i
β = k2 /k1
Ei
7. H= Ji,j |ωi ωj | + Ei |ωi ωi |
i,j=i i
T < Tc 1
N + U ni (ˆ i − 1)
ˆ n
ψ(r1 , r2 , · · · , rN , ) = φ0 (ri ) 2 i
i=1
V (x) = s1 Er1 sin2 (k1 x) + s2 Er2 sin2 (k2 x)
si i
β = k2 /k1
Ei
∆/J si , β
8. ∆ s
∆/J s, β
J β
fα (x) = A exp(−|(x − x0 )/l)|α ) α
9.
10. H= Ji,j |ωi ωj | + Ei |ωi ωi |
i,j=i i
H=J (|wm wm+1 | + |wm+1 wm |)
m
+∆ cos(2πβm + φ) |wm wm |
m