1. THE DISSIPATIVE QUANTUM MODEL OF BRAIN ∗
Giuseppe Vitiello
Salerno University, Italy
∗ G. Vitiello, My Double Unveiled. Amsterdam: John Benjamins, 2001
W. J. Freeman and G. Vitiello, Physics of Life Reviews 3, 93 (2006)
W. J. Freeman and G. Vitiello, J. Phys. A: Math. Theor. 48, 304042 (2008)
W. J. Freeman and G. Vitiello, Int. J. Mod. Phys. B 24, 3269 (2010);
W. J. Freeman, R. Livi, M. Obinata and G. Vitiello, Int. J. Mod. Phys. B 26,
1250035 (2012)
1

2. The mesoscopic activity of neocortex:
dynamical formation of spatially extended domains of amplitude mod-
ulated (AM) synchronized oscillations with near zero phase dispersion.
These “packets of waves” form in few ms, have properties of location,
size, duration (80−120 ms) and carrier frequencies in the beta-gamma
range (12 − 80 Hz),
re-synchronize in frames at frame rates in the theta-alpha range (3 −
12 Hz) through a sequence of repeated collective phase transitions.
Such patterns of oscillations cover much of the hemisphere in rabbits
and cats and over domains of linear size of 19 cm in humans
2

3. The patterns of phase-locked oscillations are intermittently present in
resting, awake subjects as well as in the same subject actively engaged
in cognitive tasks requiring interaction with environment,
so they are best described as properties of the background activity of
brains that is modulated upon engagement with the surround∗ .
Neither the electric field of the extracellular dendritic current nor
the extracellular magnetic field from the high-density electric current
inside the dendritic shafts, which are much too weak, nor the chemical
diffusion, which is much too slow, appear to be able to fully account
for the observed cortical collective activity.
∗ W.
J. Freeman, Clin. Neurophysiol. 116 (5), 1118 (2005); 117 (3), 572 (2006)
W. J. Freeman, et al., Clin. Neurophysiol. 114, 1055 (2003)
3

4. Lashley dilemma
Concept of “mass action” in the storage and retrieval of memories in
the brain:
“...Here is the dilemma. Nerve impulses are transmitted ...form cell
to cell through definite intercellular connections. Yet, all behavior
seems to be determined by masses of excitation...within general fields
of activity, without regard to particular nerve cells... What sort of
nervous organization might be capable of responding to a pattern
of excitation without limited specialized path of conduction? The
problem is almost universal in the activity of the nervous system.” ∗
Pribram: analogy between the fields of distributed neural activity in
the brain and the wave patterns in holograms † .
∗ K.
Lashley, The Mechanism of Vision, Journal Press, Provincetown MA, 1948, pp.
302-306
† K. H. Pribram, Languages of the Brain. Engelwood Cliffs NJ: Prentice-Hall, 1971
5

6. The dissipative quantum model of brain
is the extension to the dissipative dynamics of the many-body model
proposed in 1967 by Ricciardi and Umezawa ∗
the extended patterns of neuronal excitations may be described by
the spontaneous breakdown of symmetry (SBS) formalism in QFT.
Umezawa †: “In any material in condensed matter physics any par-
ticular information is carried by certain ordered pattern maintained
by certain long range correlation mediated by massless quanta. It
looked to me that this is the only way to memorize some informa-
tion; memory is a printed pattern of order supported by long range
correlations...”
∗ L.M. Ricciardi and H. Umezawa, Kibernetik 4, 44 (1967)
C. I. J. Stuart, Y. Takahashi and H. Umezawa, J.Theor. Biol. 71, 605 (1978);
Found. Phys. 9, 301 (1979)
† H.Umezawa, Math. Japonica 41, 109 (1995)
8

7. In QFT long range correlations are indeed dynamically generated
through the mechanism of SBS.
These correlations manifest themselves as the Nambu-Goldstone (NG)
boson particles or modes,
which have zero mass and therefore are able to span the whole system.
The NG bosons are coherently condensed in the system lowest energy
state, the vacuum or ground state (Bose-Einstein condensation).
Due to such correlations the system appears in an ordered state.
The vacuum density of the NG bosons provides a measure of the
degree of ordering or coherence: the order parameter, a classical
field specifying (labeling) the observed ordered pattern.
9

8. Example of NG modes: phonons, magnons, Cooper pairs.
The water matrix is more than the 80% of brain mass and it is there-
fore expected to be a major facilitator or constraint on brain dynamics.
⇔ the quantum variables are the electrical dipole vibrational field of
the water molecules and of other biomolecules ∗.
The spontaneous breakdown of the rotational symmetry of the elec-
trical dipole vibrational field dynamically generates the NG quanta,
named the dipole wave quanta (DWQ).
The neuron and the glia cells and other physiological units are NOT
quantum objects in the many-body model of brain.
∗ E.Del Giudice, S. Doglia, M. Milani and G. Vitiello, Nucl. Phys. B 251 (FS 13),
375 (1985); Nucl. Phys. B 275 (FS 17), 185 (1986).
M. Jibu and K. Yasue, Quantum brain dynamics and consciousness. Amsterdam:
John Benjamins, 1995.
M. Jibu, K. H. Pribram and K. Yasue, Int. J. Mod. Phys. B 10, 1735 (1996)
10

9. The recall of recorded information occurs under a stimulus able to
excite DWQ out of the corresponding ground state.
Such a stimulus is called “similar” to the one responsible for the
memory recording.
Similarity between stimuli thus refers not to their intrinsic features,
but to the reaction of the brain to them; to the possibility that under
their action DWQ are condensed into, or excited from the ground
state carrying the same label.
11

10. • The many-body model fails in explaining the observed coexistence
of AM patterns and also their irreversible time evolution.
• One shortcoming of the model is that any subsequent stimulus
would cancel the previously recorded memory by renewing the SBS
process, thus overprinting the ’new’ memory over the previous one
(’memory capacity problem’).
• The fact that the brain is an open system in permanent interaction
with the environment was not considered in the many-body model.
⇒ Include Dissipation!!
12

11. In the QFT formalism for the dissipative brain the environment is
described as the time-reversal image of the system ∗.
This is realized by doubling the system degrees of freedom:
external stimulus ⇒ SBS ⇒ dynamical generation of DWQ Aκ
dissipation ⇒ doubling: ˜
Aκ → (Aκ , Aκ)
˜
Aκ ≡ “time-reversed mirror image” or “doubled modes”
energy flux balance ⇔ E0 = ESyst − EEnv = h
κ ¯ Ωκ(NAκ − NAκ ) = 0
˜
∗ G.
Vitiello, Int. J. Mod. Phys. B 9, 973 (1995)
G. Vitiello, My Double Unveiled. Amsterdam: John Benjamins, 2001
E. Celeghini, M. Rasetti and G. Vitiello, Annals Phys. 215, 156 (1992)
13

12. Balancing E0 to be zero, does not fix the value of either EAκ or EAκ
˜
for any κ. It only fixes, for any κ, their difference.
⇒ at t0 we may have infinitely many perceptual states, each one in
one-to-one correspondence to a given N set: a huge memory capacity.
The important point is:
{|0 N } and {|0 N }, N = N , are ui in the infinite volume limit:
N 0|0 N −→ 0 ∀ N, N , N =N . (3)
V →∞
In contrast with the non-dissipative model, a huge number of sequen-
tially recorded memories may coexist without destructive interference
since infinitely many vacua |0 N , ∀ N , are independently accessible.
16

13. Stability of order parameter N against quantum fluctuations is a man-
ifestation of the coherence of boson condensation.
⇒ memory N not affected by quantum fluctuations. In this sense, it
is a macroscopic observable. |0 N is a “macroscopic quantum state”.
⇒ “change of scale” (from microscopic to macroscopic scale) dynam-
ically achieved through the coherent boson condensation mechanism.
19

14. In agreement with observations:
the QFT dissipative dynamics ⇒
∗ (quasi-)non-interfering degenerate vacua (AM pattern textures)
∗ (phase) transitions among them (AM patterns sequencing)
∗ huge memory capacity
The original many-body model could not describe these features.
22

15. In the “memory space”, or the brain state space (the space of uir),
{|0 N }, for each N -set, describes a physical phase of the system and
may be thought as a “point” identified by that specific N .
The system may shift, under the influence of one or more stimuli act-
ing as a control parameter, from vacuum to vacuum in the collection
of brain-environment equilibrium vacua (E0 = 0), i.e. from phase to
phase,
⇒ the system undergoes an extremely rich sequence of phase transi-
tions, leading to the actualization of a sequence of dissipative struc-
tures formed by AM patterns, as indeed experimentally observed.
23

16. Let |0(t) N ≡ |0 N at t, specified by the initial value N at t0 = 0.
Time evolution of |0(t) N = trajectory of ”initial condition” specified
by the N -set in the space of the representations {|0(t) N } .
Provided changes in the inverse temperature β are slow, the changes
in the energy Ea ≡ k Ek Nak and in the entropy Sa are related by
1
dEa = ˙
Ek Nak dt = dSa = dQ , (10)
k
β
i.e. the minimization of the free energy dFa = 0 holds at any t
⇒ change in time of the condensate, i.e. of the order parameter,
turns into heat dissipation dQ.
24

17. Dissipation ⇒ time-evolution of |0(t) N at finite volume V controlled
by the entropy variations ⇒ irreversibility of time evolution (breakdown
of time-reversal symmetry) ⇒ arrow of time (a privileged direction in
time evolution)
25

18. Mesoscopic background activity conforms to scale-free power law
noise.

19. Figure 11. Evidence is summarized showing that the mesoscopic background activity conforms to
scale-free, low-dimensional noise [Freeman et al., 2008]. Engagement of the brain in perception and other
goal-directed behaviors is accompanied by departures from randomness upon the emergence of order (A),
as shown by comparing PSD in sleep, which conforms to black noise, vs. PSD in an aroused state showing
excess power in the theta (3 − 7 Hz) and gamma (25 − 100 Hz) ranges. B. The distributions of time
intervals between null spikes of brown noise and sleep ECoG are superimposed. C,D. The distributions
are compared of log10 analytic power from noise and ECoG. Hypothetically the threshold for triggering
a phase transition is 10−4 down from modal analytic power. From [Freeman, O’Nuillain and Rodriguez,
2008 and Freeman and Zhai, 2009]
last long enough to transmit 3 to 5 cycles of the carrier frequency [Freeman, 2005], and they
also have the long correlation distances needed to span vast areas of primary sensory cortices.
These attributes of size and persistence make them prime candidates for the neural correlates
of retrieved memories.
The PSD of background noise from mutual excitation and dendritic integration contain all
frequencies in a continuous distribution, which is necessary to support the appearance of beats
in every designated pass band. Endogenous inhibitory negative feedback does not break this
scale-free symmetry. Explicit breaking of symmetry (Mode 1) can occur by applying electric
shocks that cause excitatory or inhibitory bias and initiate the band limited perturbations that
are observed in the impulse responses (Fig. 7). Spontaneous symmetry breaking (Mode 2) can
occur by a null spike. When that happens, the sensory input that activates a Hebbian assembly
already formed by learning introduces into the broken symmetry a powerful narrow-band gamma
burst (Fig. 8) that is facilitated by the increased synaptic gain, k e e, with learning (Fig. 1), the
increased control parameter, Qm , with arousal, and the asymmetric gain around the operating
point for the KII set (Fig. 6).
The crucial step in perception is the phase transition from the excited microscopic assembly
to the large-scale mesoscopic AM pattern. That possibility occurs when a null spike (Fig. 10,

20. October 2, 2008 17:13 WSPC/INSTRUCTION FILE
VitielloFORKozma2October08
Coherent states, fractals and brain waves 7
By generalizing and extending this to the case of any other “ipervolume” H one
considers thus the ratio
H(λL0 )
=p, (2.2)
H(L0 )
and assuming that Eq. (2.1) is still valid “by definition”, one obtains
p H(L0 ) = λd H(L0 ) , (2.3)
d 1 d 1 d
i.e. p = λ . For the Koch curve, setting α = p = 4 and q = λ = 3d
, p = λ gives
1
qα = 1 , where α = 4, q= , (2.4)
3d
i.e.
ln 4
d= ≈ 1.2619 . (2.5)
ln 3
50
d is called the fractal dimension, or the self-similarity dimension .
Fig. 1. The first five stages of Koch curve.
With reference to the Koch curve, I observe that the meaning of Eq. (2.3) is that
in the “deformed space”, to which u1,q belongs, the set of four segments of which
u1,q is made “equals” (is equivalent to) the three segments of which u0 is made in

21. Stage n = 1: u1,q (α) ≡ q α u0, q = 1d , α=4
3
d = 1 to be determined.
Stage n = 2: u2,q (α) ≡ q α u1,q (α) = (q α)2 u0.
By iteration:
un,q (α) ≡ (q α) un−1,q (α), n = 1, 2, 3, ...
i.e., for any n
un,q (α) = (q α)n u0.
which is the “self-similarity” relation characterizing fractals.
Notice! The fractal is mathematically defined only in the limit of
infinite number of iterations (n → ∞).

22. Notice! 1
√ (q α)n
n!
is the basis in the space of entire analytical functions, where coherent
states are represented.
|qα|2 n
∞ (qα) |n
|qα = exp(− 2 ) n=0
√
n!
a |qα = qα |qα ,
this establish a link between fractals and coherent states and confirms
the role of coherence in brain activity.
the operator (a)n acts as a “magnifying” lens: the nth iteration of
the fractal can be “seen” by applying (a)n to |qα (and restricting to
real qα):
qα|(a)n |qα = (qα)n = un,q (α), qα → Re (qα).

23. A crucial neural mechanism:
the event that initiates the transition to a perceptual state is an
abrupt decrease in the analytic power of the background activity to
near zero (a null spike), associated with the concomitant increase of
spatial variance of analytic phase.
The null spikes recur aperiodically at rates in the theta (3 − 7 Hz) and
alpha (8 − 12 Hz) ranges,
it has rotational energy at the geometric mean frequency of the pass
band, so it is called a vortex.
The vortex occupies the whole area of the phase-locked neural activity
of the cortex for a point in time.
Between the null spikes the cortical dynamics is (nearly) stationary
for ∼ 60 − 160 ms. This is called a frame.
29

24. The arriving stimulus can drive the cortex across a phase transition
process to a new AM pattern.
The observed velocity of spread of phase transition is finite, i.e. there
is no “instantaneous” phase transition.
These features have been documented as markers of the interface
between microscopic and mesoscopic phenomena.
31

25. Figure 10. Null spikes are observed by band pass filtering the EEG (A), applying the Hilbert
transform [Freeman, 2007b] to get the analytic power (B), and taking the logarithm (C). On each channel
the downward spikes coincide with spikes in analytic frequency (D) reflecting increased analytic phase
variance. The flat segment between spikes reflects the stability of the carrier frequency of AM patterns.
The spikes form clusters in time but are not precisely synchronized. One or more of these null spikes
coincides with phase transitions leading to emergence of AM patterns. The modal repetition rate of the
null spikes in Hz is predicted to be 0.641 times the pass band width in Hz [Rice, 1950, p. 90, Equation
3.8-15].
down spikes in Hz is proportional to band width in Hz by the factor of 0.641. The recurrence
rate of AM patterns in the theta range suggests that the threshold for the decrease in null
spikes at the initiation of phase transitions is on the order of 10 − 4 (D). The occurrence of beat
frequencies in the theta range (4 − 7 Hz) suggests that the width of the pass band of carrier
waves in the beta and gamma ranges (respectively 12.5 − 25 Hz and 25 − 50 Hz in human) lie
in the range of 5 − 11 Hz, with a modal value near 8 Hz [Freeman, 2009]. That range has been
verified experimentally by calculating the minimal spatial standard deviations of analytic phase
in the flat periods between null spikes (Fig. 10, B).
These experimental data provide the evidence needed to construct a dissipative dynamic
hypothesis of perception. The turbulence in the ECoG at the cortical surface illustrated in
Fig. 4 holds in every pass band in the clinical range, conforming to the scale-free dynamics
predicted from the power-law PSD of the resting ECoG (Fig. 11, A) and other variables
[Freeman, 2007a]. The existence of a pole at the origin of the complex plane (Fig. 7) shows
that cortex homeostatically holds its operating point at or very near a state of criticality, which
can justifiably be called self-organized, because it is kept at a homeostatically controlled set
point by randomly distributed, abortive phase transitions that are manifested in phase cones
(Fig. 3) having power-law distributions of durations and diameters. Few among the phase
cones have durations that exceed those expected for noise [Fig. A1.08 in Freeman, 2004a;
Section 3.4 and Fig. 2.06, E in Freeman, 2004b], and these few fall into the Rice distribution
with longer durations than inter-spike intervals in the Rayleigh distribution [Freeman, 2009].
That is significant, because these frames accompany classifiable AM patterns (Fig. 2) that

26. The possibility of deriving from the microscopic (quantum) dynamics
the classicality of trajectories in the memory space is one of the merits
of the dissipative many-body field model.
These trajectories are found to be classical deterministic chaotic tra-
jectories ∗
The manifold on which the attractor landscapes sit covers as a “clas-
sical blanket” the quantum dynamics going on in each of the repre-
sentations of the CCR’s (the AM patterns recurring at rates in the
theta range (3 − 8 Hz)).
∗ E.Pessa and G. Vitiello, Mind and Matter 1 59 (2003)
E. Pessa and G. Vitiello, Intern. J. Modern Physics B 18, 841, (2004)
G. Vitiello, Int. J. Mod. Phys. B 18, 785 (2004)
37

27. The emerging picture is that a stimulus selects a basin of attraction
in the primary sensory cortex to which it converges, often with very
little information as in weak scents, faint clicks, and weak flashes.
The convergence constitutes the process of abstraction.
Each attractor can be selected by a stimulus that is an instance of
the category (generalization) that the attractor implements by its AM
pattern:
⇒ the waking state consists of a collection of potential states, any
one of which but only one at a time can be realized through a phase
transition.
38

28. The specific ordered pattern generated through SBS by an external
input does not depend on the stimulus features. It depends on the
system internal dynamics.
⇒ The stored memory is not a representation of the stimulus.
The model accounts for the laboratory observation of lack of invari-
ance of the AM neuronal oscillation patterns with invariant stimuli
The engagement of the subject with the environment in the action-
perception cycle is the essential basis for the emergence and main-
tenance of meaning through successful interaction and its knowledge
base within the brain.
It is an active mirror, because the environment impacts onto the self
independently as well as reactively.
The brain-environment “inter-action” is ruled by the free energy min-
imization processes.
39

29. The continual balancing of the energy fluxes at the brain–environment
interface amounts to the continual updating of the meanings of the
flows of information exchanged in the brain behavioral relation with
the environment.
By repeated trial-and-error each brain constructs within itself an un-
derstanding of its surround, which constitutes its knowledge of its
own world that we describe as its Double ∗.
∗ G.
Vitiello, Int. J. Mod. Phys. B 9, 973 (1995)
G. Vitiello, My Double Unveiled. Amsterdam: John Benjamins, 2001
40

30. AiCR
32
My Double Unveiled
Giuseppe Vitiello
This introduction to the dissipative quantum model of brain
and to its possible implications for consciousness studies is
addressed to a broad interdisciplinary audience. Memory and
consciousness are approached from the physicist point of view
focusing on the basic observation that the brain is an open
system continuously interacting with its environment. The
unavoidable dissipative character of the brain functioning
turns out to be the root of the brain’s large memory capacity Giuseppe Vitiello
and of other memory features such as memory association,
memory confusion, duration of memory. The openness of the
brain implies a formal picture of the world which is modeled
Advances inin Consciousness Research
on the same brain image: a sort of brain copy or “double”
Advances Consciousness Research
where world objectiveness and the brain implicit subjectivity
My Double Unveiled
are conjugated. Consciousness is seen to arise from the
permanent “dialogue” of the brain with its Double.
The author’s narration of his (re-)search gives a cross-over of
the physics of elementary particles and condensed matter, and
the brain’s basic dynamics. This dynamic interplay makes for a
“satisfying feeling of the unity of knowledge”.
“Prof. Vitiello writings provide a fundamental advance in the quantum theory of brain
functioning, and astonishingly in the present book, without requiring any technical
mathematics.”
Gordon Globus, Irvine, CA
….the clearest exposition of the theory of brain functions, based on the highly abstract
and mathematical theory of Quantum Field. Professor Vitiello successfully carries out this
difficult task without a single equation”.
Yasushi Takahashi, Department of Physics, University of Alberta
“...by comparing different formulations of analogues concepts, this book encourages
various scientific communities (physics, biology, neurophysiology, psychology) to
reinforce a fruitful dialogue.”
Francesco Guerra , Director Faculty of Mathematical, Physical and Natural
Sciences, University of Roma “La Sapienza”
“... an exciting and delightful book. The excitement stems from his innovative use of
Quantum Field Theory (actually a doubling of such ¼elds) to explain how brain
processing can entail our awareness of our existential imbeddedness in the world and at
the same time our awareness of the aware ‘self ’.”
Karl Pribram, Center for Brain research and Information Science, Radford
University
John Benjamins Publishing Company
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31. Quantum Field Theory and its Macroscopic Manifestations Quantum Field Theory and its
Quantum Field Theory and its
Macroscopic Manifestations
Macroscopic Manifestations
Boson Condensation, Ordered Patterns and Topological Defects
”Physicists believe quantum fields to be the true protagonists of nature in the full variety of its
wonderful, manifold manifestations. Quantum field theory is the tool they created to fulfill their
visionary dream of describing with a universal, unique language all of nature, be it single particles Boson Condensation, Ordered Patterns
or condensed matter, fields or many-body objects.
This is perhaps the first book on quantum field theory whose aim is to grasp and describe with and Topological Defects
rigor and completeness, but at the same time in a compelling, fascinating way, all the facets of
the complex challenge it faces scientists with. It is a book that presents solutions but poses
questions as well; hard, demanding yet fascinating; a book that can at the same time be used as
a textbook and as a book of dreams that any scientist would like to make come true.”
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Dipartimento di Fisica, Politecnico di Torino, Torino, Italy
“This remarkable book dispels the common misconception that quantum field theory is ‘just
quantum mechanics with an infinite number of degrees of freedom’, revealing vast new
mathematical terrains, and new ways of understanding physical phenomena in both commonplace
and exotic systems.
Uniquely valuable, and covering material difficult or impossible to find coherently assembled
elsewhere, it will be welcomed by students and researchers in all fields of physics and mathematics.”
John Swain
Physics Department, Northeastern University, Boston, MA, USA
and CERN, Geneva, Switzerland
“This book gives an overall presentation of the most important aspects of quantum field theory,
leading to its macroscopic manifestations, as in the formation of ordered structures. The list of
topics, all covered in full detail and easy-to-follow steps, is really impressive.
The main features of the presentation rely on very simple and powerful unifying principles, given
by the intermixing of symmetry and dynamics, under the general texture of quantum coherence.
Most of the chapters share the typical flavor of the very intense personal research carried out by
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topics are presented in a mature and well-organized way.
I think that the book will be most useful for graduate students who are willing to be engaged in
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to the ordering of biological systems. Of course, active researchers in all formation stages, and
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authors have transfused in their work.”
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Dipartimento di Fisica, Universita di Roma, “La Sapienza”, Italy
`
“This book gives a very thorough treatment of a range of topics that are of increasing importance,
from a rather unusual, and very instructive, point of view.” Blasone
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32. “The other one, the one called Borges, is the one things happen
to....It would be an exaggeration to say that ours is a hostile rela-
tionship; I live, let myself go on living, so that Borges may contrive
his literature, and this literature justifies me....Besides, I am destined
to perish, definitively, and only some instant of myself can survive
him....Spinoza knew that all things long to persist in their being; the
stone eternally wants to be a stone and a tiger a tiger. I shall remain
in Borges, not in myself (if it is true that I am someone)....Years ago
I tried to free myself from him and went from the mythologies of the
suburbs to the games with time and infinity, but those games belong
to Borges now and I shall have to imagine other things. Thus my life
is a flight and I lose everything and everything belongs to oblivion, or
to him.
I do not know which of us has written this page.”∗
∗ JorgeLouis Borges, “Borges and I”, in El hacedor, Biblioteca Borges, Alianza
Editorial, 1960.
41

33. In conclusion,
John von Neumann noted that
“...the mathematical or logical language truly used by the central
nervous system is characterized by less logical and arithmetical depth
than what we are normally used to. ...We require exquisite numerical
precision over many logical steps to achieve what brains accomplish
in very few short steps” ∗.
The observation of textured AM patterns and sequential phase tran-
sitions in brain functioning and the dissipative quantum model de-
scribing them perhaps provide a way to the understanding of such a
view.
∗ J.
von Neumann, The Computer and the Brain. New Haven: Yale University Press,
1958, pp.80-81
42

34. Much work remains to be done in many research directions,
such as the analysis of the interaction between the boson condensate
and the details of the electrochemical neural activity,
or the problems of extending the dissipative many-body model to
account for higher cognitive functions of the brain.
At the present status of our research, the study of the dissipative
many-body dynamics underlying the richness of the laboratory obser-
vations seems to be promising.
43

35. Other predictions in agreement with experiments :
• very low energy required to excite correlated neuronal patterns,
• AM patterns have large diameters, with respect to the small sizes
of the component neurons,
• duration, size and power of AM patterns are decreasing functions
of their carrier wave number k,
• there is lack of invariance of AM patterns with invariant stimuli,
• heat dissipation at (almost) constant in time temperature,
26

36. • the occurrence of spikes (vortices) in the process of phase transi-
tions,
• the whole phenomenology of phase gradients and phase singularities
in the vortices formation,
• the constancy of the phase field within the frames,
• the insurgence of a phase singularity associated with the abrupt
decrease of the order parameter and the concomitant increase of
spatial variance of the phase field,
27

37. • the onsets of vortices between frames, not within them,
• the occurrence of phase cones (spatial phase gradients) and random
variation of sign (implosive and explosive) at the apex,
• that the phase cone apices occur at random spatial locations,
• that the apex is never initiated within frames, but between frames
(during phase transitions).
• The model leads to the classicality (not derived as the classical
limit, but as a dynamical output) of functionally self-regulated and
self-organized background activity of the brain.
28