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

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

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

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

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

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

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

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

• 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

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 =∑

κ hΩκ(NAκ−NAκ

) = 0

∗G. Vitiello, Int. J. Mod. Phys. B 9, 973 (1995)G. Vitiello, My Double Unveiled. Amsterdam: John Benjamins, 2001E. Celeghini, M. Rasetti and G. Vitiello, Annals Phys. 215, 156 (1992)

13

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 6= N ′, are ui in the infinite volume limit:

N 〈0|0〉N ′ −→V →∞

0 ∀ N , N ′ , N 6= N ′ . (3)

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

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

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

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

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 EkNak and in the entropy Sa are related by

dEa =∑

k

EkNakdt =1

βdSa = dQ , (10)

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

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

Mesoscopic background activity conforms to scale-free power law

noise.

Figure 11. Evidence is summarized showing that the mesoscopic background activity conforms toscale-free, low-dimensional noise [Freeman et al., 2008]. Engagement of the brain in perception and othergoal-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 showingexcess power in the theta (3 − 7 Hz) and gamma (25 − 100 Hz) ranges. B. The distributions of timeintervals between null spikes of brown noise and sleep ECoG are superimposed. C,D. The distributionsare compared of log10 analytic power from noise and ECoG. Hypothetically the threshold for triggeringa 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 theyalso 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 correlatesof retrieved memories.

The PSD of background noise from mutual excitation and dendritic integration contain allfrequencies in a continuous distribution, which is necessary to support the appearance of beatsin every designated pass band. Endogenous inhibitory negative feedback does not break thisscale-free symmetry. Explicit breaking of symmetry (Mode 1) can occur by applying electricshocks that cause excitatory or inhibitory bias and initiate the band limited perturbations thatare observed in the impulse responses (Fig. 7). Spontaneous symmetry breaking (Mode 2) canoccur by a null spike. When that happens, the sensory input that activates a Hebbian assemblyalready formed by learning introduces into the broken symmetry a powerful narrow-band gammaburst (Fig. 8) that is facilitated by the increased synaptic gain, kee, with learning (Fig. 1), theincreased control parameter, Qm, with arousal, and the asymmetric gain around the operatingpoint for the KII set (Fig. 6).

The crucial step in perception is the phase transition from the excited microscopic assemblyto the large-scale mesoscopic AM pattern. That possibility occurs when a null spike (Fig. 10,

October 2, 2008 17:13 WSPC/INSTRUCTION FILEVitielloFORKozma2October08

Coherent states, fractals and brain waves 7

By generalizing and extending this to the case of any other “ipervolume” H oneconsiders thus the ratio

H(λL0)H(L0)

= p , (2.2)

and assuming that Eq. (2.1) is still valid “by definition”, one obtains

p H(L0) = λdH(L0) , (2.3)

i.e. p = λd. For the Koch curve, setting α = 1p = 4 and q = λd = 1

3d , p = λd gives

qα = 1 , where α = 4, q =13d

, (2.4)

i.e.

d =ln 4ln 3

≈ 1.2619 . (2.5)

d is called the fractal dimension, or the self-similarity dimension 50.

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 thatin the “deformed space”, to which u1,q belongs, the set of four segments of whichu1,q is made “equals” (is equivalent to) the three segments of which u0 is made in

Stage n = 1: u1,q(α) ≡ q α u0, q = 13d, α = 4

d 6= 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 → ∞).

Notice! 1√n!

(q α)n

is the basis in the space of entire analytical functions, where coherent

states are represented.

|qα〉 = exp(−|qα|2

2 )∑∞

n=0(qα)n√

n!|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).

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

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

Figure 10. Null spikes are observed by band pass filtering the EEG (A), applying the Hilberttransform [Freeman, 2007b] to get the analytic power (B), and taking the logarithm (C). On each channelthe downward spikes coincide with spikes in analytic frequency (D) reflecting increased analytic phasevariance. 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 spikescoincides with phase transitions leading to emergence of AM patterns. The modal repetition rate of thenull spikes in Hz is predicted to be 0.641 times the pass band width in Hz [Rice, 1950, p. 90, Equation3.8-15].

down spikes in Hz is proportional to band width in Hz by the factor of 0.641. The recurrencerate of AM patterns in the theta range suggests that the threshold for the decrease in nullspikes at the initiation of phase transitions is on the order of 10−4 (D). The occurrence of beatfrequencies in the theta range (4 − 7 Hz) suggests that the width of the pass band of carrierwaves in the beta and gamma ranges (respectively 12.5 − 25 Hz and 25 − 50 Hz in human) liein the range of 5 − 11 Hz, with a modal value near 8 Hz [Freeman, 2009]. That range has beenverified experimentally by calculating the minimal spatial standard deviations of analytic phasein the flat periods between null spikes (Fig. 10, B).

These experimental data provide the evidence needed to construct a dissipative dynamichypothesis of perception. The turbulence in the ECoG at the cortical surface illustrated inFig. 4 holds in every pass band in the clinical range, conforming to the scale-free dynamicspredicted 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) showsthat cortex homeostatically holds its operating point at or very near a state of criticality, whichcan justifiably be called self-organized, because it is kept at a homeostatically controlled setpoint 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 phasecones 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 distributionwith 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

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

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

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

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

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ISBN 90 272 5152 5 (Eur) / 1 58811 076 1 (US)

John Benjamins Publishing Company

Giuseppe Vitiello

My D

ouble Unveiled

Advances in C

onsciousness Research

My Double UnveiledThis introduction to the dissipative quantum model of brainand to its possible implications for consciousness studies isaddressed to a broad interdisciplinary audience. Memory andconsciousness are approached from the physicist point of viewfocusing on the basic observation that the brain is an opensystem continuously interacting with its environment. Theunavoidable dissipative character of the brain functioningturns out to be the root of the brain’s large memory capacityand of other memory features such as memory association,memory confusion, duration of memory. The openness of thebrain implies a formal picture of the world which is modeledon the same brain image: a sort of brain copy or “double”where world objectiveness and the brain implicit subjectivityare conjugated. Consciousness is seen to arise from thepermanent “dialogue” of the brain with its Double.The author’s narration of his (re-)search gives a cross-over ofthe physics of elementary particles and condensed matter, andthe brain’s basic dynamics. This dynamic interplay makes for a“satisfying feeling of the unity of knowledge”.

Giuseppe Vitiello

Advances in C

onsciousness Research

AiCR32

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“... an exciting and delightful book. The excitement stems from his innovative use ofQuantum Field Theory (actually a doubling of such ¼elds) to explain how brainprocessing can entail our awareness of our existential imbeddedness in the world and atthe same time our awareness of the aware ‘self ’.”Karl Pribram, Center for Brain research and Information Science, RadfordUniversity

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Tom W. KibbleTheoretical Physics, Imperial College London, London, UK

“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.”∗

∗Jorge Louis Borges, “Borges and I”, in El hacedor, Biblioteca Borges, AlianzaEditorial, 1960.

41

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

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

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

• 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

• 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