Re: Quantum memory models? (cont.)

Date: Sun, 7 Apr 1996 17:35:40 -0700 (PDT)
From: Giuseppe Vitiello <vitiello@vaxsa.csied.unisa.it>
To: quantum-d@teleport.com
Subject: Re: Quantum memory models? (cont.)

This is an extended abstract from the paper

   "Dissipation and memory capacity in the quantum brain model"

    Int. J. Mod. Phys.B9 (1995) 973
    (quant-ph/9502006)

       by

       Giuseppe Vitiello
       Physics Department, University of Salerno
       84100 Salerno, Italy

       e-mail: vitiello@vaxsa.csied.unisa.it
       fax  +39 89 953804
       tel. +39 89 965311


By following independent routes, but stimulated by common belief in the
powerfulness of Quantum Field Theory (QFT) and fascinated by its elegance,
Herbert Frohlich, Hiroomi Umezawa, Karl Pribram and Alexander Davydov have
opened a research path, actively followed in recent years, which aimed to
study the basic dynamical laws underlying the rich phenomenology of living
systems.

One of the motivations for such an approach to the study of biological
systems comes from the fact that, although great energy and many valuable
efforts have been put into play, it remains still open the question of how
order and efficiency arise from, and then coexist with random fluctuations
in biochemistry: From one side, there is the high level of space and time
ordering and the high functional efficiency observed in living systems;
on the other side, the randomness of kinematics which rules any chemical
reaction, which by itself is not sufficient to account for those high
levels of ordering and efficiency. In the QFT approach to living matter
one searches for basic dynamical laws which together with statistical
mechanics originate ordering and functional efficiency.

Here I want to report about a recent application[1] of dissipative QFT to
the problem of memory capacity in the quantum model of brain proposed by
Ricciardi and Umezawa[2]. In doing this I will also shortly summarize the
main features of the QFT approach[3] to living matter.

It is a common observation that the brain functioning  appears  not
significantly affected  by  the  functioning  of  the  single  neuron.
A characterizing feature of the brain activity seems instead related
with the existence  of  simultaneous  responses  in  several  regions
of  the  brain  to  some  external  stimuli. Storing and recalling
information appear  as diffuse activities  of  the  brain not  lost
even after destructive  action  of  local parts  of  the  brain[4-7].

Ricciardi and Umezawa[2] have then suggested that the brain states
may  be characterized  by  the  existence, among the brain quantum
elementary constituents, of long range coherent correlations playing
a more fundamental role than the functioning of the single cell in
the brain activity. They proposed to model the memory activities as
coding  of the brain states whose stability emerges as a dynamical
feature rather than as a property of specific  neural  nets (which
would be critically damaged  by destructive  actions).The elementary
constituents are not the neurons and the other cells, which are not
quantum objects, but some dynamical  variables, called  corticons.
Information printing is achieved under the action of external stimuli
producing breakdown of the continuous phase symmetry associated to
corticons.

General  theorems of QFT show [8,9] that in the presence of spontaneous
symmetry breakdown the vacuum (zero energy state) is  an ordered state
and  collective modes (called Nambu-Goldstone modes) propagating over
the whole system are dynamically generated and are the carrier of the
ordering information (long range correlations). Therefore, in QFT order
manifests itself as a global property dynamically generated and associated
to collective  mode condensation. A bridge between the microscopic scale
and the macroscopic functional properties of the system is thus made
possible.

The collective mode is a massless mode  and  therefore  its  condensation
in the vacuum does not  add  energy to it. The stability of the ordering
is thus insured. Moreover, infinitely many vacua  with different degrees
of order may exist, corresponding to different densities of the condensate
(different values of the order parameter), which may be considered as
code numbers[2] specifying the system state. Code numbers may be organized
in classes corresponding to different kinds of dynamical symmetries. In
the infinite volume limit the vacua are each other orthogonal (unitarily
inequivalent, in the QFT language) and thus represent different physical
phases of the system, which therefore appears as a complex system equipped
with many macroscopic configurations. In the case of open systems trans-
itions may occur among vacua (phase transitions), for large but finite
volume, due to coupling with external environment. A dissipative system
thus appears as "living over many ground states"[10,11]. One may show that
even very weak (although above a certain threshold) perturbations may
drive the system through its macroscopic configurations[10]. Occasional
(random) weak perturbations are thus recognized to play an important role
in the complex behavior of living systems.

The collective mode in the quantum model of brain has been called symmetron
[2] and the information storage function is represented by the coding of
the ground  state through symmetron condensation, which also insures the
memory stability. The memory non-local character is guaranteed by the
coherence of the condensate.

Motivated by the observation that living matter is made up by water and
other biomolecules equipped with electric dipoles, Del Giudice et al.
[12] have assumed that the symmetry to be spontaneously broken is the
rotational symmetry for electrical dipoles. Also according to Frohlich
[13], the (electric) polarization density thus plays the role of order
parameter and the associated Goldstone modes have been named dipole wave
quanta (dwq). The water molecules undergo a lasering-like coherent process
with a phase locking mechanism with the quantized radiation field (super-
radiance)[14]. The time scale for the long range interaction is much
shorter (10^-14 sec) than the one of short range interactions. Water
coherent domains are therefore protected from thermalization. Moreover,
electromagnetic disturbances are shown to undergo self-focusing propa-
gation in the ordered domains and to induce polymerization effects [3,12]
which may be responsible of the formation (assembly) and of the dynamical
features of microtubula. Superradiance and self-induced transparency in
microtubula are investigated in [15].

Corticons have been identified[15] with the electric dipole field and
symmetron modes with dwq of the spontaneous breakdown of electric dipole
rotational symmetry. Excitation  of dwq modes  under external  stimuli
similar  to  the ones producing the memory printing describes the recall
process. When the dwq  modes  are  excited  the  brain  "consciously
feels"[2] the pre-existing  ordered  pattern  in  the  ground  state.
Short-term memory is associated  to metastable  excited states of dwq
condensate[2,16].

In the quantum brain model there is only one class of code numbers since
only one kind of symmetry is assumed (the dipole rotational symmetry).
Once a vacuum of specific code number has been selected by the printing
of a specific information, then no other vacuum state is successively
accessible for recording another information, unless producing, under the
external stimulus carrying the new information, a (phase) transition to
the vacuum specified by the new code number. This will destroy the
previously stored information (overprinting): the model thus appears too
simple to allow the recording of a huge number of informations and a
realistic model would require a huge number of symmetries[2].

However, I have shown[1] that, by taking into account the dissipative
dynamics of the brain, one may solve the problem of memory capacity
without the introduction of a huge number of symmetries. Let me start
by observing that once the dipole rotational symmetry has been broken
(and information has thus been recorded), then, as a consequence, time-
reversal symmetry is also broken: before the information recording
process, the brain can in principle be in anyone of the infinitely many
inequivalent vacua. After the information has been recorded, the brain
state is completely determined and the brain cannot be brought to the
state configuration in which it was before the information printing
occurred  (...NOW you know it!...). Thus, information printing introduces
the arrow of time into brain dynamics: Due to memory printing process
time evolution of the brain states is intrinsically irreversible. This
leads me to investigate the dissipative quantum brain dynamics (DQBD).

A central feature of the quantum dissipation formalism[9,11] is the
duplication of the field describing the dissipative system: Let a(k)
and ~a(k) denote the dwq mode and the doubled mode, respectively. k
generically denotes the field degrees of freedom, e.g. spatial momentum.
The ~a mode is shown to be the "time-reversed mirror image"[1,11] of
the a mode and represents the environment mode.

Taking into account dissipativity requires[1] that the memory state,
at the initial time t0, say t0 = 0, is a condensate of equal number
of a(a) modes and ~a(k) mirror modes, for any k:

    N(a(k)) = N(~a(k))   for all k

The number

    N(a(k)) - N(~a(k))   for all k

is a constant of motion and it is zero for the vacuum state. As a
consequence, there exist infinitely many vacuum states

    |0>(N)

which are orthogonal to each other for N does not equal N' (different
codes), denoting the memory states. The label N=N(a(k))...

   N(a(k)) = N(~a(k))    for all k, at t0 = 0

      specifies the set of integers defining the "initial value" of the
condensate. A huge number of sequentially recorded informations may thus
coexist without destructive interference since infinitely many vacua

   |0>(N), for all N

     are independently accessible. Recording information of code N' does
not produce destruction of previously printed information of code N not
equal to N', contrarily to the nondissipative case, where differently coded
vacua are accessible only through a sequence of phase transitions. In the
dissipative case the "brain (ground) state" is represented by the collection
(or the superposition) of the full set of memory states |0>(N) for all N:
the brain appears as a complex system with a huge number of macroscopic
states (the memory states).

In conclusion, the degeneracy among the vacua  |0>(N), for all N, plays
a crucial role in solving the problem of memory capacity.

The orthogonality in the infinite volume limit among differently coded
vacua guaranties that the corresponding printed informations are indeed
different or distinguishable informations (N is a good code) and that
each information printing is also protected against interference from
other information printing (absence of confusion} among informations).
The effect of finite (realistic) size of the system may however spoil
orthogonality and may lead to "association" of memories.

After a characteristic time the memory state |0>(N) is found[1] to
decay to the "empty" vacuum

    |0>(0)

where N(k) = 0 for all k: the information has been forgotten. In order
to not completely forget certain information, one needs to "restore"
the N code, which corresponds to "refresh" the memory by brushing up
the subject (external stimuli maintained memory). Time evolution of the
memory state is controlled by the entropy variations and the stability
condition to be satisfied at each time t by the state |0(t)>(N), implies
[1,11] minimizing the free energy functional, which in turn leads to the
Bose distribution for a(k) and ~a(k) for each k, at time t. The memory
state |0(t)>(N) is then recognized[1] to be a finite temperature state
equivalent with the thermo field dynamics vacuum state[9].

I also note that a relation exists[1] between the brain memory states
and the squeezed coherent states entering quantum optics[17].

The ~a system is a "replication" of the a system and plays a central
role in the recalling process: one can show[1] that the creation
(excitation) of the a mode is equivalent, up to a factor, to the
destruction (from the memory state) of the ~a mode. One can also
see that the ~a mode allows self-interaction of the a system, and
in this sense it plays a role in "self-recognition" processes. As
already observed, the ~a system is the "mirror in time"  system.
This fact and the role of the ~a modes in the self-recognition
processes leads me to conjecture[1], also according to the image
of consciousness as a "mirror", that tilde-system and therefore
dissipation is actually responsible for consciousness mechanisms.

In a forthcoming work I will discuss possible relations between the
above scheme and the gravity induced consciousness mechanism proposed
by Hameroff and Penrose.



[1]  G.Vitiello,Int. J. Mod. Phys. B9, 973 (1995)
     (quant-ph\9502006)

[2]  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); C.I.J. Stuart, Y. Takahashi and H. Umezawa, Found. Phys.
     9, 301 (1979)

[3]  E. Del Giudice, S. Doglia, M. Milani and G. Vitiello, in Biological
     coherence and response to external stimuli}, H. Frohlich ed.,
     Springer-Verlag, Berlin 1988, p.49; G.Vitiello, Nanobiology 1,
     221 (1992)

[4]  J.S. Clegg, in Coherent excitations in biological systems,
     H. Frohlich and F. Kemmer eds. Spriger-Verlag, Berlin 1983,
     p.189; J. Tabony and D. Job, Nanobiology 1, 131 (1992)

[5]  K.H. Pribram, in {\it Macromolecules and behavior}, J.Gaito
     ed., Academic Press,  N.Y.  1966; Languages of the brain,
     Englewood Cliffs, New Jersey, 1971; Brain and perception,
     Lawrence Erlbaum, New Jersey, 1991

[6]  R. Penrose, The Emperor's new mind, Oxford University Press,
     London 1989; Shadows of the mind, Oxford University Press,
     London 1993

[7]  M. Mezard, G. Parisi and M. Virasoro, Spin glass theory and beyond,
     World Sci.,  Singapore 1993; D.J. Amit Modeling brain functions,
     Cambridge University Press,  Cambridge 1989

[8]  C. Itzykson and J.B. Zuber, Quantum Field Theory, McGraw-Hill,
     N.Y. 1980

[9]  H. Umezawa, Advanced field theory: micro, macro and thermal concepts,
     American Institute of Physics, N.Y. 1993

[10] E. Celeghini, E. Graziano and G. Vitiello, Phys. Lett. 145A, 1
     (1990)

[11] E. Celeghini, M. Rasetti and G. Vitiello, Annals of Physics (N.Y.)
     215, 156 (1992)

[12] E. Del Giudice, S. Doglia, M. Milani and G. Vitiello, Phys.
     Lett. 95A, 508 (1983); Nucl. Phys. B251 [FS 13], 375 (1985);
     Nucl. Phys. B275 [FS 17], 185 (1986)

[13] H. Frohlich, J.Quantum Chemistry 2, 641 (1968); Riv. Nuovo Cimento
     7, 399 (1977); Adv. Electron. Phys. 53, 85 (1980)

[14] E. Del Giudice, G. Preparata and G. Vitiello, Phys. Rev.
     Lett. 61, 1085 (1988)

[15] M. Jibu , S. Hagan, S.R. Hameroff, K. H. Pribram and  K. Yasue,
     BioSystems 32, 195 (1994); M. Jibu , K. H. Pribram and  K. Yasue,
     Int. J. Mod. Phys. 10, June 1996, in print

[16] S.Sivakami and V. Srinivasan, J. Theor. Biol. 102, 287 (1983)

[17] H.P. Yuen, Phys. Rev. A13, 2226 (1976); D. Stoler, Phys. Rev. D
     1, 3217 (1970)


On Mon, 25 Mar 1996, Giuseppe Vitiello wrote:

> On this memory model (Int.J.Mod.Phys.B9(1995)973) I will present a talk
> at Tucson II on Friday, April 22. Maybe I will try to write a short note
> (abstract like) for quantum-d for those who will not be there.
>
> Giuseppe Vitiello
>
> On Fri, 22 Mar 1996, Donald Tveter wrote:
>
> > Can anyone explain the quantum memory models?
> >
> > My background is Computer Science with an interest in AI but I was an
> > undergraduate in Math and Physics so I can understand a little (but only
> > a little) of what is going on with the microtubles and interpretations
> > of quantum theory.  If you care to help me with this problem please take
> > this into account.
> >
> > I saw in the preprint archives the theory by Vitiello about how an
> > unlimited number of memories can be stored...
> >
> >        [e.g. http://xxx.lanl.gov/abs/quant-ph/9502006]
> >
> >                                             ...and apparently the newer
> > papers by Nanopoulos and his associates have a similar theory.  To a
> > computer scientist this is pretty impressive but I haven't the foggiest
> > idea how this is done.  Can anyone explain this?  I think it would be
> > especially helpful to have an example where the memory stores simple
> > data like A = 1, B = 2 and C = 3 and then retrieves the values on demand.
> >
> > Thanks,
> >
> >    [an example reference for Nanopoulos's recent ideas is
> >     http://xxx.lanl.gov/abs/quant-ph/9510003
> >                                              - rs]
>
> ---
> this document at:
> http://www.teleport.com/~rhett/quantum-d/posts/vitiello_3-25-96.html
>



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