ELIANO PESSA Department of Behavioral and Brain Sciences University of Pavia, Italy www.neurosphera.org

1. QUANTUM MODELS OF BRAIN
ELIANO PESSA
Department of Behavioral and Brain
Sciences
University of Pavia, Italy

2. SOME FEATURES OF MIND AND BRAIN
BEHAVIORS
For the present purpose we will focus our attention on
two features of both brain and mind behaviors about
which there is a common consensus :
1) Both behaviors are often characterized by
COHERENCE phenomena or COHERENT aspects
2) Brain and Mind are interrelated by both BOTTOM-UP
and TOP-DOWN influences

3. MIND
TOP-DOWN BOTTOM-UP
INFLUENCE INFLUENCE
BRAIN
Despite these influences the mind is to be considered
as a fully AUTONOMOUS entity, allowing a LOGICAL
(and not PHYSICAL) description

4. CLASSICAL PHYSICS DOES NOT
ALLOW COHERENCE
Namely classical statistical physics (and whence
Termodynamics) is ruled by a principle known as
CORRELATION WEAKENING PRINCIPLE, stating that
whatever long range correlation DIES AWAY after a
long enough evolution time.
As coherence results from long range correlations, it is
evident how the classical physics cannot be used to
explain coherence phenomena within the brain-mind
system.

5. ARE QUANTUM THEORIES USEFUL ?
Actually we have two different levels:
1) QUANTUM MECHANICS, characterized by a fixed
number of particles, a finite number of degrees of
freedom, and unitary equivalence between different
representations of the same physical system
2) QUANTUM FIELD THEORY, in which the basic
entities are field strengths, the number of degrees of
freedom is infinite (and continuous), and the number of
particles is variable

6. THE NEW PRINCIPLES INTRODUCED BY
QUANTUM THEORIES
They consist of a number of UNCERTAINTY
PRINCIPLES which essentially follow from the
postulate of the existence of an unavoidable
“VACUUM FLUCTUATION” of the world and of the
whole Universe. The fluctuations occurring in each
space-time point are correlated with the ones
occurring in every other space-time point. This
circumstance gives rise to NON-LOCAL EFFECTS
of typically quantum nature which cannot be
predicted by classical Physics.

7. MOTIVATIONS UNDERLYING THE
ATTRACTIVENESS OF QUANTUM
THEORIES
• Allow the occurrence of spontaneous (and
even large-scale) COHERENCE phenomena
without the resort to special design,
arrangement, boundary conditions, etc.
(Prototype : BOSE-EINSTEIN CONDENSATION)
• In suitable cases (Quantum Field Theory) offer
a framework for describing, understanding, and
forecasting PHASE TRANSITION phenomena

8. This implies that quantum theories can support
some form of TOP-DOWN CAUSATION
encompassing the pitfalls of the traditional
mechanistic and reductionist framework.
If we assume that all phenomena related to life,
brain, cognition, consciousness, etc. are based on
some forms of EMERGENT SELF-ORGANIZATION
then quantum theories are the best candidates for
an effective theorizing activity in these domains.

9. THE LEVELS OF ORGANIZATION OF MIND-
BRAIN SYSTEM
The scientific descriptions usually acknowledge the
existence of a high number of these levels.
THINKING
MACROSCOPIC
PHYSIOLOGICAL
PROCESSES
CELLULAR
PROCESSES
ELEMENTARY
COMPONENTS

10. THE REDUCTIONIST POSTULATE
A complete study of the whole system of previous
organizational levels has been so far impossible.
If, however, we introduce a very rough REDUCTIONIST
POSTULATE according to which all processes occuring
at the level N can be fully explained in terms of the ones
occurring at the lower level N – 1, EXCEPT FOR THE
ONES OCCURRING AT THE LEVEL LYING IMMEDIATELY
UP TO THE ONE OF ELEMENTARY COMPONENTS, then
the whole hierarchy of levels collapses to only two
levels and we can directly apply the quantum theories of
coherence (just designed for two-level hierarchical
systems).

11. THE QUANTUM BRAIN THEORIES
The reductionist hypothesis allows the building of
QUANTUM BRAIN THEORIES (UMEZAWA, JIBU,
YASUE, VITIELLO, HAMEROFF, TUSCZINSKY). They
use a number of typically quantum effects to account
for the operation of MEMORY and of other COGNITIVE
PROCESSES, including the ones characterizing the
CONSCIOUSNESS.
These theories gave rise to a number of theoretical
advances as well as of experimental predictions.

12. TYPICAL EFFECTS USED IN QUANTUM
BRAIN THEORIES
Typical examples :
- the DAVYDOV EFFECT, consisting in the generation
of a solitary wave propagating lattice deformations
along a linear polymer chain excited by an external
oscillatory input (here a NON-LOCAL input gives rise
to a LOCALIZED phenomenon)
- the FRÖHLICH EFFECT, consisting in the excitation
of a collective vibrational mode within a set of
reciprocally interacting electric dipoles, generated by
a localized external input (here a LOCALIZED input
gives rise to a NON-LOCAL and COLLECTIVE
phenomenon)

13. THE RANGE OF QUANTUM EFFECTS
It can be approximated by the THERMAL DE BROGLIE
WAVELENGTH, that is by the average wavelength of the
wave associated to each quantum particle of an ideal
gas at the temperature T. It is given by :
h = Planck constant ≅ 6.63x10-34
m = particle mass
K = Boltzmann constant ≅ 1.38x10-23

14. When the thermal De Broglie wavelength is greater than
or of the same order of the typical distances between the
particles then a QUANTUM description is needed. For
particles like electrons and room temperatures the
thermal De Broglie wavelength is of the order of the
atomic distances. This induced to think that quantum
theories are useful only to describe MICROSCOPIC
phenomena.
However this view is incorrect for a number of reasons :
• when the mass tends to zero (like for photons) or the
temperature tends to zero the thermal De Broglie wavelength
diverges
• when the uncertainty about the number of particles is very
high (creation and destruction processes being allowed) the
uncertainty about their relative phases becomes very small
and MACROSCOPIC COHERENCE phenomena are possible.

15. THE BIG PROBLEM FOR
QUANTUM BRAIN THEORIES:
DECOHERENCE
As it is well known, decoherence due to the
interaction with external environment can
destroy the coherence of quantum origin.
Two remarks :
• Decoherence is a problem only for quantum
computers. Biological systems need
decoherence in order to avoid becoming like
crystals
• Decoherence is a smaller problem in QFT
owing to the infinite number of degrees of
freedom and the infinite volume limit

16. THE ACTORS PLAYING THE
DECOHERENCE GAME
• The kind of environment and its symmetries
What models of environment?
THERMAL BATH (the simplest one)
SPIN CHAIN (endowed with symmetry)
ACTIVE MEDIA (feedback on the system)
• the NOISE
• the DISSIPATION
• the DISORDER

17. These actors interact in a very complex way
which makes the decoherence game strongly
dependent on the detailed nature of the
SPECIFIC CONTEXTS.
Some elementary examples can illustrate some
aspects of this game.
In order to understand them we can start from a
simple CLASSICAL (NEURAL) NETWORK and
transform it into a QUANTUM (NEURAL)
NETWORK.

18. A CLASSICAL NETWORK MODEL
• Neurons arranged in a plane network with toroidal topology
O O O O O O O O O O O
O O O O O O O O O O O
O O O O O O O O O O O
O O O O O O O O O O O
• Number of input lines for each neuron is always the same (4)
• Stochastic activation law
• Initial state randomly chosen

19. STOCHASTIC ACTIVATION LAW
This law has the form :
Prob(output = 1) = 1/(1 + exp[-S/T])
where S is the weighted sum of inputs minus the
threshold while T is a parameter, called
‘TEMPERATURE’
In practical cases biological neurons show a stochastic
discharge pattern

20. AN EXAMPLE OF EEG PRODUCED BY THIS
MODEL
Network of 30x30 neurons, threshold = 2, T = 1

21. The autocorrelation function of this EEG

22. THE PERIODOGRAM
THE POWER SPECTRUM

23. A QUANTUM NETWORK MODEL
Let us now compare the behavior of the previous
model with the one of a QUANTUM NETWORK MODEL
with the same structure and topology.
Here the momentarily state vector of each unit is given
by a linear combination of the two basic states “0” and
“1”. In general the coefficients ψ0 and ψ1 of this
combination are complex numbers which vary with
time. At every instant the probability of having an
output 1 is given by | ψ1 |2 .

24. The dynamical evolution of this network is given by a
suitable HAMILTONIAN OPERATOR, whose diagonal
terms are constant, while non-diagonal terms contain
a contribution coming from the output produced by
neighboring neurons, minus a given threshold.
In turn, this output is computed in a probabilistic way
according to the probabilities of “0” and “1” states
existing in the previous instant.
In principle, the evolution of this network should be
characterized by some kind of long-range
correlations.
BUT IS THIS PREDICTION CORRECT ?

25. THE EEG OF THIS NETWORK …
The same conditions as in the classical case: 30x30
neurons, identical initial probabilities, threshold = 2,
diagonal terms = 1, non-diagonal terms = 0.5

26. …but the autocorrelation function differs in a
deep way from the classical case !
Evidence for long-range effects

27. EVEN PERIODOGRAM IS DIFFERENT
…AND POWER SPECTRUM

28. ANOTHER EXAMPLE
Average activity of a quantum neural network
of 10x10 neurons with threshold = 1, non-
diagonal elements of the Hamiltonian = 1,
second-order approximation.

29. WHAT HAPPENS IN PRESENCE
OF EXTERNAL NOISE ?
Average activity of the previous network in
presence of Gaussian input noise with mean=0
and standard deviation=5.

30. As a comparison between the two plots is
difficult, it is more convenient to compare the
two autocorrelation functions.
Without Noise With Noise
A difference appears but it is better to
compare the autocorrelation functions of
the average variances.

31. Without noise With Noise
Superposition of the two plots
Looking at the variance the effect of noise is
more evident !

32. A first lesson of the above simulations is that
the effects of the quantum or classical nature of
a network are difficult to detect when looking at
the macroscopic observation of simple average
quantities, such as mean activity.
They are best detected when looking at more
complex statistical quantities.
And, even at the level of biological neural
networks, the neurons seem to be more
sensitive to higher-order statistical features of
the neural assemblies in which they are
embedded.

33. CAN THE EFFECT OF NOISE BE
COUNTERACTED ?
Let us suppose, in this regard, that a noisy
quantum neural network be interacting with
another coherent system, like a spin bath or a
spin chain.
A simple way for implementing this situations is
to add within the previous quantum neural
network a spin-spin interaction between the
quantum neurons, of quantum nature.

34. Plot of average activity vs t of a noisy quantum
neuron with a moderate spin-spin
antiferromagnetic interaction between
neighboring spins.

35. Autocorrelation Autocorrelation
function of the function of average
average activity variance
As expected, the average variance better helps
to detect weak cues of the re-establishment of
some long-range order.

36. Another lesson is that taking into account
only the destroying influence of the
environment is not enough: if there is some
interaction with another coherent system, the
possibility of a RECOHERENCE or of
counteracting decoherence remains open.
Perhaps different coherence mechanisms can
cooperate, even if each one, taken in isolation,
is characterized by a very small decoherence
time.

37. THE MACROSCOPIC SIGNATURE
OF QUANTUM PHENOMENA
How can a quantum coherence present at the
microscopic level survive up to mesoscopic
and macroscopic level ?
The previous examples suggest that, by using
observations induced by a mean-field analysis,
the detection of quantum coherence becomes
very difficult.

38. However, the simulations show that, by
looking at higher-order statistical features of
mesoscopic and macroscopic quantities, it
should be possible to detect a ‘signature’ of
quantum phenomena at the microscopic level.
Another help comes from the existence of a
number of inequalities regarding the
macroscopic observations (Bell, Leggett-Garg)
that, when not satisfied, are cues revealing an
hidden quantum nature. In some cases these
effects have been experimentally detected.
However, they cannot give any information
about the lower-level quantum processes.

39. A (PARTIAL) CONCLUSION
The actual quantum brain theories are still in a
very primitive stage, being unable to take
simultaneously into account all contributors to
the decoherence game.
Moreover, they still lack a formalism allowing to
describe the whole hierarchy of organizational
levels characterizing the mind-body system.
A number of new technical proposals have been
introduced (e.g. the DISSIPATIVE QUANTUM
FIELD THEORY, the OPEN QUANTUM FIELD
THEORY, etc.) in order to avoid these
shortcomings. Actually, however, it is still
difficult to assess their usefulness.

40. IS QUANTUM THEORY USEFUL FOR
PSYCHIATRISTS ?
So far, quantum theory appears to be useful to
describe mostly low-level phenomena. At the
higher levels it seems to be useful mostly as a
sort of framework for reasoning about
phenomena of holistic nature. Nobody
prevents, however, from thinking that, only
understood some principles underlying the
processes occurring within the wholistic
mind-brain system, quantum theory can be
used to design suitable forms of top-down
actions helping the human beings to reach a
better harmony with the environment.

41. The ultimate goal of these top-down
‘technologies’ would be the one of a world in
which human beings were able to live in a self-
sustaining harmony with the world, without any
intervention of drugs, physicians, hospitals,
and like.
The hope that this state of affairs can be
realized in the future is the basic push
underlying all applications of quantum theory
to the study of brain, cognition, and
consciousness.