Document 
Eur. Phys. J. B 13, 781-790
Quantum-mechanical tunneling in associative neural networks
M. Dugic1,3 - D. Rakovic2,3
1 Faculty of Science, Dept. Phys., P.O. Box 60, 34 000 Kragujevac, Yugoslavia
2 Faculty of Electrical Engineering, P.O. Box 35-54, 11120 Belgrade, Yugoslavia
3 The International Anti-Stress Center (IASC), Belgrade, Yugoslavia
dugic@knez.uis.kg.ac.yu
Received 15 July 1999
Abstract
We investigate the quantum-mechanical tunneling
between the "patterns" of the, so-called, associative
neural networks. Being the relatively stable minima of the
"configuration-energy" space of the networks, the "patterns" represent
the macroscopically distinguishable states of the neural nets.
Therefore, the tunneling represents a macroscopic quantum
effect, but with some special characteristics. Particularly, we
investigate the tunneling between the minima of approximately
equal depth, thus requiring no energy exchange. If there are
at least a few such minima, the tunneling represents a sort
of the "random walk" process, which implies the quantum
fluctuations in the system, and therefore "malfunctioning" in
the information processing of the nets. Due to the finite number
of the minima, the "random walk" reduces to a dynamics modeled
by the, so-called, Pauli master equation. With some plausible
assumptions, the set(s) of the Pauli master equations can be
analytically solved. This way comes the main result of this
paper: the quantum fluctuations due to the quantum-mechanical
tunneling can be "minimized" if the "pattern"-formation is
such that there are mutually "distant" groups of the "patterns",
thus providing the "zone" structure of the "pattern" formation.
This qualitative result can be
considered as a basis of the efficient deterministic functioning of the
associative neural nets.
PACS
02.50.Ey Stochastic processes -
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag