Abstract: Recent developments of the quantum model of the brain proposed by Ricciardi and Umezawa are reviewed. The unidirectionality of time evolution (the arrow of time) in the brain dynamics and the huge capacity of memory may find their origin in the fact that the brain is an open, dissipative system continuously interacting with the external world.
1 Origin and developments of the quantum brain model
In this paper I report about some recent developments [Vitiello, 1995] on the mathematical model of the brain proposed in 1967 by Luigi Maria Ricciardi and by Hiroomi Umezawa [Ricciardi and Umezawa, 1967]. These developments have brought me to find an unsuspected relation between the unidirectionality of time evolution (the arrow of time) of the brain dynamics and the capacity of memory. In such a relation the intrinsic dissipative character of the brain dynamics plays a crucial role. I will not report here on some recent work on neural network simulations of the quantum brain model [Pessa and Vitiello, 1999].
Let me start by observing that today's high level of accuracy and skill in experimental work pushes the frontiers of the quantum theory and of its applications farther and farther. Probably time becomes mature for the investigation of dynamical schemes underlying the rich phenomenology of molecular biology. The pioneering suggestions of Erwin Schrödinger [Schroedinger, 1949], the works by Ricciardi and Umezawa [Ricciardi and Umezawa, 1967], by Herbert Fröhlich and by Alexander Davydov [Froehlich, 1968; 1988], envisaging the domain of biology and neurology as a natural hunting reserve for quantum physics, could be then considered not simply as merely abstract, mathematical modeling of biological systems, but as the first steps in the exploration of the Physics of Living Matter.
The paper on brain and physics of many-body systems [Ricciardi and Umezawa, 1967] was written by Ricciardi and Umezawa when Umezawa was still at Istituto di Fisica Teorica in Naples, before leaving to Wisconsin in 1967. At that time Eduardo Caianiello, who founded the Istituto in 1957, was pursuing his research in renormalization in field theory and at once he was deeply involved in the mathematical description of nonlinear binary decision elements and neural nets. His neuronic equations in Cybernetics were already well known. At the Istituto there was a very exciting atmosphere. Many physicists and mathematicians were visiting and working in Naples. Professor Valentin Braitenberg also joined the Istituto and his contribution to the establishment of the Division of Cybernetics was essential. Caianiello soon later, in 1968, founded the Laboratory of Cybernetics at Arco Felice, in the Naples area.
In those years, as well known, many progresses were made in quantum field theory (QFT): it was the "Heroic Period" (1960-1975), as Robert Marshak calls it [Marshak,1993], of the formulation of the standard gauge theory of strong and electroweak interaction. And the Istituto in Naples was sharing such an exciting atmosphere: besides the Caianiello's group, there were other research groups working in solid state physics and in elementary particles. The activity of Umezawa and of his associates was focused on spontaneous breakdown of symmetry, a hot subject in those days of discussion on gauge theories.
