SPEAKER: George Savvidy (Institute of Nuclear and Particle Physics, NCSR "D", Athens)
TITLE: Yang Mills Classical and Quantum Mechanics and Matrix Models
ABSTRACT: I will consider the space homogeneous Yang Mills fields which are
descried by the vector potential depending only on time A(t). In that
case the YM system reduces to the so-called "Yang Mills classical and
quantum-mechanical system" that can be investigated in details in its
classical and quantum-mechanical regimes. In the classical regime it
is a maximally chaotic system. Maximally chaotic dynamical systems
(MCDS) are systems which have nonzero Kolmogorov entropy. In the
quantum-mechanical regime, the system shows a "repulsion of energy
levels" in its spacing distributions of energy levels, which is found
to be a common property of the random matrix models. The connection
with the matrix M theory and type IIB matrix model is discussed.
I review the quantization of the Artin maximally chaotic dynamical
system defined on the fundamental region of the hyperbolic-Lobachevsky
plane. This fundamental region of the modular group has finite volume
and infinite extension in the vertical axis that corresponds to a
cusp. In the classical regime the geodesic flow in this fundamental
region represents an integrable system and at the same time the most
chaotic dynamical system with non-zero Kolmogorov entropy. Our aim is
to answer to the following question: If the classical Hamiltonian
system is maximally chaotic - meaning that it has nonzero Kolmogorov
entropy and exponential convergence to the thermodynamical equilibrium
in the classical regime - what are its quantum mechanical properties?
The wave functions, the spectrum, the correlation functions....
LOCATION: Aula Paoluzi, Department of Physics, Tor Vergata University
DATE: Monday 21 Oct 2024, 14:00–15:00 CET
