Dynamical System Defined on Fundamental Region of Modular Group SL(2,Z)

by George Savvidy (NCSR "Demokritos" - Institute of Nuclear and Particle Physics (INPP))

Monday 11 Nov 2024, 14:00 → 15:00 Europe/Rome

Aula Grassano

I review the quantization of the Artin maximally chaotic dynamical
system defined on the fundamental region of the Modular Group SL(2,Z).
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....