Quantum chaos, random matrix theory, and statistical mechanics in two dimensions - a unified approach

Abstract

We present a theory where the statistical mechanics for dilute ideal gases can be derived from random matrix approach. We show the connection of this approach with Srednicki approach which connects Berry conjecture with statistical mechanics. We further establish a link between Berry conjecture and random matrix theory, thus providing a unified edifice for quantum chaos, random matrix theory, and statistical mechanics. In the course of arguing for these connections, we observe sum rules associated with the outstanding counting problem in the theory of braid groups. We are able to show that the presented approach leads to the second law of thermodynamics.

23 pages, TeX type

References in corpus (8)

• Chaos and Quantum Thermalization
• Average Entropy of a Subsystem
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Mesoscopic Fluctuations of Eigenfunctions and "Level Velocity" Distribution in Disordered Metals
• Spatial Correlation in Quantum Chaotic Systems with Time-reversal Symmetry: Theory and Experiment
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Cited by in corpus (15)

• The approach to thermal equilibrium in quantized chaotic systems
• Random free fermions: An analytical example of eigenstate thermalization
• Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems
• Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices
• A class of N-body problems with nearest- and next-to-nearest neighbour interactions
• Adiabatic geometric phases and response functions
• Strongly interacting mesoscopic systems of anyons in one dimension
• Pseudo-Hermitian random matrix theory
• Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble
• Random cyclic matrices
• Diagnosing First and Second Order Phase Transitions with Probes of Quantum Chaos
• Dissipation in finite Fermi systems
• Action scales for quantum decoherence and their relation to structures in phase space
• A Diffusion Equation for Quantum Adiabatic Systems
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model