The evolution of Liouville von Neumann master equations in the Pechukas-Yukawa framework

TL;DR

This paper introduces a new formalism for modeling the out-of-equilibrium dynamics of quantum density matrices using eigenvalue dynamics within the Pechukas-Yukawa framework, linking quantum phase transitions and decoherence.

Contribution

It develops a novel approach to describe quantum state evolution through eigenvalue dynamics, enhancing understanding of quantum phase transitions and decoherence in many-body systems.

Findings

Exact description of quantum systems via eigenvalue dynamics

Improved understanding of quantum phase transitions

Insights into decoherence mechanisms

Abstract

This paper presents a novel formalism for the out of equilibrium dynamics of the density matrix, capable of describing highly entangled many-body interactions. The evolution of quantum states is evaluated via eigenvalue dynamics of a general Hamiltonian system, perturbed by a parametrically evolving variable $\lambda(t)$ that carries the time-dependence. This is achieved using the Pechukas-Yukawa mapping of the evolution of the energy levels governed by their initial conditions on a generalised Calogero-Sutherland model of a 1D classical gas. As such, quantum systems can be described exactly in their entirety from eigenvalue dynamics. Under this description, we provide an improved understanding of the relationship between nonequilibrium quantum phase transitions and decoherence which has significant impacts to a wide range of applications.