Equilibration and "Thermalization'' in the Adapted Caldeira-Leggett model

TL;DR

This paper investigates how the Adapted Caldeira-Leggett model exhibits equilibration and primitive thermalization through dephasing, providing insights into the emergence of ergodic behavior and fundamental physical laws in quantum systems.

Contribution

It demonstrates how dephasing enables equilibration in the ACL model and links these behaviors to properties of energy eigenstates, offering a potential pathway to understanding thermalization in larger systems.

Findings

Dephasing facilitates equilibration in the ACL model.

Primitive thermalization can occur at specific parameter values.

Behavior linked to properties of global energy eigenstates.

Abstract

I explore the processes of equilibration exhibited by the Adapted Caldeira-Leggett (ACL) model, a small unitary "toy model" developed for numerical studies of quantum decoherence between an SHO and an environment. I demonstrate how dephasing allows equilibration to occur in a wide variety of situations. While the finite model size and other "unphysical" aspects prevent the notions of temperature and thermalization from being generally applicable, certain primitive aspects of thermalization can be realized for particular parameter values. I link the observed behaviors to intrinsic properties of the global energy eigenstates, and argue that the phenomena I observe contain elements which might be key ingredients that lead to ergodic behavior in larger more realistic systems. The motivations for this work range from curiosity about phenomena observed in earlier calculations with the ACL model, to much larger questions related to the nature of equilibrium, thermalization and the emergence of physical laws.