Equilibration and Thermalization in the Adapted Caldeira-Leggett Model

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.

Automated summary

This study explores the equilibration processes exhibited by the Adapted Caldeira-Leggett (ACL) model, a toy model used for quantum decoherence studies. The results demonstrate the role of dephasing in achieving equilibration in various situations. Although the model's size and other unphysical aspects limit the applicability of temperature and thermalization, certain basic aspects of thermalization can be realized under specific parameter values. The observed behaviors are linked to intrinsic properties of the global energy eigenstates, suggesting that they may be key ingredients for ergodic behavior in larger, more realistic systems.