Relaxation dynamics of multi-level tunneling systems

TL;DR

This paper presents a quantum mechanical analysis of relaxation dynamics in asymmetric double-well potentials interacting with a heat bath, emphasizing the role of higher vibrational levels in glass relaxation phenomena.

Contribution

It introduces a quantum treatment considering higher vibrational levels in asymmetric double-well potentials, relevant for understanding glass relaxation dynamics.

Findings

Relaxation dynamics can resemble classical Kramers' diffusion limits.

Arrhenius-like temperature dependence observed under certain conditions.

Higher vibrational levels significantly influence relaxation behavior.

Abstract

A quantum mechanical treatment of an asymmetric double-well potential (DWP) interacting with a heat bath is presented for circumstances where the contribution of higher vibrational levels to the relaxation dynamics cannot be excluded from consideration. The deep quantum limit characterized by a discrete energy spectrum near the barrier top is considered. The investigation is motivated by simulations on a computer glass which show that the considered parameter regime is ``typical'' for DWPs being responsible for the relaxation peak of sound absorption in glasses. Relaxation dynamics resembling the spatial- and energy-diffusion-controlled limit of the classical Kramers' problem, and Arrhenius-like behavior is found under specific conditions.