Reduced Density Matrix Approach to Phononic Dissipation in Friction

TL;DR

This paper develops a reduced density matrix method to analyze phononic energy dissipation in nanoscale friction, focusing on vibrational relaxation during surface stick-slip motion and its frequency dependence.

Contribution

It introduces a formalism for calculating the time evolution of the reduced density matrix for systems coupled to a heat reservoir, applied to friction-related vibrational relaxation.

Findings

Vibrational relaxation times depend on frequency.

The formalism accurately models energy dissipation in nanoscale friction.

Frequency-dependent relaxation times are characterized.

Abstract

Understanding mechanisms for energy dissipation from nanoparticles in contact with large samples is a central problem in describing friction microscopically. Calculation of the reduced density matrix appears to be the most suitable metho to study such systems that are coupled to a large environment. In this paper the time evolution of the reduced density matrix has been evaluated for an arbitrary system coupled to a heat reservoir. The formalism is then applied to study the vibrational relaxation following the stick-slip motion of a small adsorbate on a surface. The frequency dependence of the relaxation time is also determined.