Negative mass corrections in a dissipative stochastic environment

TL;DR

This paper investigates how a macroscopic object in a dissipative stochastic environment experiences a negative mass correction, which can enhance oscillation frequency contrary to typical friction effects, using perturbation theory and exactly solvable models.

Contribution

It introduces the concept of negative mass correction in dissipative environments and demonstrates its effects through theoretical analysis and solvable models.

Findings

Negative mass correction can increase oscillation frequency.

Perturbation theory reproduces known friction coefficients.

Effect persists beyond adiabatic approximation validity.

Abstract

We study the dynamics of a macroscopic object interacting with a dissipative stochastic environment using an adiabatic perturbation theory. The perturbation theory reproduces known expressions for the friction coefficient and, surprisingly, gives an additional negative mass correction. The effect of the negative mass correction is illustrated by studying a harmonic oscillator interacting with a dissipative stochastic environment. While it is well known that the friction coefficient causes a reduction of the oscillation frequency we show that the negative mass correction can lead to its enhancement. By studying an exactly solvable model of a magnet coupled to a spin environment evolving under standard non-conserving dynamics we show that the effect is present even beyond the validity of the adiabatic perturbation theory.