Toward irreversibility with a finite bath of oscillators

TL;DR

This paper explores how a finite oscillator bath approaches irreversibility and dissipation, revealing that different frequency distributions can produce similar irreversible behavior in the dense spectrum limit, but diverge otherwise.

Contribution

It demonstrates the conditions under which finite baths mimic infinite environments and how their dynamics differ when departing from the dense spectrum limit.

Findings

Different frequency distributions lead to the same irreversibility in the dense spectrum limit.

Departing from the dense spectrum limit causes qualitatively different dynamical behaviors.

Finite baths can approximate infinite environments under certain conditions.

Abstract

We investigate the routes by which a bath composed of a finite number of oscillators at zero temperature approaches the induction of dissipation when it nears the usual limit of dense spectrum spread in an infinite interval. It is shown that, when this limit is taken, different distributions of environment frequencies can lead to the same irreversible evolution. However, when we move away from it, the dynamics departs from irreversibility in qualitatively different manners.