Reentrant classicality of a damped system

TL;DR

This paper investigates how a damped free particle's specific heat exhibits reentrant classical behavior due to environmental spectral density, revealing unique quantum-to-classical transitions depending on the bath's spectral exponent.

Contribution

It introduces the concept of reentrant classicality in the specific heat of a damped particle, highlighting the role of spectral density in quantum thermodynamics.

Findings

Reentrant classical behavior observed for super-Ohmic baths with s>=2.

Specific heat decreases from classical value at low temperatures, then returns to classical at zero temperature.

The Ohmic case (s=1) uniquely shows zero specific heat at zero temperature.

Abstract

For a free particle, the coupling to its environment can be the relevant mechanism to induce quantum behavior as the temperature is lowered. We study general linear environments with a spectral density proportional to {\omega}^s at low frequencies and consider in particular the specific heat of the free damped particle. For super-Ohmic baths with s>=2, a reentrant classical behavior is found. As the temperature is lowered, the specific heat decreases from the classical value of k_B/2, thereby indicating the appearence of quantum effects. However, the classical value of the specific heat is restored as the temperature approaches zero. This surprising behavior is due to the suppressed density of bath degrees of freedom at low frequencies. For s<2, the specific heat at zero temperature increases linearly with s from -k_B/2 to k_B/2. An Ohmic bath, s=1, is thus very special in the sense that it represents the only case where the specific heat vanishes at zero temperature.