Specific heat anomalies of small quantum systems subjected to finite baths

TL;DR

This paper investigates the specific heat behavior of small quantum harmonic systems coupled to finite baths, revealing anomalous temperature dependence and potential negative values at low temperatures, emphasizing the importance of finite system size effects.

Contribution

It provides a detailed analysis of the specific heat anomalies in small quantum systems with finite baths, highlighting effects not captured by infinite bath models.

Findings

Specific heat approaches N_S k_B at high T

Anomalous low-temperature behavior including negativity

Dependence of specific heat on N_S, N_B, and coupling strength

Abstract

We have studied the specific heat of the $(N_S+N_B)$ model for an $N_S$-body harmonic oscillator (HO) system which is strongly coupled to an $N_B$-body HO bath without dissipation. The system specific heat of $C_S(T)$ becomes $N_S k_B$ at $T \rightarrow \infty$ and vanishes at $T = 0$ in accordance with the third law of thermodynamics. The calculated $C_S(T)$ at low temperatures is not proportional to $N_S$ and shows an anomalous temperature dependence, strongly depending on $N_S$, $N_B$ and the system-bath coupling. In particular at very low (but finite) temperatures, it may become {\it negative} for a strong system-bath coupling, which is in contrast with {\it non-negative} specific heat of an HO system with $N_S=1$ reported by G-L. Ingold, P. H\"{a}nggi and P. Talkner [Phys. Rev. E {\bf 79}, 061105 (2005)]. Our calculation indicates an importance of taking account of finite $N_S$ in studying open quantum systems which may include an arbitrary number of particles in general.