Multilevel quantum Otto heat engines with identical particles

TL;DR

This paper investigates multilevel quantum Otto heat engines using identical particles, analyzing work ratios for Bosons and Fermions across different temperature regimes and energy spectra, revealing how quantum statistics influence engine performance.

Contribution

It introduces a detailed analysis of quantum Otto engines with identical particles, highlighting the effects of quantum statistics and energy spectra on work output across temperature regimes.

Findings

Work ratios differ from 2 due to wave function symmetry.

Temperature regimes significantly affect work ratios.

Energy spectrum form influences the engine's behavior.

Abstract

A quantum Otto heat engine is studied with multilevel identical particles trapped in one-dimensional box potential as working substance. The symmetrical wave function for Bosons and the anti-symmetrical wave function for Fermions are considered. In two-particle case, we focus on the ratios of $W^i$ ($i=B,F$) to $W_s$, where $W^B$ and $W^F$ are the work done by two Bosons and Fermions respectively, and $W_s$ is the work output of a single particle under the same conditions. Due to the symmetric of the wave functions, the ratios are not equal to $2$. Three different regimes, low temperature regime, high temperature regime, and intermediate temperature regime, are analyzed, and the effects of energy level number and the differences between the two baths are calculated. In the multiparticle case, we calculate the ratios of $W^i_M/M$ to $W_s$, where $W^i_M/M$ can be seen as the average work done by a single particle in multiparticle heat engine. For other working substances whose energy spectrum have the form of $E_n\sim n^2$, the results are similar. For the case $E_n\sim n$, two different conclusions are obtained.