Quantum heat engine in the relativistic limit: The case of a Dirac particle

TL;DR

This paper investigates the efficiency of quantum heat engines using a relativistic Dirac particle in a potential well, comparing a novel cycle with a quantum Carnot cycle and analyzing their limits.

Contribution

It introduces two quantum heat engine schemes involving a Dirac particle and derives their efficiencies, connecting relativistic and nonrelativistic regimes.

Findings

Derived efficiency expressions from Dirac spectrum

Converge to known Schrödinger results in nonrelativistic limit

Compared relativistic and nonrelativistic quantum engine cycles

Abstract

We studied the efficiency of two different schemes for a quantum heat engine, by considering a single Dirac particle trapped in an infinite one-dimensional potential well as the "working substance." The first scheme is a cycle, composed of two adiabatic and two isoenergetic reversible trajectories in configuration space. The trajectories are driven by a quasistatic deformation of the potential well due to an external applied force. The second scheme is a variant of the former, where isoenergetic trajectories are replaced by isothermal ones, along which the system is in contact with macroscopic thermostats. This second scheme constitutes a quantum analog of the classical Carnot cycle. Our expressions, as obtained from the Dirac single-particle spectrum, converge in the nonrelativistic limit to some of the existing results in the literature for the Schr\"odinger spectrum.