Quantum Carnot heat engine with an effective external electric field perturbation

Abstract

The classical approach to heat engines is not enough to study devices in the atomic scale as it utilizes spin-systems as working substances whose behavior is dictated by quantum mechanics. We constructed a quantum heat engine that follows the Carnot cycle with two reversible isothermal and isomagnetic processes in contact with heat baths of two different temperatures, based on the Lipkin-Meshkov-Glick (LMG) model. The engine runs between two magnetic fields with one kept constant and the other magnetic field varied. A perturbation in the form of an effective external electric field in the x-direction, δJ_x, was introduced to the system where δ ≪ 1. Up to the second-order energy correction was determined using the time-independent perturbation theory and the unperturbed LMG eigenstates as basis. The entropy, internal energy, and the work done in each cycle were determined and used to obtain the efficiency of the system with spins N = 2. For a fixed set of values for the high-temperature heat bath and the low-temperature heat bath, this work demonstrates that the system's efficiency is dependent on δ and the varying magnetic field. The system's maximum efficiency was found to approach the value of the Carnot limit.