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Jurnal Fisika dan Aplikasinya

Relativistic Quantum Brayton Engine Based on Two Non-Interacting Dirac Particles in a One-Dimensional Potential Well

Titis Qorin Nabila, Heru Sukamto, Agus Purwanto

Published Jul 13, 2026• 0 citations
Publisher

Abstract

A quantum heat engine converts heat into work based on the principles of quantum thermodynamics.This study investigates a quantum heat engine composed of two Dirac particles confined in a one-dimensional potential well. The potential well is limited to three discrete energy levels, and the two non-interacting Dirac particles are treated as identical. The system operates under a quantum Brayton cycle, consisting of isobaric and adiabatic processes. The total work output is calculated using the energy levels derived from the relativistic Dirac equation. The efficiency curve is obtained by plotting a theoretical expression as a function of the ratio LA/λ, where λ is the Compton wavelength. The efficiency increases monotonically with LA/λ, approaching an asymptotic maximum, and is further enhanced by larger values of the parameter α, which drive the engine toward near-optimal performance.

DOI
10.12962/j24604682.v21i3.10589

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A quantum heat engine converts heat into work based on the principles of quantum thermodynamics.This study investigates a quantum heat engine composed of two Dirac particles confined in a one-dimensional potential well. The potential well is limited to three discrete energy levels, and the two non-interacting Dirac particles are treated as identical. The system operates under a quantum Brayton cycle, consisting of isobaric and adiabatic processes. The total work output is calculated using the energy levels derived from the relativistic Dirac equation. The efficiency curve is obtained by plotting a theoretical expression as a function of the ratio LA/λ, where λ is the Compton wavelength. The efficiency increases monotonically with LA/λ, approaching an asymptotic maximum, and is further enhanced by larger values of the parameter α, which drive the engine toward near-optimal performance.
A quantum Brayton engine using a massless Boson trapped in a one-dimensional potential well as a working substance has been constructed to be studied. We used a modified analogical model by the first law of thermodynamics for a quantum system implementation. The system was built with Klein Gordon equation, relativistic quantum mechanics Hamiltonian, without the mass term of the Hamiltonian and it was trapped in a one-dimensional potential well. Then, it underwent the quantum ideal Brayton cycle process. The quantum Brayton process consisted of adiabatic compression, isobaric expansion, adiabatic expansion, and isobaric compression processes. This relativistic quantum mechanics Brayton engine has found that the efficiency formulation was similar to the classical one. This study obtained the conformity results between the quantum relativistic and classical Brayton engines. By this cycle process, we also invented that the ratio of heat capacity under constant pressure and volume of the system was 2. It could indicate that the efficiency of quantum relativistic Brayton engine is higher than the classical one.
It is considered that the cycle of a quantum heat engine using many non-interacting spin-1/2 systems as the working substance is composed of two adiabatic and two isomagnetic field processes and is referred to as a spin quantum Brayton engine cycle. Based on the quantum master equation and semi-group approach, expressions for the efficiency and power output of the cycle are derived. By using numerical solutions, the power output of the heat engine subject to finite cycle duration is optimized. The maximum power output and the corresponding parameters are calculated numerically. The optimal region of the efficiency and the optimal ranges of temperatures of the working substance and times spent on the two isomagnetic field processes are determined, so that the general optimum performance characteristics of the cycle are revealed. Moreover, the optimal performance of the cycle in the high-temperature limit is also analysed in detail. The results obtained here are further generalized, so that they may be directly used to describe the performance of a quantum Brayton heat engine using spin-J systems as the working substance.
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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 Schrödinger spectrum.
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Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.