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Nusantara Science and Technology Proceedings

Quantum Stirling Engine with Multiple States in One Dimensional Potential Well

Nailul Hasan

Published Nov 12, 2021• 0 citations
Publisher

Abstract

The quantum analogy for of ideal Stirling engine in one dimensional potential well has been explored. It contains single particles with multiple quantum states which is a superposition of many states. The volume in the classical engine is replaced by the length or width of the well. As in the classical one, the quantum Stirling engine consists of two isothermal processes and two isobaric processes. In the analogy of isobaric processes is constant width. The isothermal processes in the quantum engine here are defined by the constant internal energy of particles. Energy conservation is used to calculate the efficiency and work in each process. We found that the efficiency of the quantum Stirling engine has similarities with the classical Stirling engine.

DOI
10.11594/nstp.2021.1452

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Abstract QLE which has the working substance of a quantum system, a single particle confined in a one-dimensional potential box, has been constructed theoretically in this paper. The quantum system replaces the role of the classical system which has a working substance in the form of gas confined in a piston cylinder. The piston that moves back and forth is substituted by a 1D potential box wall that can move freely to change the width of the potential box. In this way, the three classical thermodynamic processes in the CLE (Classical Lenoir Engine), namely isochoric, isotherm, and isobar, can be analogous to the quantum system. Finally, we find that the thermal efficiency formulation of QLE has the similarity of shape to the CLE efficiency equation. However, a higher ratio of specific heat for QLE makes the efficiency value greater than CLE at each same compression ratio.
The quantum engine cycle serves as an analogous representation of the macroscopic nature of heat engines and the quantum regime of thermal devices composed of a single element. In this work, we follow the formalism of a quantum engine proposed by Bender et al. [1] where they observed quantum Carnot cycle with a single particle of mass m confined to an infinite one-dimensional potential well of width L as a working medium. Using this model, a quantum-mechanical analogue of the Stirling cycle [SC] and Ericsson cycle [EC] have been constructed through changes of both, the width of the well and its quantum state. The efficiency of quantum engines is derived, which is found to be analogous to classical thermodynamic engines. Keywords: Quantum thermodynamics, Quantum mechanics, Ericsson cycle, Stirling cycle, Quantum heat engines, Nano-engines.
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In this work we follow the Bender et al paper [1] to study the quantum analogues of the Stirling and Ericsson polytropic cycles. In the context of the classical thermodynamics, the Stirling and Ericsson cycles correspond to reversible heat engines with two isothermal processes joined by two polytropic branches which occur in a device called regenerator. If this device is an ideal one, the efficiency of these cycles is the Carnot efficiency. Here, we introduce the quantum analogues of the Stirling and Ericsson cycles, the first one based on a double square potential well with a finite potential barrier, since in this system the tunnel effect could be the analogue to the regeneration classical process, therefore the isochoric quantum branches would really correspond to an internal energy storage, and the last one with an unknown system where the isobaric quantum processes don’t induce changes in its quantum state. With these systems the quantum engines have cycles consisting of polytropic and isothermal quantum processes analogues to the corresponding classical processes. We show that in both cases the quantum cycles have an efficiency given by ηCQM = 1 − EC/EH, which is the same expression for the quantum analogue of the Carnot cycle studied by Bender.