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Jurnal Fisika Unand

Three-State Quantum Heat Engine Based on Carnot Cycle

Trengginas Eka Putra Sutantyo

Published Feb 11, 2020• 14 citations
Publisher

Abstract

In this paper,we consider three models of quantum heat engines based on Carnot cycle using three energy levels; (1) the ground state, (2) the degenerate state, and (3) the highest energy state. We investigate the variation in the transition state by selecting three different degenerated states. The result we obtained still analogous with the classical heat engine efficiency and also the previous Quantum Carnot Engine model, which only depends on the initial width and the final width of the potential well in isothermal expansion. Moreover, the effect of transition state generally can be accepted for multistate quantum heat engines with 3D systems in cubic potential.

DOI
10.25077/jfu.9.1.142-149.2020

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In this paper,we consider three models of quantum heat engines based on Carnot cycle using three energy levels; (1) the ground state, (2) the degenerate state, and (3) the highest energy state. We investigate the variation in the transition state by selecting three different degenerated states. The result we obtained still analogous with the classical heat engine efficiency and also the previous Quantum Carnot Engine model, which only depends on the initial width and the final width of the potential well in isothermal expansion. Moreover, the effect of transition state generally can be accepted for multistate quantum heat engines with 3D systems in cubic potential.
Carnot cycle consists of isothermal and adiabatic processes which are reversible. Using analogy in quantum mechanics, these processes can be well explained by replacing variables in classical process with a quantum system. Quantum system which is shown in this paper is a particle that moves under the influence of a cubic potential which is restricted only to the state of the two energy levels. At the end, the efficiency of the system is shown as a function of the width ratio between the initial conditions and the farthest wall while expanding. Furthermore, the system efficiency will be considered 1D and 2D cases. The providing efficiencies are different due to the influence of the degeneration of energy and the degrees of freedom of the system.
The difference between quantum isoenergetic process and quantum isothermal process comes from the violation of the law of equipartition of energy in the quantum regime. To reveal an important physical meaning of this fact, here we study a special type of quantum heat engine consisting of three processes: isoenergetic, isothermal and adiabatic processes. Therefore, this engine works between the energy and heat baths. Combining two engines of this kind, it is possible to realize the quantum Carnot engine. Furthermore, considering finite velocity of change of the potential shape, here an infinite square well with moving walls, the power output of the engine is discussed. It is found that the efficiency and power output are both closely dependent on the initial and final states of the quantum isothermal process. The performance of the engine cycle is shown to be optimized by control of the occupation probability of the ground state, which is determined by the temperature and the potential width. The relation between the efficiency and power output is also discussed.
A multiple-state quantum Carnot engine based on single particle in one dimensional potential well is evaluated. The general forms of adiabatic and isothermal force as well as work are given. We apply them first to the simplest case of two-state system, and then to three-state and general n-state system. The first isothermal expansion starts from single ground state and cease to single highest state. In Addition to the simplest case, isothermal expansions may terminate not to highest state but an intermediate state but with the same of the total expansion. The result is that the efficiency of the multi-state machine could be enhanced by reducing the volume of isothermal expansion for the same of the total volume expansion.
A quantum heat engine of a specific type is studied. This engine contains a single particle confined in the infinite square well potential with variable width and consists of three processes: the isoenergetic process (which has no classical analogs) as well as the isothermal and adiabatic processes. It is found that the engine possesses exotic properties in its performance. The efficiency takes the maximum value when the expansion ratio of the engine is appropriately set, and, in addition, the lower the temperature is, the higher the maximum efficiency becomes, highlighting aspects of the influence of quantum effects on thermodynamics. A comment is also made on the relevance of this engine to that of Carnot.
In this paper, the effects of identical particles and energy-level degeneracy on the work output of the quantum Otto and Stirling heat engines are studied. For quantum Otto heat engine, we find the effects of degeneracy in the ground state and in the excited state are same in the high-temperature limitation while the work done by a system with n-fold degeneracy in the excited state (ground state) is n ([Formula: see text]) times the one without degeneracy in the single-particle case. Moreover, the effects of the identical two-level systems with degeneracy in the ground state or excited state as working substances are discussed. The results of such problem for the Stirling and Carnot heat engines are similar. By analytical derivations in two limit conditions, we conclude that for the cycles which are composed of the quantum adiabatic process, isochoric process and isothermal process have similar results.
The two-level quantum heat engines have been studied extensively. Before that, the optimization of most heat engines was mainly concentrated in non-degenerate cases. We consider the level degeneracy, then calculate the maximum operation time and the irreversible dissipation coefficient of the two-level system under the scheme of linear tuned levels. In the high-temperature limit, we find that the level degeneracy affects the maximum power of the two-level heat engine. Especially in the case of the same degeneracy of the ground state and the excited state, the influence is the greatest. In addition, we also show that the degeneracy does not affect the efficiency at maximum power and the consistent relation of the two-level Carnot-like heat engine.