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arXiv:2203.02564

The efficiency of Quantum Mechanical Carnot Engine using the Woods Saxon model

Enock Oluwole Oladimeji, T. T. Ibrahim, A. N. Ikot, Durojaiye Jude Koffa, H. O. Edogbanya, Emmanuel Chukwuebuka Umeh, J. Audu, Uzer, J. M.

Published Mar 4, 2022• 1 citation
arXivHTMLPDF

Abstract

The quantum engine cycle serves as an analogous representation of classical heat engines for microscopic systems and the quantum regime of thermal devices is composed of a single element. In this work, the Quantum-Mechanical properties of a non-linear quantum oscillator described by the Woods-Saxon [WS] model are examined. The Quantum-Mechanical analogue of the Carnot cycle was constructed using changes in both the width L of the well and the quantum state of the potential well. The efficiency of the quantum engine, consisting of adiabatic and isothermal processes based on the Woods-Saxon [WS] potential is derived. The result is shown to be analogous to that of the classical engine and found to agree, within an appropriate limit, with existing results obtained from other potential models. This implies that the [WS] potential can be used as an alternative model in quantum engines.

DOI
10.48550/arxiv.2203.02564

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The quantum engine cycle serves as an analogous representation of classical heat engines for microscopic systems and the quantum regime of thermal devices is composed of a single element. In this work, the Quantum-Mechanical properties of a non-linear quantum oscillator described by the Woods-Saxon [WS] model are examined. The Quantum-Mechanical analogue of the Carnot cycle was constructed using changes in both the width L of the well and the quantum state of the potential well. The efficiency of the quantum engine, consisting of adiabatic and isothermal processes based on the Woods-Saxon [WS] potential is derived. The result is shown to be analogous to that of the classical engine and found to agree, within an appropriate limit, with existing results obtained from other potential models. This implies that the [WS] potential can be used as an alternative model in quantum engines.
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
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.
A cyclic thermodynamic heat engine,which combines adiabatic and isothermal processes and consists of classical ideal gas as working substance,runs most efficiently if it is reversible.In this paper,A new cyclic model of quantum Carnot heat engine whose working substance consists of non-interacting extreme relativistic particles confined to an infinite potential well,is set up.It is shown that the engine whose cycle consists of adiabatic and isothermal quantum processes are close analogues of the corresponding classical processes and that the efficiency of this engine is equal to the Carnot efficiency because quantum dynamics is reversible.Consequently,the expectation value of the Hamiltonian in the expression of the efficiency is similar to the temperature in that of the classical one.
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.
Carnot model of heat engine is the most efficient cycle consisting of isothermal and adiabatic processes which are reversible. Although ideal gas usually used as a working fluid in the Carnot engine, Bender used quantum particle confined in 1D potential well as a working fluid. In this paper, by following Bender we generalize the situation to 2D symmetric potential well. The efficiency is express as the ratio of the initial length of the system to the final length of the compressed system. The result then is shown that for the same ratio, 2D potential well is more efficient than 1D potential well.
The quantum analog of Carnot cycles in few-particle systems consists of two quantum adiabatic steps and two isothermal steps. This construction is formally justified by use of a minimum work principle. It is then shown, using minimal assumptions of work or heat in nanoscale systems, that the heat-to-work efficiency of such quantum heat engine cycles can be further optimized via two conditions regarding the expectation value of some generalized force operators evaluated at equilibrium states. In general the optimized efficiency is system specific, lower than the Carnot efficiency, and dependent upon both temperatures of the cold and hot reservoirs. Simple computational examples are used to illustrate our theory. The results should be an important guide towards the design of favorable working conditions of a realistic quantum heat engine.