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Journal of Modern Physics

Multiple-State Quantum Carnot Engine

Eny Latifah, Agus Purwanto

Published Jan 1, 2011• 25 citations
Publisher

Abstract

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.

DOI
10.4236/jmp.2011.211169

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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.
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.
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.
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.
In this article, we study the quantum Carnot engine using a one-dimensional infinite well potential model in which two particles are non-interacting, indistinguishable and have the same mass. We find that the efficiency of this model is the same as that of the one-dimensional infinite potential well model in which there is one particle. Moreover, efficiency can be measured only when L_C/L_A≥2, where L_A and L_C are the potential well widths during isothermal and adiabatic expansion, respectively.
A quantum ericson-engine that consists of a single particle with multiple states, has been explored. It is a quantum analogy to the classical ericson-engine consisting of a combination of two isothermal processes and two isobaric processes. By analogizing a particle in a one-dimensional infinite potential well as a gas in a piston-cylinder, quantum thermodynamic processes in a quantum ericson-engine can be explained from the analogies of classical processes such as isothermal, and isobaric. The results of the research show that the thermal efficiency of the quantum ericson-engine has similarities with the classical ericson-engine.
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.