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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Quantum refrigeration cycles using spin- 1 2 systems as the working substance

Jizhou He, Jincan Chen, Ben Hua

Published Mar 7, 2002• 139 citations
Publisher

Abstract

The cycle model of a quantum refrigerator composed of two isothermal and two isomagnetic field processes is established. The working substance in the cycle consists of many noninteracting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. Especially, the case at high temperatures is analyzed in detail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of the quantum refrigerator using spin-J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot refrigerator are derived simply.

DOI
10.1103/physreve.65.036145

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The cycle model of a quantum refrigerator composed of two isothermal and two isomagnetic field processes is established. The working substance in the cycle consists of many noninteracting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. Especially, the case at high temperatures is analyzed in detail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of the quantum refrigerator using spin-J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot refrigerator are derived simply.
A new model of a quantum refrigeration cycle composed of two adiabatic and two isomagnetic field processes is established. The working substance in the cycle consists of many non-interacting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semi-group approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate and power input, are given. It is found that the coefficient of performance of this cycle is in the closest analogy to that of the classical Carnot cycle. Furthermore, at high temperatures the optimal relations of the cooling rate and the maximum cooling rate are analysed in detail. Some performance characteristic curves of the cycle are plotted, such as the cooling rate versus the maximum ratio between high and low ``temperatures'' of the working substances, the maximum cooling rate versus the ratio between high and low ``magnetic fields'' and the ``temperature'' ratio between high and low reservoirs. The obtained results are further generalized and discussed, so that they may be directly applied to describing the performance of the quantum refrigerator using spin- J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot and Ericsson refrigeration cycles are derived by analogy.
The general performance characteristics of an irreversible quantum refrigeration cycle using many non-interacting spin-1/2 systems as the working substance and consisting of two adiabatic and two isomagnetic field processes are investigated, based on the quantum master equation and semi-group approach. Expressions for several important performance parameters such as the coefficient of performance, cooling rate and power input are derived. By using numerical solutions, the cooling rate of the refrigeration cycle subject to the finite cycle duration is optimized. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal region of the coefficient of performance and the optimal ranges of the temperatures of the working substance and the times spent on the two isomagnetic field processes are determined. 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 the quantum refrigeration cycle using spin- J systems as the working substance.
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily.
The cycle model established here, for which the heat leakage and internal irreversibility are considered, consists of two irreversible non-isentropic adiabatic and two isomagnetic field processes. The working substance is composed of many non-interacting spin systems. Based on quantum master equation of an open system in the Heisenberg picture and semi-group approach, the general performance analysis of quantum refrigeration cycle is performed. Expressions for several important performance parameters, such as the cooling rate, coefficient of performance, rate of entropy production and power input, are derived. By using numerical calculations, the cooling rate as a natural optimization goal for a refrigerator is optimized with respect to external magnetic field. The characteristic curves of the cooling rate, rate of entropy production and power input subject to coefficient of performance are plotted. The optimal regions of the cooling rate, coefficient of the performance (COP) and temperatures of the working substance, are determined.
Based on the quantum master equation and semi-group approach,the general performance characteristics of the cycle working with many noninteracting harmonic oscillators are investigated,which consists of two isothermal and two adiabatic processes.Expressions for some important performance parameters,such as the coefficient of performance,cooling rate,power input,and rate of the entropy production are derived.Especially,the optimal performance of the cycle in high-temperature limit is discussed in detail.The results(obtained) here can provide some new theoretical bases for the optimal design of refrigeration cycle of unconventional working substance in the low-temperature.
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.