本文基于理想费米气体的状态方程，分析了以理想费米气体为工质的量子Ericsson制冷循环中的回热特征，推导出其制冷循环的制冷系数表达式，并在高温和低温条件下对制冷系数进行了讨论，这将对低温制冷机的研究提供理论依据。

本文基于量子主方程和半群方法，分析了以谐振子系统为工质的量子制冷循环中的回热特征及时间演化公式，推导出制冷系数、制冷率和输入功率的一般表达式，在高温极限下详细推导出它们的具体优化特征。这里所获得的结论可以与经典制冷循环的结论进行比较，发现有许多类似之处。

基于理想量子气体的状态方程。分析了量子气体斯特林制冷循环中的回热特征,推导出循环的制冷系数一般表达式. 获得了在强简并和弱简并条件下循环的制冷系数，对全面理解气体斯特林制冷机的性能有所帮助。

The irreversible 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 noninteracting 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 close analogues of that ofclassical Carnot cycle. Some performance characteristics curves between the cooling rate and the maximum "temperature" ratio of the workingsubstances are plotted. Further, at high temperatures the optimal relations of the cooling rate and the maximum cooling rate are analyzed indetail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of hequantumrefrigerator using spin-J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot and Ericsson refrigeration cycles are derived analogously.