Wang Rui, Wang Jianhui, He Jizhou, Ma Yongli
Department of Physics, Nanchang University, Nanchang 330031, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):042119. doi: 10.1103/PhysRevE.87.042119. Epub 2013 Apr 23.
We consider the finite-time operation of a quantum heat engine whose working substance is composed of a two-level atomic system. The engine cycle, consisting of two quantum adiabatic and two quantum isochoric (constant-frequency) processes and working between two heat reservoirs at temperatures T(h) and T(c)(<T(h)), is a quantum version of the classical Otto cycle. By optimizing the power output with respect to two frequencies, we obtain the efficiency at maximum power output (EMP) and analyze numerically the effects of the times taken for two adiabatic and two isochoric processes on the EMP. In the absence of internally dissipative friction, we find that the EMP is bounded from the upper side by a function of the Carnot efficiency η(C), η(+)=η(C)(2)/[η(C)-(1-η(C))ln(1-η(C))], with η(C)=1-T(c)/T(h). This analytic expression is confirmed by our exact numerical result and is identical to the one derived in an engine model based on a mesoscopic or macroscopic system. If the internal friction is included, we find that the EMP decreases as the friction coefficient increases.
我们考虑一种量子热机的有限时间运行，其工作物质由一个两能级原子系统组成。该热机循环由两个量子绝热过程和两个量子等容（恒定频率）过程构成，在温度为(T(h))和(T(c))（(T(c)<T(h))）的两个热库之间运行，是经典奥托循环的量子版本。通过相对于两个频率优化功率输出，我们得到了最大功率输出时的效率（EMP），并数值分析了两个绝热过程和两个等容过程所用时间对EMP的影响。在没有内耗散摩擦的情况下，我们发现EMP的上限由卡诺效率(\eta(C))的一个函数给出，即(\eta(+)=\eta(C)^2/[\eta(C)-(1 - \eta(C))\ln(1 - \eta(C))])，其中(\eta(C)=1 - T(c)/T(h))。这个解析表达式得到了我们精确数值结果的证实，并且与基于介观或宏观系统的发动机模型中推导的表达式相同。如果考虑内摩擦，我们发现EMP随着摩擦系数的增加而降低。
