Optimization on a three-level heat engine working with two noninteracting fermions in a one-dimensional box trap

We setup a three-level heat engine model that works with two noninteracting fermions in a one-dimensional box trap. Besides two quantum adiabatic processes, the quantum heat engine cycle consists of two isoenergetic processes, along which the particles are coupled to energy baths at a high constant energy E-H and a low constant energy E-C, respectively. Based on the assumption that the potential wall moves at a very slow speed and there exists a heat leakage between two energy baths, we derive the expressions of the power output and the efficiency, and then obtain the optimization region for the heat engine cycle. Finally, we present a brief performance analysis of a Carnot engine between a hot and a cold bath at temperatures T-H and T-C, respectively. We demonstrate that under the same conditions, the efficiency eta = 1 - (E-C/E-H) of the engine cycle is bounded from above the Carnot efficiency eta(c) = 1 - (T-C/T-H). (C) 2012 American Institute of Physics. [doi:10.1063/1.3681295]