General performance characteristics of a quantum heat pump cycle using harmonic oscillators as the working substance

The cycle model of a regenerative quantum heat pump working with many non-interacting harmonic oscillators is established. The cycle consists of two isothermal and two constant-frequency processes. The general performance characteristics of the cycle are investigated, based on the quantum master equation and semi-group approach. Expressions for some important performance parameters, such as the heating load, coefficient of performance, power input, and rate of the entropy production, are derived. Some interesting cases are discussed. Especially, the optimal performance of the cycle in the high-temperature limit is discussed in detail. Some important characteristic curves of the cycle, such as the heating load versus the coefficient of performance, the power input versus the coefficient of performance, the entropy production rate versus the coefficient of performance, and so on, are presented. The maximum heating load and the corresponding coefficient of performance are calculated. Moreover, the optimal power input, cycle time and temperatures of the working substance in the isothermal processes are analyzed. The optimal region of the coefficient of performance and the optimal ranges of the temperatures of the working substance in the two isothermal processes are determined. In addition. it is proved that the results obtained here can he directly used to derive the optimal performance of a harmonic quantum Carnot heat pump.