Speeding Up Classical and Quantum Adiabatic Processes: Implications for Work Functions and Heat Engine Designs

摘要

Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. But now it is possible to speed up both classical and quantum adiabatic processes by adding control protocols. In classical systems, we work out the control protocols by analyzing the classical adiabatic approximation. In quantum systems, we mainly follow the idea of transitionless driving by Berry [J. Phys. A: Math. Theor. Vol.42 365303 (2009)]. Such fast-forward adiabatic processes can be performed at an arbitrarily fast speed, and in the meanwhile reduce the work fluctuation. In both cases, we use a parametric oscillator model to work out explicitly the work function and the work fluctuation in three types of processes: fast-forward adiabatic processes, adiabatic processes, and non-adiabatic processes. We show the significant reduction on work fluctuation in fast-forward adiabatic process. We further illustrate how the fast-forward process improves the converging rate of the Jarzynski equality between work statistics and a free energy difference. As an application, we show that fast-forward adiabatic processes not only enhance the output power but also improve the efficiency of a quantum engine.