Geometric Heat Pump: Controlling Thermal Transport with Time-dependent Modulations

Abstract

The second law of thermodynamics dictates that heat simultaneously flows from the hot to cold bath on average. To go beyond this picture, a range of works in the past decade show that, other than the average dynamical heat flux determined by instantaneous thermal bias, a non-trivial flux contribution of intrinsic geometric origin is generally present in temporally driven systems. This additional heat flux provides a free lunch for the pumped heat and could even drive heat against the bias. We review here the emergence and development of this so called "geometric heat pump", originating from the topological geometric phase effect, and cover various quantum and classical transport systems with different internal dynamics. The generalization from the adiabatic to the non-adiabatic regime and the application of control theory are also discussed. Then, we briefly discuss the symmetry restriction on the heat pump effect, such as duality, supersymmetry and timereversal symmetry. Finally, we examine open problems concerning the geometric heat pump process and elucidate their prospective significance in devising thermal machines with high performance.

Geometry-based circulation of local thermal current in quantum harmonic and Bose Hubbard systems

“…Geometry plays a crucial role in transport phenomena [1]. For example, the ring geometry provides a natural shape for persistent current induced by magnetic flux [2][3][4].…”