Periodic Thermodynamics

Abstract

This paper develops the thermodynamics of quantum Floquet systems, i.e., quantum systems driven by an arbitrarily strong periodic perturbation, which are in weak interaction with a heat bath. The physics differs in an essential way from that of undriven systems, because the usual energy conservation law, for interactions between the system and heat bath, is changed to Δε+ΔE=0, ±ω, ±2ω,... where ω is the driving frequency, Δε is the difference of the so-called quasi-energies of the Floquet states and ΔE the excitation energy of the bath. That is, a transition between two given physical Floquet states will be accompanied by bath transitions with many different energy changes, ΔE=−Δε+mω, where m is an arbitrary integer. This results in a breakdown of detailed balance. There is a steady state in which the system has periodic fluctuations of period T=2π/ω. The steady state density matrix is diagonal in the Floquet states, with all Floquet states having finite weights, even at zero temperature. Experimentally favorable conditions for studying periodic thermodynamics are briefly discussed.