Adiabatic response and quantum thermoelectrics for ac-driven quantum systems

Abstract

We generalize the theory of thermoelectrics to include coherent electron systems under adiabatic ac driving, accounting for quantum pumping of charge and heat as well as for the work exchanged between electron system and driving potentials. We derive the relevant response coefficients in the adiabatic regime and show that they obey generalized Onsager reciprocity relations. We analyze the consequences of our generalized thermoelectric framework for quantum motors, generators, heat engines, and heat pumps, characterizing them in terms of efficiencies and figures of merit. We illustrate these concepts in a model for a quantum pump.

Dynamics of energy transport and entropy production in ac-driven quantum electron systems

“…Our analysis will be based on the approach presented in Ref. [13], which consists of a linear response picture akin to Kubo theory in δμ α combined to an adiabatic expansion inV. For the sake of clarity, we consider a two-terminal setup with left and right reservoirs, α = L,R, and μ L = μ and μ R = μ − δμ.…”

“…The separation of energy in heat and useful work and dissipation is the key for a thermodynamical description. In quantum systems under ac driving, the identification of these different components of energy is a nontrivial task which is paramount to cold atoms [1], nanomechanical [2,3], nanoscale optoelectronical [4], and mesoscopic electron physics [5][6][7][8][9][10][11][12][13][14][15][16]. Typically, the central piece of these systems contains a small number of particles and are driven out of equilibrium, which renders a usual thermodynamical description unreliable.…”

“…The foundations of this area were in part developed after the proposal of the Jarzynski's equality [17] and Crook's theorem [18] and a subsequent number of fluctuations relations [19][20][21][22][23][24][25][26][27][28][29][30]. Recently, linear response proposals in close relation to thermodynamics have been formulated for open quantum systems and quasiclassical systems under periodic driving [13,[31][32][33]. The proper definition of the heat exchange between a quantum driven system and its macroscopic environment has been recently addressed in the context of few-level or spin systems in contact to phononic baths [34][35][36] and in systems of coupled quantum harmonic oscillators [37][38][39].…”

Nonlinear charge and energy dynamics of an adiabatically driven interacting quantum dot

“…For low frequencies, the latter can be calculated within the adiabatic formalism of Ref. 24, which corresponds to linear-response inV g (t) (see Appendix A). The result is…”

“…24. Taking into account that the time-dependent perturbation V g (t)n d changes slowly in time, expanding H(t ′ ) around t ′ = t, the evolution operator is approximated up to linear order iṅ V g (t) as followŝ…”