Thermodynamics of the polaron master equation at finite bias

Abstract

We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent lowdimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system. C 2015 AIP Publishing LLC. [http://dx

Nature of heat in strongly coupled open quantum systems

“…Many performance studies have thus considered steady state setups (see e.g. [26][27][28][29][30][31][32] ). However, the situation is very different when considering strong coupling setups where the system is driven by a time-dependent process since in this case changes in the coupling energy must be accounted for.…”

Quantum Thermodynamics with Degenerate Eigenstate Coherences

“…For many processes that only depend on populations or for steady state dynamics where eigenstates coherences are always vanishing, a classical stochastic thermodynamics (ST) [19][20][21] can be easily built for the population dynamics. This provides a consistent framework for the study of the thermodynamics of open quantum systems at both the average and the single trajectory level [22][23][24][25][26][27][28]. However, various time-dependent processes do depend on eigenstate coherences.…”

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

“…In particular, if one wishes to address the performance of a steadily working heat engine, the general results derived in [11][12][13][14][15][16][17][18][19][20][21] are not of great help because they either focus on integrated changes of thermodynamic values (e.g., the total heat exchanged in a finite time instead of the rate of heat exchange) and additionally rely on an initially decorrelated system-environment state [11][12][13] and/or coupling only to a single thermal reservoir [11,[13][14][15][16][17];or they remain very formal [18][19][20][21]. Furthermore, model-specific studies are either based on simple or exactly solvable models from the field of quantum transport [22][23][24][25] and quantum Brownian motion [26][27][28][29], or spin-boson models [30][31][32] often in combination with specific transformations applicable only to special Hamiltonians (polaron transformations) [31,[33][34][35][36]; or the investigations are restricted to numerical studies [37].The goal of this paper is to close the gap between the general results, which are often hard to apply in practice, and studies restricted to...…”