Abstract
We establish a theoretical method which goes beyond the weak coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel-coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies we do not rely on a Markovian weak coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.
Highlights
Many problems in quantum transport are modeled by an impurity Hamiltonian Himp linearly coupled to a bath of free fermions described viaH = Himp + + k ck† ck . (1) k kHere, ck(†) annihilates a fermion of energy k in the bath, which is tunnel coupled with complex amplitude tk to the system via a fermionic annihilation operator d(†) of the system
We have developed the theory of fermionic reaction coordinates (RCs), which provides a tool to extend the range of validity of the usual ME, especially for very structured, i.e., strongly non-Markovian, spectral density (SD)
The benefit of our approach is that the ME approach still allows to treat interactions in the system exactly, it can be straightforwardly applied to nonequilibrium situations and has a transparent thermodynamic interpretation
Summary
III and IV), we make use of our method to study two (spinless) Coulomb-coupled quantum dots in contact with three heat reservoirs This setup is raising increasing attention within the context of quantum thermodynamics, as it provides a prototypical example of a thermoelectric device transporting electrons against a potential bias due to an energetic flow from a hot to a cold bath [47,48]. It is well studied in the weak-coupling and Markovian regimes, theoretically [49,50] as well as experimentally [51,52]. Another complementary paper studies the impact of strong-coupling effects for nonautonomous, i.e., measurement-based, feedback loops on the thermodynamic performance of a MD [57]
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