SciPost Phys. 10, 135 (2021) ·
published 8 June 2021
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We develop the 'duality approach', that has been extensively studied for
classical models of transport, for quantum systems in contact with a thermal
'Lindbladian' bath. The method provides (a) a mapping of the original model to
a simpler one, containing only a few particles and (b) shows that any dynamic
process of this kind with generic baths may be mapped onto one with equilibrium
baths. We exemplify this through the study of a particular model: the quantum
symmetric exclusion process introduced in [D. Bernard, T. Jin, Phys. Rev. Lett.
123, 080601 (2019)]. As in the classical case, the whole construction becomes
intelligible by considering the dynamical symmetries of the problem.
SciPost Phys. 9, 054 (2020) ·
published 20 October 2020
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A large family of diffusive models of transport that has been considered in
the past years admits a transformation into the same model in contact with an
equilibrium bath. This mapping holds at the full dynamical level, and is
independent of dimension or topology. It provides a good opportunity to discuss
questions of time reversal in out of equilibrium contexts. In particular,
thanks to the mapping one may define the free-energy in the non-equilibrium
states very naturally as the (usual) free energy of the mapped system.
