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Lindblad dynamics of the quantum spherical model
The purely relaxational non-equilibrium dynamics of the quantum spherical
model as described through a Lindblad equation is analysed. It is shown that
the phenomenological requirements of reproducing the exact quantum equilibrium
state as stationary solution and the associated classical Langevin equation in
the classical limit fix the form of the Lindblad dissipators, up to an
overall time-scale. In the semi-classical limit, the models' behaviour become
effectively the one of the classical analogue, with a dynamical exponent ,
and an effective temperature , renormalised by the quantum
coupling . A distinctive behaviour is found for a quantum quench, at zero
temperature, deep into the ordered phase , for dimensions.
Only for dimensions, a simple scaling behaviour holds true, with a
dynamical exponent , while for dimensions , logarithmic
corrections to scaling arise. The spin-spin correlator, the growing length
scale and the time-dependent susceptibility show the existence of several
logarithmically different length scales.Comment: 61 pages, 14 figure
The Wigner Entropy Production Rate
The characterization of irreversibility in general quantum processes is an
open problem of increasing techno- logical relevance. Yet, the tools currently
available to this aim are mostly limited to the assessment of dynamics induced
by equilibrium environments, a situation that often does not match the reality
of experiments at the microscopic and mesoscopic scale. We propose a theory of
irreversible entropy production that is suited for quantum systems exposed to
general, non-equilibrium reservoirs. We illustrate our framework by addressing
a set of physically relevant situations that clarify both the features and the
potential of our proposal
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