Non-equilibrium steady state of "glassy" systems (2011)
The study of systems with non-equilibrium steady state (NESS) has
become of great interest in recent years. The paradigm for NESS is a
system which is coupled to two equilibrated reservoirs "A" and "B" that
are characterized by different temperatures and . The
steady state of the system is not canonical.
A particular case of special interest is having one reservoirs (call it
"A") that is replaced by a stationary driving source, while the
relaxation is provided by a bath (call it "B") that has some finite
temperature. This is still
the same paradigm because formally the driving source "A" can be
regarded as a bath that has an infinite temperature .
There is a class of "glassy" systems for which the rate of energy
absorption is a semi-linear (rather than linear)
functional with respect to the power spectrum of the driving source.
This is due to the percolation-like nature of the dynamics. We
demonstrate that a weak coupling to a bath would lead in such case to a
novel non-canonical steady state
that has glassy characteristics. Furthermore, we have
discovered a related quantum saturation effect that sets an upper limit
on the NESS temperature, irrespective of the driving intensity.
Recently we have extended this work, studying the NESS of
"galassy" systems that have a nontrivial topology. Specifically we
analyzed the dependence of the induced current in a ring. due to the
sparsity there is an intermediate regime of driving intensities for
which one can establish a relation to the work of Sinai regarding
random walk in random environment.
The figure above illustrates a ring made up of N
isolated sites with on site energies E_n.
The ring is coupled to a heat reservoir (represented by the blue
"environment") and subjected to a noisy driving field (represented by
the red sun) that induces a current in the ring.
In the lower figures the current is plotted as a function of the scaled
driving intensity and imaged for various "sigma" of glassiness. The
last panel demonstrates the statistics over many realizations.
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