Walter H. Aschbacher
On a quantum phase transition in a steady state out of equilibrium
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ABSTRACT. Within the rigorous axiomatic framework for the description of quantum
mechanical systems with a large number of degrees of freedom, we show that
the nonequilibrium steady state, constructed in the quasifree fermionic
system corresponding to the isotropic XY chain in which a finite sample,
coupled to two thermal reservoirs at different temperatures, is exposed to
a local external magnetic field, is breaking translation invariance and
exhibits a strictly positive entropy production rate. Moreover, we prove
that there exists a second-order nonequilibrium quantum phase transition
with respect to the strength of the magnetic field as soon as the system
is truly out of equilibrium.