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Non-equilibrium Relaxation and Aging Kinetics

Uwe Tauber, Virginia Tech

If systems characterized by slow (algebraic) relaxation are prepared in an
out-of-equilibrium initial state, one can observe a "physical aging regime"
in the ensuing approach to equilibrium that is governed by broken time
translation invariance and non-trivial, often universal scaling laws.
Dynamical systems near a critical point constitute prototypical and now
well-understood examples. Indeed, measuring critical exponents in the
intermediate aging rather than the asymptotic stationary temporal regime is
now a standard numerical tool. In this talk, I will first apply these
concepts to simple driven lattice gases that relax towards non-equilibrium
stationary systems displaying generic scale invariance. The expected simple
aging behavior in the two-time density auto-correlation function is verified
through Monte Carlo simulations in one, two, and three dimensions. Next I
shall address the continuous non-equilibrium phase transition in driven
Ising lattice gases in two dimensions. Whereas the temporal scaling of the
density auto-correlation function in the non-equilibrium steady state does
not allow a precise measurement of the associated critical exponents, these
can be accurately determined from the aging scaling of the two-time
auto-correlations and the order parameter evolution following a quench to
the critical point. In the second part of the talk, I will present numerical
results for the non-equilibrium relaxation kinetics of interacting magnetic
flux lines in disordered type-II superconductors at low temperatures and low
magnetic fields, represented by means of a three-dimensional elastic line
model. Investigating the vortex density and height auto-correlations as well
as the flux line mean-square displacement allows us to carefully disentangle
different relaxation mechanisms (e.g., vortex line fluctuations and
positional relaxation), and to assess their relative impact on the kinetics
of dilute vortex matter at low temperatures. We observe the emergence of
genuine glassy dynamics, caused by the competing effects of vortex pinning
and long-range repulsive interactions between the flux lines. We contrast
the effects of random point-like pinning centers and correlated columnar
defects. We also compare data from Monte Carlo simulations with results from
Langevin molecular dynamics.