Statistical dynamics of some nonequilibrium systems
Zimmer, Michael Frank
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https://hdl.handle.net/2142/18870
Description
Title
Statistical dynamics of some nonequilibrium systems
Author(s)
Zimmer, Michael Frank
Issue Date
1993
Doctoral Committee Chair(s)
Oono, Yoshitsugu
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
statistical dynamics
nonequilibrium systems
xternal time-dependent fields
nonpotential forces
oarse-grained Ising model
Language
en
Abstract
"In this thesis I investigate some statistical mechanical models that have nonequilibrium
features either because of: external time-dependent fields; forces not satisfying
detailed balance; nonpotential forces.
A large part of this thesis is devoted to the detailed study of the coarse-grained
Ising model coupled with a time-dependent magnetic field. The model is the timedependent
Ginzburg-Landau equation (i.e., Model A) with an oscillating magnetic
field; the mean-field approximation neglects noise and gradient terms. I numerically
solve for the time-averaged magnetization, and study the phase boundary as a
function of field and temperature. A previous work utilizing an equilibrium scheme
(Glauber Dynamics) is argued to be insufficient; it predicts a discontinuous change
in the order parameter (for low temperature), whereas my result (which has no equilibrium
assumptions) predicts a continuous change.
There are very few detailed studies of the role of fluctuations in nonequilibrium
systems, especially those with time-dependent fields. One of the most interesting effects
of fluctuations occurs near a continuous phase transition, where thermodynamic
variables scale with nontrivial exponents. To pursue this, the problem is formulated
in a field-theoretic manner, and is investigated in an analogous way. It is found
that the oscillating field does not change the (ultraviolet) divergences that appeared
without the field. However, it does have the more physical effect of altering the longdistance,
long-time behavior of thermodynamic functions such as the susceptibility.
On approaching the continuous phase transition line, it is predicted that there will
be an anomalously large dissipation. This result is found from a (doubly) resummed
perturbation expansion; the corrections to scaling exponents in this expression are
also found.
Equilibrium systems satisfy identities relating the response and correlation functions,
known as fluctuation dissipation theorems (FDTs) of the first kind. In (some)
derivations of these identities, use is made of time-reversal symmetry and detailed
balance, and so it is expected these identities will break down for nonequilibrium
systems. Also, it is known that a field-theoretic formulation of the stochastic models
(in ""superspace"") reveals symmetries that lead to sets of Ward-Takahashi identities
(WTis); in equilibrium models one of these is the FDT. From this, WTis were
found that consisted of the usual FDT, plus a contribution that broke the previously
mentioned symmetry. Since they are nonperturbative, they represent a potentially
valuable clue to unraveling the mysteries of nonequilibrium statistical mechanics."
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