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Title:Statistical dynamics of some nonequilibrium systems
Author(s):Zimmer, Michael Frank
Doctoral Committee Chair(s):Oono, Yoshitsugu
Department / Program:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Physics, General
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 time-dependent 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 long-distance, 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.
Issue Date:1993
Rights Information:Copyright 1993 Zimmer, Michael Frank
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9411835
OCLC Identifier:(UMI)AAI9411835

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