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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 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  statistical dynamics
nonequilibrium systems xternal timedependent fields nonpotential forces oarsegrained Ising model 
Abstract:  In this thesis I investigate some statistical mechanical models that have nonequilibrium features either because of: external timedependent fields; forces not satisfying detailed balance; nonpotential forces. A large part of this thesis is devoted to the detailed study of the coarsegrained Ising model coupled with a timedependent magnetic field. The model is the timedependent GinzburgLandau equation (i.e., Model A) with an oscillating magnetic field; the meanfield approximation neglects noise and gradient terms. I numerically solve for the timeaveraged 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 timedependent 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 fieldtheoretic 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, longtime 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 timereversal symmetry and detailed balance, and so it is expected these identities will break down for nonequilibrium systems. Also, it is known that a fieldtheoretic formulation of the stochastic models (in "superspace") reveals symmetries that lead to sets of WardTakahashi 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 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/18870 
Rights Information:  1993 Michael Frank Zimmer 
Date Available in IDEALS:  20110425 
Identifier in Online Catalog:  3645090 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois