Type of Document Dissertation Author Toroczkai, Zoltan URN etd-347162539751141 Title Analytic Results For Hopping Models With Excluded Volume Constraint Degree PhD Department Physics Advisory Committee
Advisor Name Title Zia, Royce K. P. Committee Chair Curtin, Willliam A. Jr. Committee Member Dennison, Brian K. Committee Member Schmittmann, Beate Committee Member Slawny, Joseph Committee Member Keywords
- Hopping model
- Non-equilibrium steady states
- Random walk
Date of Defense 1997-09-04 Availability unrestricted AbstractThe Theory of Brownian Vacancy Driven Walk
We analyze the lattice walk performed by a tagged member of
an infinite 'sea' of particles filling a d-dimensional
lattice, in the presence of a single vacancy. The vacancy is
allowed to be occupied with probability 1/2d by any of its
2d nearest neighbors, so that it executes a Brownian walk.
Particle-particle exchange is forbidden; the only
interaction between them being hard core exclusion. Thus,
the tagged particle, differing from the others only by its
tag, moves only when it exchanges places with the hole.
In this sense, it is a random walk "driven" by the
Brownian vacancy. The probability distributions for its
displacement and for the number of steps taken, after
n-steps of the vacancy, are derived. Neither is a Gaussian!
We also show that the only nontrivial dimension where the
walk is recurrent is d=2. As an application, we compute the
expected energy shift caused by a Brownian vacancy in a
model for an extreme anisotropic binary alloy. In the last
chapter we present a Monte-Carlo study and a mean-field
analysis for interface erosion caused by mobile vacancies.
One-Dimensional Periodic Hopping Models with
Broken Translational Invariance.Case of a Mobile
We study a random walk on a one-dimensional periodic lattice
with arbitrary hopping rates. Further, the lattice contains
a single mobile, directional impurity (defect bond), across
which the rate is fixed at another arbitrary value. Due to
the defect, translational invariance is broken, even if all
other rates are identical. The structure of Master equations
lead naturally to the introduction of a new entity,
associated with the walker-impurity pair which we call the
quasi-walker. Analytic solution for the distributions in
the steady state limit is obtained. The velocities and
diffusion constants for both the random walker and impurity
are given, being simply related to that of the
quasi-particle through physically meaningful equations.
As an application, we extend the Duke-Rubinstein reputation
model of gel electrophoresis to include polymers with
impurities and give the exact distribution of the steady
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