Abstract/Details

A numerical exploration of the statistical behavior of the discretized nonlinear Schroedinger equation


2004 2004

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Abstract (summary)

In this dissertation, we consider the equilibrium as well as near-equilibrium statistical behavior of the discretized nonlinear Schrödinger equation (NLS). We create a modified version of the Metropolis algorithm for generating empirical distributions that approximate the mixed ensemble Gibbs distribution for the NLS. The mixed ensemble is canonical in energy and microcanonical in particle number invariant. After generating and analyzing many such empirical distributions spanning a full range of equilibrium behaviors, we study their near-equilibrium responses to perturbations via linear response theory. This leads us to the discovery of a regime in which near-equilibrium ensembles resist relaxation toward equilibrium when evolved under the NLS dynamics. Within this regime, perturbed mean observables relax in two stages; they undergo a rapid disruption followed by an extremely slow equilibration. In some cases of the latter stage, there is no observable rate of decay towards equilibrium. We propose that quasiperiodicity of individual solutions may be the dynamical mechanism that underlies this two stage behavior. We exhibit a direct correspondence between the two stage regime and the regime within which quasiperiodicity prevails.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Gibbs distribution; Metropolis algorithm; Quasiperiodicity; Schrodinger equation; Statistical behavior
Title
A numerical exploration of the statistical behavior of the discretized nonlinear Schroedinger equation
Author
Eisner, Adam
Number of pages
80
Publication year
2004
Degree date
2004
School code
0118
Source
DAI-B 65/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780496132218, 0496132210
Advisor
Turkington, Bruce
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3152688
ProQuest document ID
305176618
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305176618
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