Abstract/Details

Weak coupling limit for a tracer particle with rapid scatterings by light particles with point interactions


2007 2007

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Abstract (summary)

The primary result of this dissertation is a rigorous analysis of a scattering process for a test particle in the weak coupling limit. The reduced dynamics of the scattering process describes the free dynamics of a particle in 1 or 3 dimensions interlaced with scatterings with particles whose interaction is given by a point potential; the limiting dynamics describes a particle in an electro-magnetic field with an idealized non-classical noise. The weak coupling limit arises by taking the mass ratio λ = [special characters omitted] of a single scattering particle to the test particle to be near zero while the frequency of collisions increases proportionally to [special characters omitted]. The limiting dynamics is accurate up to second order in λ and the strength of both the vector potential of the induced electromagnetic field and the white noise is proportional to λ. We conjecture that after a second limit corresponding to a gas reservoir in an equilibrium state, the dynamics converge to a form studied for decoherence by Gallis and Fleming in 1990. We conclude by discussing decoherence related quantities of these limiting equilibrium dynamics.

Indexing (details)


Subject
Mathematics;
Optics
Classification
0405: Mathematics
0752: Optics
Identifier / keyword
Pure sciences; Decoherence; Light particles; Point interactions; Rapid scatterings; Scattering operators; Tracer particle; Weak coupling limit
Title
Weak coupling limit for a tracer particle with rapid scatterings by light particles with point interactions
Author
Clark, Jeremy Thane
Number of pages
242
Publication year
2007
Degree date
2007
School code
0029
Source
DAI-B 68/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549213246
University/institution
University of California, Davis
University location
United States -- California
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3280570
ProQuest document ID
304901316
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304901316
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