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Rigorous Bounds on Transmission, Reflection, and Bogoliubov Coefficients

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thesis
posted on 2023-03-14, 23:25 authored by Boonserm, Petarpa

This thesis describes the development of some basic mathematical tools of wide relevance to mathematical physics. Transmission and reflection coefficients are associated with quantum tunneling phenomena, while Bogoliubov coefficients are associated with the mathematically related problem of excitations of a parametric oscillator. While many approximation techniques for these quantities are known, very little is known about rigorous upper and lower bounds. In this thesis four separate problems relating to rigorous bounds on transmission, reflection and Bogoliubov coefficients are considered, divided into four separate themes: Bounding the Bogoliubov coefficients; Bounding the greybody factors for Schwarzschild black holes; Transformation probabilities and the Miller-Good transformation; Analytic bounds on transmission probabilities.

History

Copyright Date

2009-01-01

Date of Award

2009-01-01

Publisher

Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Mathematics

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level

Doctoral

Degree Name

Doctor of Philosophy

Victoria University of Wellington Item Type

Awarded Doctoral Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research

Advisors

Visser, Matt