Title

Classical and Quantum Markov Chains Derived from Billiard-like Systems

Author

Joshua Covey, Washington University in St. LouisFollow

ORCID

http://orcid.org/0000-0002-6098-3585

Date of Award

Spring 5-15-2022

Author's School

Graduate School of Arts and Sciences

Author's Department

Mathematics

Degree Name

Doctor of Philosophy (PhD)

Degree Type

Dissertation

Abstract

Random billiards are a class of random dynamical systems related to dynamical billiards. We extend the study of random billiards and their associated Markov chains in two new directions. First, we introduce a new class of billiard-like systems called lensed billiards, which introduce a step potential to the usual billiard set-up, and conduct an exploratory study of random lensed billiards where we are mainly interested in how the newly-introduced potential parameter relates to the spectral gap and set of moments of the Markov operator associated to the random lensed system.

Second, we recast the mathematical set-up of random billiards to the operator theoretic framework used in open quantum systems, which we use to obtain a description of the quantum counterparts of the Markov chains associated to the random billiards we are interested in. When viewed from this perspective, we see that scattering theory plays a prominent role in the quantum case.

Language

English (en)

Chair and Committee

Renato Feres

Committee Members

Yanli Song

Comments

Update embargo

Recommended Citation

Covey, Joshua, "Classical and Quantum Markov Chains Derived from Billiard-like Systems" (2022). Arts & Sciences Electronic Theses and Dissertations. 2637.
https://openscholarship.wustl.edu/art_sci_etds/2637