First Advisor

Jay Gopalakrishnan

Date of Award

Spring 6-2024

Document Type

Thesis

Degree Name

Bachelor of Science (B.S.) in Mathematics and University Honors

Department

Mathematics and Statistics

Language

English

Subjects

PT-symmetry, optics, exceptional points

DOI

10.15760/honors.1594

Abstract

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration of two smaller disks with gain and loss media. We find a rich variety of exceptional points, re-entrant PT-symmetric phases, and a non-monotonic dependence of the PT-symmetry breaking threshold on the system parameters. Previous explorations of spectra of PT-symmetric systems have mainly been limited to finite discrete models or problems in one dimension. By leveraging systems on a two-dimensional continuum, we show how the complexity and variability of the spectral behavior increases. Finally, by considering small analytically computable examples, we study the concept of exceptional points and their relation to the PT-symmetry breaking threshold.

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Persistent Identifier

https://archives.pdx.edu/ds/psu/42410

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