Quantum Scarring in a Two-Dimensional Elliptical Harmonic Oscillator

Abstract

Perturbation-induced quantum scarring is a recently discovered phenomenonin a quantum well perturbed by local potential bumps.In this phenomenon,the probability density of an eigenstate in a perturbed system is enhanced along a periodic orbit of the unperturbed classical counterpart. In this Thesis, we examine perturbation-induced scarring in a two-dimensional anisotropic (elliptic) oscillator characterized by the anisotropy parameter, i.e., the frequency ratio of the confining potential. In particular, we show that some eigenstates of the perturbed oscillator are scarred by the so-called Lissajous orbits occurring at specific anisotropy parameters. Furthermore, the stability of these Lissajous scars is preliminarily analyzed.