A semiclassical heat trace expansion for the perturbed harmonic oscillator

TL;DR

This paper develops a semiclassical heat trace expansion for perturbed harmonic oscillators, enabling inverse spectral analysis by adapting techniques from prior semiclassical studies.

Contribution

It introduces a novel semiclassical heat trace expansion for perturbed harmonic oscillators, extending existing methods to this setting.

Findings

Derived a new heat trace expansion for perturbed harmonic oscillators.

Applied the expansion to obtain inverse spectral results.

Extended semiclassical techniques to a new class of quantum systems.

Abstract

In this paper we study a semiclassical heat trace expansion for perturbations of the harmonic oscillator, by adapting to the semiclassical setting techniques developed by Hitrik and Polterovich in [HP]. We use the expansion to obtain certain inverse spectral results.