Harmonic oscillators from displacement operators and thermodynamics

TL;DR

This paper explores the quantum and thermodynamic properties of displaced harmonic oscillators, establishing connections between displacement operators, Weyl ordering, and deriving thermodynamic quantities from their spectra.

Contribution

It introduces a novel analysis of displaced harmonic oscillators, linking Hermitian displacement operators with Weyl ordering and calculating thermodynamic properties from their energy spectra.

Findings

Established connection between Hermitian displacement operator and Weyl ordering

Characterized quantum properties of displaced harmonic oscillators

Derived thermodynamic quantities from energy spectra

Abstract

In this investigation, the displacement operator is revisited. We established a connection between the Hermitian version of this operator with the well-known Weyl ordering. Besides, we characterized the quantum properties of a simple displaced harmonic oscillator, as well as of a displaced anisotropic two-dimensional non-Hermitian harmonic oscillator. By constructing the partition functions for both harmonic oscillators, we were able to derive several thermodynamic quantities from their energy spectra. The features of these quantities were depicted and analyzed in details.