System of interacting harmonic oscillators in rotationally invariant noncommutative phase space

TL;DR

This paper investigates how rotationally invariant noncommutative phase space affects the energy spectra of systems of interacting harmonic oscillators and free particles, revealing that noncommutativity influences energy levels more significantly as particle number increases.

Contribution

It introduces a model of interacting harmonic oscillators in a rotationally invariant noncommutative phase space and analyzes the impact of noncommutativity on their energy spectra, including free particles.

Findings

Noncommutativity of coordinates increases energy level shifts with more particles.

Spectrum of free particles resembles that of harmonic oscillators with a frequency linked to momentum noncommutativity.

Noncommutative effects become more pronounced in many-particle systems.

Abstract

Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of $N$ interacting harmonic oscillators in uniform filed and a system of $N$ particles with harmonic oscillator interaction are studied. We analyze effect of noncommutativity on the energy levels of these systems. It is found that influence of coordinates noncommutativity on the energy levels of the systems increases with increasing of the number of particles. The spectrum of $N$ free particles in uniform field in rotationally-invariant noncommutative phase space is also analyzed. It is shown that the spectrum corresponds to the spectrum of a system of $N$ harmonic oscillators with frequency determined by the parameter of momentum noncommutativity.