Chemical potential and variable number of particles control the quantum state: Quantum oscillators as a showcase

TL;DR

This paper explores how chemical potential and variable particle numbers influence the quantum states of harmonic oscillators, demonstrating control over the system's spectrum and accessible states through these parameters.

Contribution

It introduces a model of open quantum systems with variable particle numbers, showing how chemical potential controls the quantum state spectrum in oscillator ensembles.

Findings

Chemical potential acts as a control parameter for quantum states.

Variable particle number imposes a mandatory energy condition.

Spectrum manipulation via chemical potential enables state control.

Abstract

Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit, we apply a model of a Hamiltonian for open quantum systems in equilibrium with a particle reservoir to ensembles of quantum oscillators. By treating (i) a dilute gas of vibrating particles and (ii) a chain of coupled oscillators as showcases, we demonstrate that the property of varying number of particles leads to a mandatory condition on the energy of the system. In particular, the chemical potential plays the role of a parameter of control that can externally manipulate the spectrum of a system and the corresponding accessible quantum states.