Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems.They are able to capture universal properties that serve as references jacques marie mage baudelaire 2 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 oval hexagon glass jar and (ii) a chain of coupled oscillators as showcases, we demonstrate that the property of varying numbers 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.