Two-dimensional isotropic harmonic oscillator on a time-dependent sphere

Abstract

In this paper, we investigate a two-dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a fluctuating background, transition probabilities per unit time are obtained. Transitions are possible if the energy eigenvalues of the oscillator E i and frequencies of the fluctuating background ω n satisfy the following two simple relations: E j≃E i ω n (stimulated emission) and E j≃E i + h d ω n (absorption). This indicates that a background fluctuating at a frequency of ω n interacts with the oscillator as a quantum field of the same frequency. We believe this result is also applicable for an arbitrary quantum system defined on a fluctuating maximally symmetric background. © 2012 IOP Publishing Ltd.