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

摘要

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.