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

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 omega(n) satisfy the following two simple relations: E-j similar or equal to E-i - (h) over bar omega(n) (stimulated emission) and E-j similar or equal to E-i + (h) over bar omega(n) (absorption). This indicates that a background fluctuating at a frequency of omega(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.