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arXiv · 1210.5609

Two Dimensional Isotropic Harmonic Oscillator on a Time-dependent Sphere

Ali Mahdifar·Behrouz Mirza·Rasoul Roknizadeh
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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 $\omega_n$ satisfy the following two simple relations: $E_{j}\simeq E_{i}-\hbar\omega_{n}$ (stimulated emission) or $E_{j}\simeq E_{i}+\hbar\omega_{n}$ (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.

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Ali Mahdifar, Behrouz Mirza, Rasoul Roknizadeh. 2012-10-20. Two Dimensional Isotropic Harmonic Oscillator on a Time-dependent Sphere. https://doi.org/10.1088/1751-8113/45/46/465301

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