Random phase approximation and its extension for the quantum O(2) anharmonic oscillator

Details Random phase approximation and its extension for the quantum O(2) anharmonic oscillator Random phase approximation and its extension for the quantum O(2) anharmonic oscillator

2003-07-07

arxiv.org/abs/hep-ph/0307085v1

Eur.Phys.J. A19 (2004) 289-300

Physics

High Energy Physics

High Energy Physics - Phenomenology

26 pages, Latex file, no figure

Scientific paper

10.1140/epja/i2003-10121-4

We apply the random phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPA approximations using the equation of motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPA approximations. Then we use a time-dependent approach where the standard RPA frequencies are obtained as small oscillations around the static solution in the time-dependent Hartree-Bogoliubov equation. We draw a parallel between the two approaches.

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