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

Abstract

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.

arXiv comment26 pages, Latex file, no figure

References in corpus (4)

• RPA approach to rotational symmetry restoration in a three-level Lipkin model
• A Non-Perturbative Treatment of the Pion in the Linear Sigma-Model
• The Poisson structure of the mean-field equations in the Phi^4 theory
• Symmetry conserving non-perturbative s-wave renormalization of the pion in hot and baryon dense medium

Cited by in corpus (1)

• Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator