Random-phase approximation and its extension for the O(2) anharmonic oscillator
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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 RPAs 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 RPAs. Then we use a time-dependent approach where the standard-RPA frequencies are obtained as small oscillations arround the static solution in the time-dependent Hartree-Bogoliubov equation. We draw the parallel between the two approaches.
KeywordsStatic Solution Break Symmetry Small Oscillation Anharmonic Oscillator Zero Frequency
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