TIME DEPENDENT RESONATING HARTREE-BOGOLIUBOV THEORY

Abstract

We develop a theory of excitations in a Fermion system with large quantum fluctuations that can be described by resonance of time dependent non-orthogonal Hartree-Bogoliubov (HB) wave functions with different correlation structures. First, we will derive a new kind of variation equation called the time dependent Resonating HB equation in order to determine both the time dependent Resonating HB wave functions and coefficients of a superposition of the HB wave functions. Next, we will get a new approximation for excitations from time dependent small fluctuations of the Resonating HB ground state, i.e., the Resonating HB RPA. It gives two kinds of excitations. One is the collective excitations called vibrons due to secular vibrations of orbitals in the Res HB wave function. The Res HB RPA gives many different classes of the vibrons arising from different HB wave functions involved in the ground state. Another kind of excitations arises from secular vibrations of the mixing coefficients of the Res HB wave functions. These new excitations called resonons are shown to correspond to the excited states in the Res HB theory due to the resonance of the HB wave functions. The Res HB RPA gives a unified description of the vibrons and resonons and their Interactions.