Quantum adiabatic approximation to interacting boson-fermion systems

和也 金子

Pagiotis Vasilopoulos, C. M. Van Vliet

The inhomogeneous master equation obtained in a previous paper is employed to derive a hierarchy of moment equations (quantum mechanical) analogous to the BBGKY hierarchy; the method used is the generating function according to Laplace. In this master equation, and in all these moment equations as well, the effect of the interaction between the particles of the system is represented by relaxation terms; further, there are streaming terms due to the external field. The interactions considered are of a binary nature, fermion–boson or boson–boson. The resulting equations have a simple form (especially for fermion–boson interaction) since the terms representing the interaction can be cast in a form in which only the Boltzmann operator (appropriate to the one-body description) and the second order Fokker–Planck moment appear. The Boltzmann equations obtained by the new method are the same as before (K. M. van Vliet. J/Math. Phys.).

Aurel Bulgac

A sum rule for the so-called quantum phases is established, without assuming adiabatic evolution. By considering two interacting quantum systems, conventionally designated as a boson and a fermionic one, we evaluate the effective bosonic action after integrating out the fermionic variables. This effective action contains a nontrivial topological part, which has the same origin as the quantum adiabatic phase. However, the derivation does not rely on any adiabatic assumption.

Y. K. Gambhir, Peter A. Ring, Peter Schuck

Joachim Brand

A time-dependent Kohn–Sham scheme for 1D bosons with contact interaction is derived based on a model of spinor fermions. This model is specifically designed for the study of the strong interaction regime close to the Tonks gas. It allows us to treat the transition from the strongly interacting Tonks–Girardeau to the weakly interacting quasicondensate regime and provides an intuitive picture of the extent of fermionization in the system. An adiabatic local-density approximation is devised for the study of time-dependent processes. This scheme is shown to yield not only accurate ground-state properties but also overall features of the elementary excitation spectrum, which is described exactly in the Tonks-gas limit.

Виктор Павлович Маслов