Asymptotically exact solutions for Fermi systems

I.V. Simenog

Heide Narnhofer, Walter E Thirring

史娟荣，朱敏，莫嘉琪, SHI Juan-rong, Zhu Min +1 more

A nonlinear disturbed model for a class of Fermi gases in optical lattices was investigated. Firstly, in the nondisturbed case, the exact solution of the model path curves of Fermi gases in optical lattices was given. Secondly, the generalized functional analysis homotopic mapping was introduced and an iterative system was constructed, the arbitrary order asymptotic solution to the nonlinear disturbed model for the path curves of Fermi gases in optical lattices was obtained. Finally, a nonlinear small disturbance system was studied. With the proposed method, the asymptotic expressions of the path curves can be conveniently formulated and further extended.

Raj K. Pathria, Paul D. Beale

I. A. Privorotskiǐ

The properties of a Fermi system with a non-zero angular momentum pair interaction are investigated. Uncoupling of the three-particle Green function that yields a solution with isotropic and anisotropic gaps is suggested. It is shown that the solution with the anisotropic gap is asymptotically exact. The difficulties that appear in deriving the solutions with the isotropic gap are discussed. (auth)

Guang-Ming Zhang, Zhao-Bin Su, Lu Yu

An asymptotically exact partition function of the multichannel resonant-level model is obtained through Tomonaga-Luttinger bosonization. A Fermi-liquid vs non-Fermi-liquid transition, resulting from a competition between the Kondo resonance and the x-ray edge singularity, is elucidated explicitly via renormalization-group theory. In the strong-coupling limit, the model is renormalized to the Toulouse limit.