Binomial Difference Ideal and Toric Difference Variety

In this paper, the concepts of binomial difference ideals and toric difference varieties are defined and their properties are proved. Two canonical representations for Laurent binomial difference ideals are given using the reduced Groebner basis of Z[x]-lattices and regular and coherent difference ascending chains, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms of their support lattices which are Z[x]-lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Four equivalent definitions for toric difference varieties are presented. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric, and in the negative case, to compute the reflexive, well-mixed, and perfect closures of I. An algorithm is given to decompose a finitely generated perfect binomial difference ideal as the intersection of reflexive prime binomial difference ideals.Comment: 72 page

Kondo Spin Screening Cloud in Two-dimensional Electron Gas with Spin-orbit Couplings

A spin-1/2 Anderson impurity in a semiconductor quantum well with Rashba and Dresselhaus spin-orbit couplings is studied by using a variational wave function method. The local magnetic moment is found to be quenched at low temperatures. The spin-spin correlations of the impurity and the conduction electron density show anisotropy in both spatial and spin spaces, which interpolates the Kondo spin screenings of a conventional metal and of a surface of three-dimensional topological insulators.Comment: accepted by the Journal of Physics: Condensed Matte

Bose-Einstein condensation in strong-coupling quark color superconductor near flavor SU(3) limit

Near the flavor SU(3) limit, we propose an analytical description for color-flavor-locked-type Bardeen-Cooper-Schrieffer (BCS) phase in the Nambu Jona-Lasinio (NJL) model. The diquark behaviors in light-flavor and strange-flavor-involved channels and Bose-Einstein condensation (BEC) of bound diquark states are studied. When the attractive interaction between quarks is strong enough, a BCS-BEC crossover is predicted in the environment with color-flavor-locked pairing pattern. The resulting Bose-Einstein condensed phase is found to be an intergrade phase before the emergence of the previous-predicted BEC phase in two-flavor quark superconductor.Comment: 15 pages, 5 figures; 2nd versio