On soft σ-algebras

The concept of soft sets, which was first introduced by Molodstov, is a new method to deal with uncertainty. In this work, we generalize probability theory to soft probability theory. We first introduce a soft σ-algebra as a collection of soft sets over an initial universe set X with a fixed set of parameters E and show the soft σ-algebra is a parameterized family of σ-algebras over X, then present some of its properties. Finally, we discuss on the soft probability space

Spin-orbit coupling and perpendicular Zeeman field for fermionic cold atoms: observation of the intrinsic anomalous Hall effect

We propose a scheme for generating Rashba spin-orbit coupling and perpendicular Zeeman field simultaneously for cold fermionic atoms in a harmonic trap through the coupling between atoms and laser fields. The realization of Rashba spin-orbit coupling and perpendicular Zeeman field provides opportunities for exploring many topological phenomena using cold fermionic atoms. We focus on the intrinsic anomalous Hall effect and show that it may be observed through the response of atomic density to a rotation of the harmonic trap.Comment: 5 pages, 4 figure