Poisson Distribution for a Sum of Additive Functions

We consider the limit distribution of values of a sum of additive arithmetic functions with shifted argument. The case of the Poisson limit distribution is studied. The functions considered take at most two values on the set of primes, 0 and 1, and satisfy some additional conditions. Some examples are given.      

Double and negative reflection of cold atoms in non-Abelian gauge potentials

Atom reflection is studied in the presence of a non-Abelian vector potential proportional to a spin-1/2 operator. The potential is produced by a relatively simple laser configuration for atoms with a tripod level scheme. We show that the atomic motion is described by two different dispersion branches with positive or negative chirality. As a consequence, atom reflection shows unusual features, since an incident wave may split into two reflected ones at a barrier, an ordinary specular reflection, and an additional nonspecular one. Remarkably, the latter wave can exhibit negative reflection and may become evanescent if the angle of incidence exceeds a critical value. These reflection properties are crucial for future designs in non-Abelian atom optics.