Quantum cluster algebras

Cluster algebras were introduced by S. Fomin and A. Zelevinsky in math.RT/0104151; their study continued in math.RA/0208229, math.RT/0305434. This is a family of commutative rings designed to serve as an algebraic framework for the theory of total positivity and canonical bases in semisimple groups and their quantum analogs. In this paper we introduce and study quantum deformations of cluster algebras.Comment: Minor corrections; final version, to appear in Advances in Mathematics; 41 page

Angular distribution of radiation by relativistic electrons in a thin crystal

The results of theoretical investigation of angular distributions of radiation from a relativistic electron passing through a thin crystal at a small angle to the crystal axis are presented. The electron trajectories in crystal were simulated using the binary collision model which takes into account both coherent and incoherent effects at scattering. The angular distribution of radiation was calculated as a sum of radiation from each electron. It is shown that there are nontrivial angular distributions of the emitted photons, which is connected to the superposition of the coherent scattering of electrons by atomic rows (doughnut scattering effect) and the suppression of the radiation due to the multiple scattering effect (similar to the Landau-Pomeranchuk-Migdal effect in an amorphous matter). The orientation dependence of angular distribution of radiation is also analyzed

New analysis of the common nuclear dependence of the EMC effect and short-range correlations

The strong repulsive core of the nucleon-nucleon (NN) interaction at short distances prevents nucleons from becoming close to each other. This gives rise to high-momentum nucleons in the nucleus that cannot be explained in the context of the mean field and are commonly called short-range correlations (SRCs). They are responsible for the strength seen in momentum distribution tails seen in all nuclei, and we can obtain a relative measure of SRCs via cross section ratios to light nuclei. Recent inclusive scattering data from Jefferson Lab have allowed a precise determination of the A-dependence of SRCs in nuclei and suggests that, like the EMC effect, it is especially sensitive to the nuclear local density. These new results, as well as a new analysis of the relationship between SRCs and the EMC effect, will be presented and discussed.Comment: CIPANP Proceeding