Kinetic Limit for Wave Propagation in a Random Medium

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit epsilon to 0 the disorder averaged Wigner function on the kinetic scale, time and space of order epsilon^(-1), is governed by a linear Boltzmann equation.Comment: 71 pages, 3 figure

Spherical Spectral Synthesis and Two-Radius Theorems on Damek-Ricci Spaces

We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems

Geometry of entangled states

Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively different states (which cannot be related by local transformations). Thus we generalize earlier results obtained for the simplest 2 x 2 system, which lead to a stratification of the 6D set of N=4 pure states. We define the concept of absolutely separable states, for which all globally equivalent states are separable.Comment: 16 latex pages, 4 figures in epsf, minor corrections, references updated, to appear in Phys. Rev.