Anderson localisation for an interacting two-particle quantum system on Z{\mathbb Z}

We study spectral properties of a system of two quantum particles on an integer lattice with a bounded short-range two-body interaction, in an external random potential field $V(x,\omega)$ with independent, identically distributed values. The main result is that if the common probability density $f$ of random variables $V(x,\omega)$ is analytic in a strip around the real line and the amplitude constant $g$ is large enough (i.e. the system is at high disorder), then, with probability one, the spectrum of the two-particle lattice Schroedinger operator $H(\omega)$ (bosonic or fermionic) is pure point, and all eigen-functions decay exponentially. The proof given in this paper is based on a refinement of a multiscale analysis (MSA) scheme proposed by von Dreifus and Klein, adapted to incorporate lattice systems with interaction.Comment: 38 pages; main results have been reported earlier on international conference

The von Neumann entropy and information rate for integrable quantum Gibbs ensembles, 2

This paper considers the problem of data compression for dependent quantum systems. It is the second in a series under the same title. As in the previous paper, we are interested in Lempel--Ziv encoding for quantum Gibbs ensembles. Here, we consider the canonical ideal lattice Bose- and Fermi-ensembles. We prove that as in the case of the grand canonical ensemble, the (limiting) von Neumann entropy rate $h$ can be assessed, via the classical Lempel--Ziv universal coding algorithm, from a single eigenvector of the density matrix.Comment: 20 page