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

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

2007-05-04

arxiv.org/abs/0705.0657v1

Physics

Mathematical Physics

38 pages; main results have been reported earlier on international conferences

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Anderson localisation for an interacting two-particle quantum system on ${\mathbb Z}$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Anderson localisation for an interacting two-particle quantum system on ${\mathbb Z}$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Anderson localisation for an interacting two-particle quantum system on ${\mathbb Z}$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-616188