Taming two interacting particles with disorder

Two interacting particles at the metal - insulator

To investigate the innuence of electronic interaction on the metal-insulator transition (MIT), we consider the Aubry-Andr e (or Harper) model which describes a quasiperiodic one-dimensional quantum system of non-interacting electrons and exhibits an MIT. For a two-particle system, we study the effect of a Hubbard interaction on the transition by means of the transfer-matrix method and nite-size...

Two interacting particles in a disordered chain III: Dynamical aspects of the interplay Disorder - Interaction

The interplay between the quantum interferences responsible for one particle localization over a length L1, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L2 > L1, is illustrated by a study of the motion of two particles put close to each other at the initial time. Localization is reached in two steps....

Dynamics of two interacting particles in classical billiards

The problem of two interacting particles moving in a d-dimensional billiard is considered here. A suitable coordinate transformation leads to the problem of a particle in an unconventional hyperbilliard. A dynamical map can be readily constructed for this general system, which greatly simplifies calculations. As a particular example, we consider two identical particles interacting through a scr...

Collective Behaviors in Two-Dimensional Systems of Interacting Particles

Supersymmetry and models for two kinds of interacting particles.

We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians that appear in certain superspaces. Some of the resulting Hamiltonians have a direct interpretation as models for two kinds of interacting particles. One model may serve to describe interacting electrons in a lower and upper band of a one-dimensional ...