Lilia Meza-Montes

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 screened Coulomb potential in a one-dimensional billiard. We find that the screening plays an important role in the dynamical behavior of the system and only in the limit of vanishing screening length can the particles be considered as bouncing balls. For more general screening and energy values, the system presents strong nonintegrability with resonant islands of stability. {copyright} {ital 1997} {ital The American Physical Society}

Electron interactions, classical integrability, and level statistics in quantum dots

Abstract The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple system is made strongly non-integrable in the classical regime by the introduction of particle interactions. In particular, we present a two-particle classical system contained in a d -dimensional billiard with hard walls. Similarly, a corresponding two-dimensional quantum dot problem with three particles is shown to have interesting spectral properties as function of the interaction strength and applied magnetic fields.

Effect of interactions on the integrability and level statistics of two particles in an infinite quantum well

We determine the energy spectrum of a system consisting of two particles which interact through a screened Coulomb potential. The spinless particles are confined in a one-dimensional infinite well. The integrable bouncing-ball limit and the bare potential cases, the latter one for di⁄erent strengths, are considered. In both cases, the level of distribution for the integrable limits do not follow a Poisson distribution. In the second case, however, a transition from the singular distribution of free particles to a Wigner-like form takes place as the strength of the bare potential increases. This is similar to the transition for typical systems with mixed dynamics. ( 1998 Elsevier Science B.V. All rights reserved.