Scattering From a Two Dimensional Array of Flux Tubes: A Study of The Validity of Mean Field Theory

Дата и время публикации : 1993-07-19T06:04:00Z

Авторы публикации и институты :
Ken Kiers
Nathan Weiss

Ссылка на журнал-издание: Phys.Rev. D49 (1994) 2081-2091
Коментарии к cтатье: 23 pages, University of British Columbia Preprint UBCTP93-010
Первичная категория: hep-th

Все категории : hep-th, cond-mat, hep-ph

Краткий обзор статьи: Mean Field Theory has been extensively used in the study of systems of anyons in two spatial dimensions. In this paper we study the physical grounds for the validity of this approximation by considering the Quantum Mechanical scattering of a charged particle from a two dimensional array of magnetic flux tubes. The flux tubes are arranged on a regular lattice which is infinitely long in the “$y$” direction but which has a (small) finite number of columns in the “$x$” direction. Their physical size is assumed to be infinitesimally small. We develop a method for computing the scattering angle as well as the reflection and transmission coefficients to lowest order in the Aharonov–Bohm interaction. The results of our calculation are compared to the scattering of the same particle from a region of constant magnetic field whose magnitude is equal to the mean field of all the flux tubes. For an incident plane wave, the Mean Field approximation is shown to be valid provided the flux in each tube is much less than a single flux quantum. This is precisely the regime in which Mean Field Theory for anyons is expected to be valid. When the flux per tube becomes of order 1, Mean Field Theory is no longer valid.

Category: Physics