Peculiar Macroscopic And Microscopic Properties Of A Fractional Quantum Hall Layer

Abstract

At a surface between electromagnetic media the Maxwell equations allow either the usual boundary conditions, or exactly one alternative: continuity of E(perpendicular), H(perpendicular), D(parallel), B(parallel). These `flipped' conditions on the top and bottom surfaces of an FQH layer capture all its known static electromagnetic properties and so may be considered a deduction from microscopic quantum theory, yet are unobtainable in any realistic, purely classical model. An unrealistic model with free magnetic monopole currents illustrates this. At the microscopic level, the FQH system is a laboratory for the particle concept. Identifying quasiparticles in terms of kinematics or in terms of asymptotic states gives two different perspectives. The kinematics exhibits exclusion rules similar to those in exactly solvable models for quantum systems in one space dimension. An effort here to tie some of these aspects together may be useful as a foundation for a future more comprehensive assessment of the roles and limitations of quasiparticles.