A Microscopic Theory of Dynamics in Fractional Quantum Hall Liquids.

Ian Dunn, Columbia University

A two-dimensional electron gas in the presence of a strong magnetic field exhibits a quantized Hall resistance. To understand this extraordinary macroscopic quantum phenomenon, a collective excitation known as a magnetoroton has been proposed, studied and measured. We propose the first microscopic theory of magnetoroton dynamics in close analogy with the theory of roton dynamics in liquid helium. The helium theory provides information about the dynamics solely from ground state static observables. Likewise, our theory provides the dynamic structure factor given only the static structure factor. We employ a projection scheme where we calculate the dynamics within a chosen subspace of the lowest Landau level. Our theory can be improved systematically by extending this subspace. This theory will provide lineshapes previously inaccessible by computation, theory or experiment. Calculations of the dynamic structure factor are in progress.

Abstract Author(s): I.S. Dunn, T.C. Berkelbach, D.R. Reichman