Topological Quantum Numbers

University Of Washington, Seattle WA

Investigators

Abstract

This award supports theoretical research and education on topological defects in condensed matter physics. Research will focus on three areas: (1) The PI will use results from the previous grant period related to the forces acting on quantized vortices to make detailed studies of vortices in liquid helium, in dilute systems of trapped atoms, and in superconductors. A clear understanding of the vortices in superconductors is particularly important, as it is the dynamics of vortices that primarily determines dissipation of energy in superconducting magnets. (2) Trapped atoms at low temperatures will be studied with an aim to understand what happens when the interactions are not very weak, and to understand how the rotational motion observed in such systems relates to rotational motion in superfluid helium and to the penetration of magnetic flux in superconductors. (3) The PI will continue work on the construction of a theory of the size of corrections to topological quantum numbers. It is supposed that corrections to flux quantization in superconductors and to quantization of electrical conductance in the quantum Hall effect can readily be made negligibly small; modern determinations of fundamental constants are based on the precision of the Josephson voltage-frequency relation and of the integer quantum Hall effect. The PI intends to examine more closely the corrections to quantization in the Josephson effects for neutral superfluids, and the possible edge corrections to the quantum Hall effect. %%% This award supports theoretical research and education on topological defects in a wide range of condensed matter systems. Topological defects play a fundamental and ubiquitous role in condensed matter and materials physics. They are key players in dissipation processes in superconductors and in determining the mechanical strength of materials. This award is concerned with fundamental aspects of topological defects and has an emphasis on the study of a particular kind of topological defect, vortices in superfluids and superconductors. 'Superfluid' includes not only the traditional superfluid states of the helium liquids that occur upon cooling to very low temperatures, but also the quantum coherent states recently realized in dilute gases of alkali atoms. The latter is not only of fundamental interest but contributes to the emerging area of quantum coherence control; quantum computing may be viewed as an application in this area. ***