Department of Applied Mathematics at the University of Colorado at Boulder
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Speaker:  

Scott Strong

Date of Talk:  

04/18/13

Affiliation:  

Department of Applied Mathematics and Statistics, Colorado School of Mines

Title:  

Quantum Hydrodynamics And Vortex Filaments

Abstract

If hydrodynamics is the study of continuum models that flow under the application of shear stresses then quantum hydrodynamics (QH) corresponds to a subset of these models where the macroscopic continuum presents behavior associated with microscopic quantum systems. The term QH originated from reformulations of the single-particle Schrödinger equation that appear hydrodynamic in form but do not describe fluids in the traditional sense. Regardless, this perspective highlights the salient points of QH. Namely, nodes of the Schrödinger wave function correspond to vortex states and quantization introduces a vortex winding number. Similar to this single particle case is the important example of a single species dilute alkali gas which is made to condense by ultra cooling into the nanokelvin range. Such a condensate, originally predicted by Bose and Einstein, preserves the aforementioned quantized quantities and constitutes an experimentally realizable quantum fluid. Important here is the quantum vortex state where rotation manifests as vortex filaments, i.e., highly localized curl defects that essentially thread the condensate. In this talk we present an overview of the hydrodynamic description of quantum mechanics [1], its connection to effective evolution equations of many-body quantum dynamics consistent with Bose-Einstein condensation [2] and mathematical models of the vorticity fields contained within. [4, 3]

References
[1] E. Madelung. Eine anschauliche deutung der gleichung von schrdinger. Naturwissenschaften, 14(45):1004-1004, 1926.
[2] B. Schlein. Derivation of Eective Evolution Equations from Microscopic Quantum Dynamics. ArXiv e-prints, July 2008.
[3] S. A. Strong. The vortex filament work flow. In Preparation, 2013.
[4] S. A. Strong and L. D. Carr. Generalized local induction equation, elliptic asymptotics, and simulating super fluid turbulence. Journal of Mathematical Physics, 53(3):033102, March 2012.