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Published on: February 1, 2017
Stochastic theory of quantum vortex on a sphere
1Research Organization of Science and Engineering, Ritsumeikan University-BKC, Kusatsu City, Japan.
Summary
This study presents a stochastic theory for quantum vortices in superfluid films on a sphere, modeling vortex motion using Langevin and Fokker-Planck equations to analyze pinning potential effects.
Area of Science:
- Condensed Matter Physics
- Quantum Fluids
- Statistical Mechanics
Background:
- Quantum vortices are fundamental excitations in superfluids.
- Superfluid films on curved surfaces present unique physical phenomena.
- Understanding vortex dynamics is crucial for superfluid applications.
Purpose of the Study:
- To develop a stochastic theory for quantum vortices on a 2D sphere.
- To investigate the influence of pinning potentials on vortex behavior.
- To analyze the interplay between pinning strength and temperature.
Main Methods:
- Derivation of vortex equation from Landau-Ginzburg theory.
- Formulation of the Langevin and Fokker-Planck equations for vortex dynamics.
- Application of functional integral techniques for analysis.
- Asymptotic analysis in the small diffusion limit.
Main Results:
- The vortex equation is shown to be a Langevin equation with random forces.
- The Fokker-Planck equation describes the distribution function of point vortices.
- Analysis reveals distinct weak and strong coupling regimes based on pinning potential and temperature.
- A compact expression for the distribution function is derived for small diffusion.
Conclusions:
- The stochastic theory provides a framework for understanding quantum vortex dynamics in confined geometries.
- Pinning potentials play a critical role in determining vortex behavior and statistical properties.
- The study offers insights into vortex behavior on spherical and other non-spherical surfaces.
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