Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory

Physical Review. E
Athanasios C TzemosG Contopoulos

Abstract

We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero. In suitably defined coordinates (comoving with the nodal line) the generic structure of the flow implies the formation of 3D quantum vortices. We show that such vortices are accompanied by nearby invariant lines of the comoving quantum flow, called X lines, which are normally hyperbolic. Furthermore, the stable and unstable manifolds of the X lines produce chaotic scatterings of nearby quantum (Bohmian) trajectories, thus inducing an intricate form of the quantum current in the neighborhood of each 3D quantum vortex. Generic formulas describing the structure around 3D quantum vortices are provided, applicable to an arbitrary choice of 3D wave function. We also give specific numerical examples as well as a discussion of the physical consequences of chaos near 3D quantum vortices.

References

Jun 1, 1994·Physical Review. a·H Wu, D W Sprung
Apr 28, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C EfthymiopoulosG Contopoulos
Aug 8, 2009·Physical Review Letters·Chia-Chun ChouRobert E Wyatt
Jan 26, 2011·Physical Chemistry Chemical Physics : PCCP·Basile F E CurchodUrsula Rothlisberger
Jun 4, 2011·Science·Sacha KocsisAephraim M Steinberg
Jul 16, 2013·Journal of Physics. Condensed Matter : an Institute of Physics Journal·A AlarcónX Oriols

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