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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

Quantum vortices within the complex quantum Hamilton-Jacobi formalism.

Chia-Chun Chou1, Robert E Wyatt

  • 1Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712, USA. chiachun@mail.utexas.edu

The Journal of Chemical Physics
|June 24, 2008
PubMed
Summary

This study explores quantum vortices using the quantum Hamilton-Jacobi formalism, revealing how wave function nodes and complex action discontinuities create quantized circulation. It details the distinct flow patterns of quantum momentum and Polya vector fields near these nodes.

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Area of Science:

  • Quantum mechanics
  • Mathematical physics

Background:

  • Quantum vortices are topological defects in quantum fluids.
  • Understanding their formation and properties is crucial for quantum fluid dynamics.

Purpose of the Study:

  • To investigate quantum vortices within the quantum Hamilton-Jacobi formalism.
  • To analyze the behavior of quantum momentum and Polya vector fields around wave function nodes.
  • To illustrate the quantization of circulation in multidimensional complex spaces.

Main Methods:

  • Application of the quantum Hamilton-Jacobi formalism.
  • Analysis of wave function nodes and complex action discontinuities.
  • Use of harmonic oscillator eigenstates for nonstationary states.
  • Examination of coupled harmonic oscillators for multidimensional analysis.

Main Results:

  • Quantum vortices form around wave function nodes, with quantized circulation arising from complex action discontinuities.
  • Quantum momentum fields exhibit hyperbolic flow, while Polya vector fields show circular flow around nodes.
  • The Polya vector field is parallel to probability density contours.
  • Transient excited state quantum vortices and multidimensional circulation quantization were illustrated.

Conclusions:

  • The quantum Hamilton-Jacobi formalism provides a framework for understanding quantum vortex formation.
  • Distinct local structures of quantum momentum and Polya vector fields near wave function nodes were demonstrated.
  • This work elucidates the origin of quantized circulation in complex spaces.