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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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Testing wave turbulence theory for the Gross-Pitaevskii system
Ying Zhu1, Boris Semisalov2,3,4, Giorgio Krstulovic2
1Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France.
Physical Review. E
|August 17, 2022
Summary
Numerical simulations validate weak wave turbulence theory. The wave-kinetic equation accurately predicts Gross-Pitaevskii equation dynamics for wave turbulence, confirming theoretical models.
Area of Science:
- Nonlinear physics
- Quantum turbulence
Background:
- Weak wave turbulence theory describes the statistical behavior of weakly interacting waves.
- The Gross-Pitaevskii equation (GPE) models Bose-Einstein condensates and nonlinear wave phenomena.
- The wave-kinetic equation (WKE) offers a simplified description of wave turbulence dynamics.
Purpose of the Study:
- To test the predictive power of weak wave turbulence theory.
- To compare numerical solutions of the GPE with the WKE.
- To investigate the evolution of wave statistics towards Gaussianity.
Main Methods:
- Numerical simulations of the Gross-Pitaevskii equation (GPE).
- Numerical solutions of the associated wave-kinetic equation (WKE).
- Analysis of wave-action spectrum and probability density functions (PDFs) of Fourier mode intensities.
Main Results:
- The WKE accurately predicts GPE dynamics for approximately two nonlinear kinetic times without adjustable parameters.
- Qualitative agreement between GPE and WKE persists for longer durations, with minor quantitative deviations.
- Wave statistics were observed to evolve towards Gaussianity on a timescale comparable to the kinetic time.
Conclusions:
- Direct numerical simulations of the GPE and WKE show excellent agreement, providing strong support for weak wave turbulence theory.
- The study validates the WKE as a reliable tool for describing wave turbulence under specific conditions.
- Deviations at longer times highlight potential limitations of WKE assumptions and numerical considerations.
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