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Nonlinear Schrodinger flow in a periodic potential

Barra1, Gaspard, Rica

  • 1Center for Nonlinear Phenomena and Complex Systems, Universite Libre de Bruxelles, Brussels, Belgium.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 14, 2000
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Researchers studied nonlinear Schrödinger equation solutions in periodic potentials. Above a critical current, steady states disappear, leading to time-dependent solutions.

Area of Science:

  • Nonlinear physics
  • Quantum mechanics
  • Mathematical physics

Background:

  • The nonlinear Schrödinger equation (NLSE) models various physical phenomena, including Bose-Einstein condensates and nonlinear optics.
  • Spatially periodic potentials introduce complex behaviors in NLSE solutions.
  • Understanding steady states and transitions is crucial for predicting system dynamics.

Purpose of the Study:

  • To investigate solutions of the defocusing nonlinear Schrödinger equation (NLSE) within a spatially periodic potential.
  • To analytically study the ground-state solution and steady flows.
  • To characterize the emergence of time-dependent solutions beyond a critical current.

Main Methods:

  • Analytical methods were employed to study the ground-state solution and steady flows.

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  • Numerical simulations were used to describe the time-dependent solutions generated above the critical current.

    • Main Results:

    • The study identified the ground-state solution and characterized steady flows in the system.
    • A critical current threshold was determined, above which steady states cease to exist.
    • Time-dependent solutions were generated and described numerically for supercritical currents.

    Conclusions:

    • The system exhibits a transition from steady flow to time-dependent dynamics at a critical current.
    • The findings provide insights into the complex behavior of NLSE solutions in periodic potentials.
    • This research contributes to the understanding of nonlinear dynamics in physical systems.