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Condensation of classical nonlinear waves.

Colm Connaughton1, Christophe Josserand, Antonio Picozzi

  • 1Laboratoire de Physique Statistique, ENS-CNRS, Paris, France.

Physical Review Letters
|February 21, 2006
PubMed
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Classical wave equations can form condensates, similar to Bose-Einstein condensation. A phase transition occurs in 3D but not 2D, with nonlinear interactions causing a subcritical condensation. This matches numerical results.

Area of Science:

  • Classical wave phenomena
  • Nonlinear dynamics
  • Statistical physics

Background:

  • Classical wave equations can exhibit complex behaviors.
  • Wave turbulence theory describes statistical properties of waves.
  • Bose-Einstein condensation is a quantum phenomenon.

Purpose of the Study:

  • To investigate the formation of large-scale coherent structures (condensates) in classical wave equations.
  • To develop a thermodynamic description of classical condensation.
  • To compare classical condensation with quantum Bose-Einstein condensation.

Main Methods:

  • Using the defocusing nonlinear Schrödinger equation as a model system.
  • Applying wave turbulence theory with an ultraviolet cutoff.
  • Employing a modified wave turbulence theory to account for nonlinear interactions.

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Main Results:

  • A phase transition to an equilibrium state occurs in three dimensions for low energy densities.
  • No phase transition is observed in two dimensions.
  • Nonlinear interactions lead to a subcritical transition to condensation.
  • Theoretical predictions show quantitative agreement with numerical simulations.

Conclusions:

  • Classical wave condensation exhibits similarities to quantum Bose-Einstein condensation.
  • Dimensionality plays a crucial role in the occurrence of phase transitions.
  • Wave turbulence theory provides a valid framework for describing classical condensation.