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Condensation of classical nonlinear waves

Colm Connaughton·Christophe Josserand·Antonio Picozzi·Yves Pomeau·Sergio Rica
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Abstract

We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schrödinger equation as a representative model. We formulate a thermodynamic description of the condensation process by using a wave turbulence theory with ultraviolet cut-off. In 3 dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in 2 dimensions, in analogy with standard Bose-Einstein condensation in quantum systems. Numerical simulations show that the thermodynamic limit is reached for systems with $16^3$ computational modes and greater. On the basis of a modified wave turbulence theory, we show that the nonlinear interaction makes the transition to condensation subcritical. The theory is in quantitative agreement with the simulations.

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Colm Connaughton, Christophe Josserand, Antonio Picozzi, Yves Pomeau, Sergio Rica. 2005-02-21. Condensation of classical nonlinear waves. https://doi.org/10.1103/physrevlett.95.263901

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