Instability of the Rayleigh-Jeans spectrum in weak wave turbulence theory

Details Instability of the Rayleigh-Jeans spectrum in weak wave turbulence theory Instability of the Rayleigh-Jeans spectrum in weak wave turbulence theory

2009-03-27

arxiv.org/abs/0903.4802v2

Phys. Rev. E 79, 061122 (2009)

Physics

Condensed Matter

Statistical Mechanics

Accepted for publication in Phys. Rev. E; new figure, references and discussion added. 17 pages, 3 figures

Scientific paper

10.1103/PhysRevE.79.061122

We study the four-wave kinetic equation of weak turbulence linearized around the Rayleigh-Jeans spectrum when the collision integral is associated with short-range interactions between non-relativistic bosonic quasiparticles. The technique used for the analysis of the stability is based on the properties of the Mellin transform of the kernel in the integral equation. We find that any perturbation of the Rayleigh-Jeans distribution evolves towards low momentum scales in such a form that, when $t \to \infty$, all the particles occupy a sphere of radius arbitrary small.

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