Abstract

The nonlinear quantum kinetic equation for the interaction of sound waves is solved via analytic and numerical techniques. In the classical regime energy cascades to higher frequency (\ensuremath{\omega}) according to the steady-state power law ${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}3/2}$. In the quantum limit, the system prefers a reverse cascade of energy which follows the power law ${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}6}$. Above a critical flux, a new type of spectrum appears which is neither self-similar nor close to equilibrium. This state of nonlinear quantum wave turbulence represents a flow of energy directly from the classical source to the quantum degrees of freedom.

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