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By employing a nonlinear quantum kicked rotor model, we investigate thetransport of energy in multidimensional quantum chaos. Parallel numericalsimulations and analytic theory demonstrate that the interplay betweennonlinearity and Anderson localization establishes a perfectly classicalcorrespondence in the system, neglecting any quantum time reversal. Theresulting dynamics exhibits a nonlinearly-induced, enhanced transport of energythrough soliton wave particles.

Nonlinearly-enhanced energy transport in many dimensional quantum chaos