Nonlinearly-enhanced energy transport in many dimensional quantum chaos

Abstract

By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter.

Dynamical localization of coupled relativistic kicked rotors

“…During a few decades, it was believed that interactions generally destroy localization due to the associated dephasing. In particular, interactions were studied directly [12][13][14][15][16][17][18][19][20] , and modeled by introducing noise [21][22][23][24][25][26][27] , dissipation 24,28,29 , and nonlinearity [30][31][32][33][34][35] . Some experimental probes [36][37][38][39][40][41] also tentatively suggested delocalization.…”

Dynamical localization of interacting ultracold atomic kicked rotors

“…On the other hand, while the single-rotor systems have been extensively studied and are well understood (see [11][12][13][14] for a comprehensive presentation of the subject), the situation is less clear for two or more kicked rotors (see, e.g., [15]). In fact, it was believed that interactions between rotors generally destroy localization [16][17][18][19][20][21][22][23][24]. However Qin et al [25] have recently studied the dynamical localization of two quantum kicked rotors with contact interaction.…”