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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.
Highlights
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos
Quantum-classical correspondences mediated by Anderson localization possess many implications in the irreversible behavior of time reversible systems, which are at the basis of a long standing physical debate –i.e., the Loschmidt paradox[19]
Nontrivial effects are expected to occur on the energy transport, due to the rich interplay between localization and nonlinearity, as well as by the additional degrees of freedom that can interact in the dynamics
Summary
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. Recent theoretical work performed on d-dimensional disordered lattices show that at any finite nonlinearity there exist a finite probability for the observation of Anderson localization effects[31] In this scenario, nontrivial effects are expected to occur on the energy transport, due to the rich interplay between localization and nonlinearity, as well as by the additional degrees of freedom that can interact in the dynamics. Nontrivial effects are expected to occur on the energy transport, due to the rich interplay between localization and nonlinearity, as well as by the additional degrees of freedom that can interact in the dynamics In this Article, we theoretically investigate this problem by employing both numerical simulations and analytic techniques. To pursue a general theory, we here consider the following two dimensional model:
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