title: 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.
authors.affiliation: PRIMALIGHT, Faculty of Electrical Engineering, Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia.
authors.forename: D S
authors.initials: DS
authors.lastname: Brambila
authors.forename: A
authors.initials: A
authors.lastname: Fratalocchi
mesh_terms: D003198:Computer Simulation; D004735:Energy Transfer; D008956:Models, Chemical; D017711:Nonlinear Dynamics; D011789:Quantum Theory; D013816:Thermodynamics
references.citation: Phys Rev Lett. 2008 Jul 25;101(4):044101
references.pmid: 18764331
references.citation: Phys Rev Lett. 2008 Jun 20;100(24):240403
references.pmid: 18643556
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jul;62(1 Pt A):427-37
references.pmid: 11088477
references.citation: Phys Rev Lett. 1993 Jun 21;70(25):3915-3918
references.pmid: 10053998
references.citation: Phys Rev Lett. 2009 Aug 21;103(8):080401
references.pmid: 19792695
references.citation: Phys Rev Lett. 1988 Aug 8;61(6):655-658
references.pmid: 10039396
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Feb;83(2 Pt 1):021118
references.pmid: 21405829
references.citation: Phys Rev Lett. 1993 Jan 4;70(1):33-36
references.pmid: 10053251
references.citation: Phys Rev Lett. 2002 Feb 11;88(6):067901
references.pmid: 11863853
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jun;73(6 Pt 2):066603
references.pmid: 16906993
references.citation: Nature. 2007 Mar 1;446(7131):52-5
references.pmid: 17330037
references.citation: Phys Rev A. 1991 Sep 15;44(6):R3423-R3426
references.pmid: 9906430
references.citation: Phys Rev Lett. 2005 Nov 11;95(20):200404
references.pmid: 16384040
references.citation: Phys Rev Lett. 2005 Feb 25;94(7):070404
references.pmid: 15783793
references.citation: Nature. 2008 Jun 12;453(7197):891-4
references.pmid: 18548065
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 2):046619
references.pmid: 12443361
references.citation: Phys Rev Lett. 2008 Jan 11;100(1):013906
references.pmid: 18232768
references.citation: Opt Express. 2012 Jul 30;20(16):18156-64
references.pmid: 23038363
references.citation: Science. 2011 Jun 24;332(6037):1541-4
references.pmid: 21566156
references.citation: Phys Rev Lett. 2006 Feb 3;96(4):043902
references.pmid: 16486824
references.citation: Phys Rev Lett. 1988 Aug 8;61(6):659-661
references.pmid: 10039397
references.citation: Nature. 2008 Jun 12;453(7197):895-8
references.pmid: 18548066
references.citation: Phys Rev Lett. 2011 Dec 9;107(24):240602
references.pmid: 22242983
references.citation: Phys Rev Lett. 2005 Apr 29;94(16):160401
references.pmid: 15904199
references.citation: Phys Rev Lett. 2008 Aug 15;101(7):074102
references.pmid: 18764538
references.citation: Phys Rev Lett. 2002 Apr 29;88(17):170406
references.pmid: 12005738