Abstract
We perform novel energy and norm density resolved wave packet spreading studies in the disordered Gross-Pitaevskii (GP) lattice to confine energy density fluctuations. We map the locations of GP regimes of weak and strong chaos subdiffusive spreading in the 2D density control parameter space and observe strong chaos spreading over several decades. We obtain a renormalization of the ground state due to disorder, which allows for a new disorder-induced phase of disconnected insulating puddles of matter due to Lifshits tails. Inside this Lifshits phase, the wave packet spreading is substantially slowed down.
Highlights
Disorder is inevitable naturally in all materials due to the impurities or defects caused by external fields
The computationally tested asymptotic weak chaos regime was observed to yield αw = 1/3. This result can be derived assuming that the probability of a normal mode being resonant and chaotic is proportional to energy and/or norm density in the wave packet [11]
The wave packet spreading in both the Lifshits phase and the self-trapping regime is characterized by a substantial slowing down from the subdiffusive spreading as observed for weak and strong chaos
Summary
Disorder is inevitable naturally in all materials due to the impurities or defects caused by external fields. In the presence of nonlinear wave interaction terms, delocalization can arise and lead to chaotic dynamics, which destroys Anderson localization through incoherent spreading [9,10,11] This phenomenon was studied experimentally with ultracold atomic gases [12]. The computationally tested asymptotic weak chaos regime was observed to yield αw = 1/3 This result can be derived assuming that the probability of a normal mode being resonant and chaotic is proportional to energy and/or norm density in the wave packet [11] (notably this assumption results in dependence of both αw and αs on the lattice dimension and different choices of N -body interactions [1]). We observe strong chaos and map strong and weak chaos in the density parameter space, including a localization regime coined Lifshits phase (LP) due to a disorder-induced ground state renormalization
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