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Density Resolved Wave Packet Spreading in Disordered Gross-Pitaevskii Lattices
by Yagmur Kati, Xiaoquan Yu, Sergej Flach
|As Contributors:||Yagmur Kati|
|Arxiv Link:||https://arxiv.org/abs/2006.06286v2 (pdf)|
|Submitted by:||Kati, Yagmur|
|Submitted to:||SciPost Physics|
|Subject area:||Condensed Matter Physics - Computational|
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.
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Anonymous Report 1 on 2020-7-12 Invited Report
In this paper, the authors are revisiting the problem of wave packet spreading in a disordered nonlinear Schroedinger chain. This problem has attracted a lot of interest in the last 10-12 years, including several publications by the same research group. The novel aspect of the present study is the control on both conserved quantities of the system, norm and energy. In earlier works, the initial conditions had only a given norm, while the energy was different in different disorder realisations (averaged over), while here the system's behaviour is studied for given norm an energy.
The most important result of the paper is the observation of the strong chaos regime, characterised by the exponent alpha = 1/2 in contrast to the weak chaos with alpha = 1/3. This regime was not found in earlier studies of the nonlinear Shroedinger chain precisely because the energy of each initial condition was not well controlled. It was seen only in the Klein-Gordon chain which has only one conserved quantity (the energy). This is an interesting result which definitely deserves a publication.
Unfortunately, the authors only present evidence for the existence of the strong chaos regime, but not a systematic study of the conditions where this regime occurs. It was argued in earlier publications that strong chaos should occur when the norm density exceeds the mean frequency spacing in the localisation volume. This could be checked numerically (a) by looking at different initial conditions, and (b) by looking at the time when the strong chaos crosses over to the weak chaos which should inevitably occur during the wave packet expansion, but no systematic quantitative study is presented. As far as the energy is concerned, no condition is given at all, even as a conjecture. For this reason, the paper seems to me more suitable for publication in Scipost Physics Core rather than in Scipost Physics.
I have a couple of minor comments, mostly concerning the presentation of technical details.
1. Could the authors explain in more detail their reasons for choosing the method of minimising the Hamiltonian in Sec. 3? I always thought that the most standard way would be to use some gradient-based method. Also, I would naively expect the authors' method to be efficient in minimising local configurations, but not in equilibrating populations of two distant Lifshitz minima. I am not questioning the authors' results, which are correctly verified by the local chemical potential test, but I guess many readers (including myself) would appreciate some idea of why this method was chosen.
2. In Sec. 7, I am a bit surprised by the authors' statement that in the non-Gibbs regime the norm density in the spreading fraction cannot be determined and the regime cannot be characterised. Why is it impossible to determine the norm in the self-trapped fraction and subtract it? Also, the wave packet second moment growth is supposed to characterise the spreading fraction, since the self-trapped fraction is frozen, isn't it? The exponent in Fig. 5(d) does not seem to saturate. Is it possible to go to longer times and see if it goes beyond 1/3 (maybe by choosing different initial conditions)?