Scaling of energy spreading in a disordered Ding-Dong lattice
- We study numerical propagation of energy in a one-dimensional Ding-Dong lattice composed of linear oscillators with elastic collisions. Wave propagation is suppressed by breaking translational symmetry, and we consider three ways to do this: position disorder, mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an initially localized wavepacket is irregular, due to the appearance of chaos, and subdiffusive. For a range of energies and of weak and moderate levels of disorder, we focus on the macroscopic statistical characterization of spreading. Guided by a nonlinear diffusion equation, we establish that the mean waiting times of spreading obey a scaling law in dependence of energy. Moreover, we show that the spreading exponents very weakly depend on the level of disorder.
Author details: | Arkady PikovskyORCiDGND |
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DOI: | https://doi.org/10.1088/1742-5468/ab7e30 |
ISSN: | 1742-5468 |
Title of parent work (English): | Journal of statistical mechanics: theory and experiment |
Publisher: | IOP Publishing Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/05/13 |
Publication year: | 2020 |
Release date: | 2023/03/21 |
Tag: | connections between chaos and statistical physics; nonlinear dynamics; transport properties |
Volume: | 2020 |
Issue: | 5 |
Article number: | 053301 |
Number of pages: | 12 |
Funding institution: | Russian Science FoundationRussian Science Foundation (RSF) [17-12-01534] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 50 Naturwissenschaften |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |