Subdiffusion in one-dimensional Hamiltonian chains with sparse interactions
| Jazyk: | English |
|---|---|
| ISSN: | 0022-4715 1572-9613 |
| DOI: | 10.1007/s10955-020-02496-1⟩ |
| Přístupová URL adresa: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::596e90f1516c80ab17a1bafb8cc8d2b6 https://hal.archives-ouvertes.fr/hal-02296140 |
| Rights: | OPEN |
| Přírůstkové číslo: | edsair.doi.dedup.....596e90f1516c80ab17a1bafb8cc8d2b6 |
| Autor: | Wojciech De Roeck, François Huveneers, Stefano Olla |
| Přispěvatelé: | Catholic University of Leuven - Katholieke Universiteit Leuven (KU Leuven), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), ANR-15-CE40-0020,LSD,Large Stochastic Dynamical Models in Non-Equilibrium Statistical Physics(2015), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), ANR-15-CE40-0020,LSD,Modèles stochastiques en grande dimension pour la physique statistique hors équilibre(2015) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Anderson Localization
subdiffusion FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas symbols.namesake [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 0103 physical sciences Statistical physics [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] 010306 general physics Quantum Condensed Matter - Statistical Mechanics Mathematical Physics Physics Science & Technology Statistical Mechanics (cond-mat.stat-mech) Anharmonicity Statistical and Nonlinear Physics Mathematical Physics (math-ph) Slow transport ABSENCE Fick's laws of diffusion DIFFUSION Physics Mathematical [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Disordered systems Griffiths Regions Physical Sciences symbols Hamiltonian (quantum mechanics) DECAY |
| Zdroj: | Journal of Statistical Physics Journal of Statistical Physics, Springer Verlag, In press, ⟨10.1007/s10955-020-02496-1⟩ Journal of Statistical Physics, Springer Verlag, 2020, 180, pp.678-698. ⟨10.1007/s10955-020-02496-1⟩ |
| ISSN: | 0022-4715 1572-9613 |
| DOI: | 10.1007/s10955-020-02496-1⟩ |
| Popis: | We establish rigorously that transport is slower than diffusive for a class of disordered one-dimensional Hamiltonian chains. This is done by deriving quantitative bounds on the variance in equilibrium of the energy or particle current, as a function of time. The slow transport stems from the presence of rare insulating regions (Griffiths regions). In many-body disordered quantum chains, they correspond to regions of anomalously high disorder, where the system is in a localized phase. In contrast, we deal with quantum and classical disordered chains where the interactions, usually referred to as anharmonic couplings in classical systems, are sparse. The system hosts thus rare regions with no interactions and, since the chain is Anderson localized in the absence of interactions, the non-interacting rare regions are insulating. Part of the mathematical interest of our model is that it is one of the few non-integrable models where the diffusion constant can be rigorously proven not to be infinite. 22 pages, 2 figures, to appear in Journal of Statistical Physics (JSP) v1-->v2: Lemma in section 3.1 expanded, otherwise only minor changes |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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