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Subdiffusion in one-dimensional Hamiltonian chains with sparse interactions

De Roeck, Wojciech; Huveneers, François; Olla, Stefano (2020), Subdiffusion in one-dimensional Hamiltonian chains with sparse interactions, Journal of Statistical Physics, 180, p. 678–698. 10.1007/s10955-020-02496-1

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griffiths_phase10.pdf (533.8Kb)
Type
Article accepté pour publication ou publié
Date
2020
Journal name
Journal of Statistical Physics
Number
180
Publisher
Springer
Published in
Paris
Pages
678–698
Publication identifier
10.1007/s10955-020-02496-1
Metadata
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Author(s)
De Roeck, Wojciech
Katholieke Universiteit Leuven
Huveneers, François
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
Anderson Localization; Disordered systems; subdiffusion; Griffiths Regions

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