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Step Density Profiles in Localized Chains

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1610.06076.pdf (303.1Kb)
Date
2017
Indexation documentaire
Sciences connexes (physique, astrophysique)
Subject
Nonequilibrium; Transport; Localization
Nom de la revue
Journal of Statistical Physics
Volume
167
Numéro
5
Date de publication
2017
Pages article
1143–1163
Nom de l'éditeur
Kluwer Academic Publishers etc.
DOI
http://dx.doi.org/10.1007/s10955-017-1769-z
URI
https://basepub.dauphine.fr/handle/123456789/17102
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Auteur
Huveneers, François
De Roeck, Wojciech
Dhar, A.
Schütz, M.
Type
Article accepté pour publication ou publié
Résumé en anglais
We consider two types of strongly disordered one-dimensional Hamiltonian systems coupled to baths (energy or particle reservoirs) at the boundaries: strongly disordered quantum spin chains and disordered classical harmonic oscillators. These systems are believed to exhibit localization, implying in particular that the conductivity decays exponentially in the chain length L. We ask however for the profile of the (very slowly) transported quantity in the steady state. We find that this profile is a step-function, jumping in the middle of the chain from the value set by the left bath to the value set by the right bath. This is confirmed by numerics on a disordered quantum spin chain of 9 spins and on much longer chains of harmonic oscillators. From theoretical arguments, we find that the width of the step grows not faster than L−−√, and we confirm this numerically for harmonic oscillators. In this case, we also observe a drastic breakdown of local equilibrium at the step, resulting in a heavily oscillating temperature profile.

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