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Step Density Profiles in Localized Chains

Huveneers, François; De Roeck, Wojciech; Dhar, Abhishek; Schütz, M. (2017), Step Density Profiles in Localized Chains, Journal of Statistical Physics, 167, 5, p. 1143–1163. 10.1007/s10955-017-1769-z

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1610.06076.pdf (303.1Kb)
Type
Article accepté pour publication ou publié
Date
2017
Journal name
Journal of Statistical Physics
Volume
167
Number
5
Publisher
Kluwer Academic Publishers etc.
Pages
1143–1163
Publication identifier
10.1007/s10955-017-1769-z
Metadata
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Author(s)
Huveneers, François

De Roeck, Wojciech
Instituut voor Theoretische Fysica [ITF]
Dhar, Abhishek
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Schütz, M.
Instituut voor Theoretische Fysica [ITF]
Abstract (EN)
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.
Subjects / Keywords
Nonequilibrium; Transport; Localization

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