Journal of Statistical Physics

, Volume 167, Issue 5, pp 1143–1163 | Cite as

Step Density Profiles in Localized Chains

  • Wojciech De Roeck
  • Abhishek Dhar
  • François Huveneers
  • Marius Schütz
Article
  • 130 Downloads

Abstract

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 \(\sqrt{L}\), 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.

Keywords

Nonequilibrium Transport Localization 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Wojciech De Roeck
    • 1
  • Abhishek Dhar
    • 2
  • François Huveneers
    • 3
  • Marius Schütz
    • 1
  1. 1.Instituut voor Theoretische FysicaKU LeuvenLouvainBelgium
  2. 2.International Centre for Theoretical SciencesTIFRBengaluruIndia
  3. 3.PSL Research University, CNRS, CEREMADEUniversité Paris-DauphineParisFrance

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