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Einstein Relation for a Driven Disordered Quantum Chain in the Subdiffusive Regime.

M Mierzejewski1, P Prelovšek2,3, J Bonča2,3

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Quantum particles exhibit subdiffusive propagation on disordered chains when coupled to hard-core bosons. A generalized Einstein relation (GER) connects this spread to a time-dependent drift velocity under an electric field.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Disordered systems

Background:

  • Quantum particle transport in disordered systems is crucial for understanding many physical phenomena.
  • Subdiffusion is a key transport regime observed in various complex systems.
  • The interplay between quantum particles and bosons in disordered environments presents unique theoretical challenges.

Purpose of the Study:

  • To investigate the subdiffusive propagation of a quantum particle coupled to itinerant hard-core bosons on a disordered chain.
  • To establish a generalized Einstein relation (GER) for this system.
  • To explore the validity of GER beyond linear response and under strong driving fields.

Main Methods:

  • Theoretical establishment of a generalized Einstein relation (GER).
  • Analysis of subdiffusive spread and time-dependent drift velocity.
  • Numerical calculations using full quantum evolution.
  • Comparison with simpler rate equations for boson-assisted transitions.

Main Results:

  • A quantum particle coupled to hard-core bosons exhibits subdiffusive propagation on a disordered chain.
  • A novel GER was established, linking subdiffusion to an unusual time-dependent drift velocity induced by an electric field.
  • The GER remains valid beyond the linear response regime, holding true even under strong driving fields.
  • Nonlinear field effects can lead to Stark-like localization.

Conclusions:

  • The generalized Einstein relation provides a robust framework for understanding subdiffusive transport in this quantum system.
  • The findings extend the applicability of Einstein relations to nonlinear regimes in disordered quantum systems.
  • The study offers insights into boson-assisted transport mechanisms and Anderson localization phenomena.