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

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.