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Transport in topologically disordered one-particle, tight-binding models.

Abdellah Khodja¹, Hendrik Niemeyer, Jochen Gemmer

¹Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, D-49069 Osnabrück, Germany. akhodja@uos.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 18, 2013

Summary

This study quantifies transport parameters in disordered quantum systems, finding the Einstein relation holds for metallic regimes. Some models exhibit Boltzmann-like behavior, while others do not, despite delocalization.

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Area of Science:

Quantum physics
Condensed matter physics

Background:

Disordered quantum systems, like Lifshitz models, exhibit complex electronic properties.
Anderson localization affects low-energy states, but metallic regimes feature delocalized states.

Purpose of the Study:

To quantitatively determine transport parameters (conductivity, mean free path) in disordered quantum systems.
To investigate the validity of the Einstein relation in metallic regimes.
To analyze transport behavior in relation to Boltzmann equation predictions.

Main Methods:

Utilizing linear response theory for high temperatures and low fillings.
Employing both numerical and analytical approaches.
Examining spatially completely disordered quantum models.

Main Results:

The Einstein relation was confirmed to hold, linking conductivity and diffusion coefficient.
Transport behavior aligned with Boltzmann equation predictions for some models.
Discrepancies in Boltzmann equation applicability were observed even in delocalized systems.

Conclusions:

The Einstein relation is a robust descriptor for transport in these metallic quantum systems.
Boltzmann equation applicability is model-dependent, even for delocalized states.
Further investigation is needed to understand transport deviations in certain disordered systems.