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Transport in weak dynamic disorder: a unified theory
1Laboratory of Mathematics and Applied Mathematics and School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
Summary
Dynamic disorder in quantum systems facilitates particle transport, potentially leading to novel behaviors like Lévy flights. This study resolves long-standing debates on transport persistence, impacting light and matter wave dynamics.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Statistical mechanics
Background:
- Static disorder causes Anderson localization (AL) in quantum particles.
- Dynamic disorder is known to destroy AL and enhance transport.
Purpose of the Study:
- Investigate quantum particle transport under weak dynamic disorder.
- Analyze the long-term behavior of transport in disordered systems.
Main Methods:
- Utilized Wigner representation to derive a linear Boltzmann equation.
- Analyzed transport in the weak dynamic disorder limit.
Main Results:
- Obtained existing and novel transport behaviors, including Lévy flights in momentum space.
- Demonstrated that diffusive transport approximation is non-physical for dimensions > 1.
- Argued for the persistence of non-diffusive transport in the long-time limit.
Conclusions:
- Resolved the debate on whether diffusive or non-diffusive transport prevails.
- Results have significant implications for light hypertransport, matter waves in disordered media, and polymer physics.
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