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Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets
Sen Mu1, Jiangbin Gong1,2,3,4, Gabriel Lemarié1,2,3,5
1Department of Physics, National University of Singapore, Singapore 117542, Singapore.
Physical Review Letters
|February 9, 2024
Summary
Researchers found Kardar-Parisi-Zhang (KPZ) universality in 2D Anderson localized wave packets. This reveals algebraic scaling, Tracy-Widom distributions, and stretched exponential corrections to localization.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Wave phenomena
Background:
- Anderson localization describes wave packet confinement in disordered media.
- The Kardar-Parisi-Zhang (KPZ) equation models dynamic interfaces and stochastic processes.
- Wave packet dynamics in disordered systems are crucial for understanding transport phenomena.
Purpose of the Study:
- To identify Kardar-Parisi-Zhang (KPZ) universality class features in 2D Anderson localized wave packets.
- To analyze the scaling behavior and probability distributions of wave density logarithm fluctuations.
- To investigate the connection between KPZ physics and the localization properties of wave packets.
Main Methods:
- Numerical analysis of wave packet propagation in a 2D disordered potential.
- Characterization of wave density logarithm fluctuations using scaling analysis.
- Application of the directed polymer model to understand KPZ physics in this context.
Main Results:
- Fluctuations exhibit algebraic scaling with distance (exponent 1/3).
- Fluctuations follow a Tracy-Widom probability distribution.
- Transverse fluctuations of the dominant path show a roughness exponent of 2/3.
- Anderson localized wave packets display stretched exponential corrections to exponential localization.
Conclusions:
- The study confirms the presence of KPZ universality in 2D Anderson localized wave packets.
- This connection provides new insights into the nature of localization and wave propagation in disordered systems.
- The findings bridge the gap between disordered systems and stochastic growth models.
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