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Multifractality of instantaneous normal modes at mobility edges.
1Institute of Physics, National Chiao-Tung University, HsinChu, Taiwan 300, Republic of China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
This study reveals universal multifractality in fluid dynamics at the localization-delocalization transition. Instantaneous normal modes (INMs) exhibit multifractal characteristics, matching predictions from the Anderson model.
Area of Science:
- Physics
- Complex Systems
- Fluid Dynamics
Background:
- Previous work identified mobility edges (MEs) in the instantaneous normal mode (INM) spectrum of simple fluids.
- Understanding the behavior of INMs at these critical points is crucial for characterizing localization-delocalization transitions.
Purpose of the Study:
- To investigate the multifractal properties of INMs at the mobility edges of a simple fluid.
- To provide numerical evidence for universal multifractality at the localization-delocalization transition.
Main Methods:
- Multifractal analysis using box-size and system-size scalings.
- Calculation of mass exponents and singularity spectrum for INMs.
- Examination of probability density and spatial correlation functions of squared vibrational amplitudes.
Main Results:
- INM eigenvectors at mobility edges demonstrate a multifractal nature.
- Generalized fractal dimensions and singularity spectrum were consistent across different MEs.
- The singularity spectrum of multifractal INMs closely matches that of the Anderson model at critical disorder.
Conclusions:
- The study provides strong numerical evidence for universal multifractality at the localization-delocalization transition in fluids.
- The findings suggest a deep connection between the multifractal properties of INMs and the Anderson model.
- Further analysis explored relationships between probability density, spatial correlation, and multifractal exponents.
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