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Anomalous diffusion of discrete solitons driven by evolving disorder.
Zhi-Yuan Sun1,2, Xin Yu1
1Institute of Fluid Mechanics, Beihang University, Beijing 100191, China.
Physical Review. E
|July 22, 2020
Summary
This study simulates anomalous diffusion using discrete solitons in disordered lattices. Small solitons exhibit Richardson diffusion, while larger ones show transient diffusion, suggesting non-ergodic behavior in soliton transport.
Area of Science:
- Nonlinear physics
- Condensed matter physics
- Statistical mechanics
Background:
- Anomalous diffusion describes particle transport deviating from standard Brownian motion.
- Solitons are self-reinforcing solitary waves exhibiting particle-like properties.
- Disordered systems present complex dynamics due to random imperfections.
Purpose of the Study:
- To investigate anomalous diffusion in discrete solitons within evolving disordered lattices.
- To analyze the impact of soliton size on diffusion characteristics.
- To explore the ergodicity of soliton transport phenomena.
Main Methods:
- Simulation of discrete soliton transport in a lattice model.
- Introduction of evolving disorder to the lattice structure.
- Analysis of ensemble-averaged and time-averaged observables.
Main Results:
- Small solitons display Richardson-type diffusion.
- Larger solitons exhibit transient diffusion under ensemble averaging.
- Time-averaged observables show ballistic scaling for all soliton sizes.
- Soliton size significantly alters the distribution of observables.
Conclusions:
- The study reveals size-dependent anomalous diffusion in discrete solitons.
- Results indicate a violation of ergodicity in soliton diffusive processes.
- Findings contribute to understanding the interplay of discreteness, disorder, and nonlinearity.
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