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Nonlinear lattice dynamics of Bose-Einstein condensates.
Mason A Porter1, R Carretero-González, P G Kevrekidis
1School of Mathematics and Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. mason@math.gatech.edu
Chaos (Woodbury, N.Y.)
|April 20, 2005
Summary
The Fermi-Pasta-Ulam model inspires research into solitary waves in Bose-Einstein condensates (BECs). These nonlinear dynamics in BECs reveal complex structures like solitons and vortices, crucial for nonlinear science.
Area of Science:
- Nonlinear Hamiltonian systems
- Condensed matter physics
- Soliton dynamics
Background:
- The Fermi-Pasta-Ulam (FPU) model, established 50 years ago, investigates thermalization and nonlinear dynamics in many-body systems.
- Solitary wave dynamics in lattices are crucial for understanding phenomena like energy relaxation and DNA denaturation.
Purpose of the Study:
- To review recent research on Bose-Einstein condensates (BECs) in deep periodic potentials.
- To highlight the relevance of BECs as a platform for studying nonlinear phenomena, inspired by the FPU model.
Main Methods:
- Analysis of solitary-wave dynamics in nonlinear lattice systems.
- Investigating BECs with tunable parameters (dimensionality, nonlinearity, components) and trapping potentials.
- Reducing BEC dynamics to nonlinear chains in specific potentials.
Main Results:
- BECs provide a versatile experimental system for studying solitary waves and their interactions.
- Deep periodic potentials in BECs can be reduced to nonlinear chains.
- These reduced systems exhibit complex nonlinear structures such as solitons, intrinsic localized modes, and vortices.
Conclusions:
- The study of BECs in periodic potentials offers significant insights into nonlinear science, building upon the legacy of the FPU model.
- BECs are a powerful tool for exploring fundamental nonlinear phenomena and their diverse physical applications.