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Localization in physical systems described by discrete nonlinear Schrodinger-type equations.
A R Bishop1, G Kalosakas, K O Rasmussen
1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
This study explores localized modes in nonlinear systems, detailing their behavior in electronic materials, Bose-Einstein condensates, and optical waveguides. Findings reveal diverse applications and transitions of these localized modes.
Area of Science:
- Physics
- Nonlinear Dynamics
- Condensed Matter Physics
Background:
- Localized modes are crucial in nonlinear systems.
- The discrete nonlinear Schrödinger equation serves as a key model.
- Understanding these modes is vital for various physical phenomena.
Purpose of the Study:
- To present explicit results on localized modes in three distinct physical systems.
- To investigate applications ranging from Raman scattering to Bose-Einstein condensates and optical waveguides.
- To analyze the behavior of localized modes in different physical contexts.
Main Methods:
- Utilizing the discrete nonlinear Schrödinger equation as a foundational model.
- Applying theoretical analysis to diverse physical systems.
- Examining Raman scattering spectra, Bose-Einstein condensate delocalization, and optical waveguide instabilities.
Main Results:
- Demonstrated intrinsic localized vibrational modes in complex electronic materials.
- Observed abrupt and irreversible delocalizing transitions in trapped Bose-Einstein condensates.
- Characterized instabilities of localized modes in coupled optical waveguide arrays.
Conclusions:
- Localized modes exhibit diverse behaviors and applications across different physical systems.
- The discrete nonlinear Schrödinger equation provides a versatile framework for studying these phenomena.
- Results offer insights into material science, quantum physics, and photonics.