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Statistical mechanics of a discrete nonlinear system
Rasmussen1, Cretegny, Kevrekidis
1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Physical Review Letters
|October 6, 2000
Summary
Statistical mechanics reveals a phase transition in the discrete nonlinear Schrödinger equation at infinite temperature. This transition creates localized breather excitations, linking statistical mechanics and nonlinear dynamics.
Area of Science:
- Statistical mechanics
- Nonlinear dynamics
- Quantum physics
Background:
- The discrete nonlinear Schrödinger equation (DNLS) is a fundamental model in nonlinear physics.
- Understanding its statistical mechanics is crucial for describing systems with localized energy.
- Previous studies have explored its dynamics but lacked a comprehensive statistical mechanical framework.
Purpose of the Study:
- To investigate the statistical mechanics of the DNLS equation.
- To identify and characterize phase transitions within the DNLS system.
- To explore the interplay between statistical mechanics and nonlinear dynamics.
Main Methods:
- Analytical techniques to establish equilibrium measures.
- Numerical simulations to explore system behavior.
- Analysis of the partition function for discontinuities.
Main Results:
- Standard Gibbsian equilibrium measures are constructed for positive temperatures.
- A phase transition is identified beyond T = infinity, marked by a partition function discontinuity.
- Breatherlike localized excitations emerge as a manifestation of this phase transition.
Conclusions:
- The DNLS equation exhibits a distinct phase transition at infinite temperature.
- This transition is directly linked to the creation of localized, breatherlike structures.
- The study elucidates the connection between statistical mechanics and nonlinear dynamics in the DNLS system.
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