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Published on: May 30, 2014
Nonlinear energy transfer in classical and quantum systems
Leonid Manevitch1, Agnessa Kovaleva
1Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia.
Summary
This study reveals how slowly varying parameters affect energy transfer in coupled nonlinear oscillators. It shows distinct behaviors in quasilinear, moderately nonlinear, and strongly nonlinear systems, offering approximate solutions for nonlinear Landau-Zener tunneling.
Area of Science:
- Nonlinear Dynamics
- Coupled Oscillators
- Energy Transfer
Background:
- Investigating energy transfer in weakly coupled systems with time-varying parameters is crucial for understanding complex dynamics.
- The behavior of nonlinear oscillators under parametric modulation presents significant theoretical and practical challenges.
Purpose of the Study:
- To analyze the effect of slowly-varying parameters on energy transfer in a weakly coupled system of two nonlinear oscillators.
- To establish the connection between slow passage through resonance and nonlinear Landau-Zener (LZ) tunneling.
- To develop approximate analytical solutions for transient processes in nonlinear systems.
Main Methods:
- Modeling a system of two coupled nonlinear oscillators, with one having a slowly time-varying frequency.
- Analyzing the equations governing slow passage through resonance and identifying their equivalence to nonlinear LZ tunneling.
- Distinguishing and characterizing three types of dynamical behavior: quasilinear, moderately nonlinear, and strongly nonlinear.
- Developing and validating explicit approximate solutions through numerical simulations.
Main Results:
- Three distinct dynamical regimes (quasilinear, moderately nonlinear, strongly nonlinear) were identified based on parameter variations.
- Quasilinear systems show gradual energy transfer, while moderately nonlinear systems exhibit abrupt energy localization transitions.
- Strongly nonlinear systems display a transition from energy localization to strong energy exchange between oscillators.
- The study provides approximate solutions for transient processes in moderately and strongly nonlinear systems, validated numerically.
Conclusions:
- The research provides an analytical framework for understanding transient dynamics in weakly coupled nonlinear oscillators with slowly varying parameters.
- The findings offer an approximate method for solving nonlinear Landau-Zener (LZ) tunneling problems with various initial conditions and finite time intervals.
- This work contributes to the fundamental understanding of parametric resonance and energy transfer in nonlinear systems.
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