Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap

Area of Science:

• Physics
• Nonlinear Dynamics
• Quantum Mechanics

Background:

• The nonlinear Schrödinger (NLS) equation describes various physical phenomena.
• Understanding long-term dynamics in NLS systems is crucial for applications.
• Isotropic harmonic oscillator potentials are common in physical systems.

Purpose of the Study:

• To investigate the long-term weakly nonlinear evolution governed by the 2D NLS equation with a harmonic potential.
• To identify and analyze recurrence phenomena and long-lived states within this system.
• To explore potential implications for nonlinear optics and Bose-Einstein condensates.

Main Methods:

• Focusing on the weakly nonlinear regime.
• Utilizing a resonant approximation to capture dynamics dominated by mode interactions.
• Analyzing Fermi-Pasta-Ulam-like recurrence phenomena and two-mode states.

Main Results:

• Resonant interactions between quartets of linear normal modes dominate the dynamics.
• Identified Fermi-Pasta-Ulam-like recurrence phenomena.
• Discovered time-independent mode amplitude spectra in two-mode states, leading to long-lived breathers.

Conclusions:

• The resonant approximation accurately captures key dynamics of the 2D NLS equation with harmonic potentials.
• The identified phenomena suggest mechanisms for stable, localized energy states (breathers).
• Findings have potential applications in nonlinear optics and matter-wave dynamics in Bose-Einstein condensates.