Periodic orbits in Fermi-Pasta-Ulam-Tsingou systems

Area of Science:

• Nonlinear dynamics
• Statistical mechanics
• Condensed matter physics

Background:

• The Fermi-Pasta-Ulam-Tsingou (FPUT) paradox describes nonergodic behavior in nonlinear oscillator chains before thermalization.
• Systems initially resemble the Toda model, relaxing to metastable states.
• Longer timescales reveal resonances driving FPUT systems toward equilibrium.

Purpose of the Study:

• To review existing knowledge on metastable states, solitons, and q-breathers in FPUT systems.
• To investigate the role of q-breather orbit bifurcations in the thermalization process.
• To explore the formation of composite periodic orbits.

Main Methods:

• Analysis of FPUT system dynamics and phase space trajectories.
• Examination of q-breather spectra and frequency resonances (mΩ1=Ωk).
• Identification of composite periodic orbits arising from bifurcations.

Main Results:

• Q-breather orbit bifurcations are driven by frequency resonances.
• Resonances manifest as peaks in the breather energy spectrum.
• New composite periodic orbits, nonlinear combinations of q-breathers, emerge after bifurcations.
• These resonances are absent in integrable systems due to conservation laws.

Conclusions:

• Q-breathers and their associated resonances play a crucial role in the thermalization pathway of FPUT systems.
• Orbit bifurcations lead to complex dynamics, including composite periodic orbits.
• The presence of resonances and composite orbits distinguishes non-integrable FPUT systems from integrable ones.