Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D

Area of Science:

• Statistical Mechanics
• Nonlinear Dynamics
• Physical Chemistry

Background:

• Particle trajectories in Langevin dynamics can synchronize when sharing common noise.
• Synchronization is typically studied in equilibrium systems.

Purpose of the Study:

• To present an exact solution for Langevin dynamics in a time-dependent harmonic potential.
• To extend the concept of synchronization to nonequilibrium systems.
• To quantify synchronization levels across different damping regimes.

Main Methods:

• Exact solution for Langevin dynamics in a harmonic, time-dependent potential.
• Calculation of synchronization level (trajectory mismatch).
• Analysis across underdamped, critically damped, and overdamped regimes.
• Asymptotic expansions for limiting cases.

Main Results:

• An exact solution for synchronized Langevin dynamics in time-dependent potentials was derived.
• Synchronization levels were calculated for various damping regimes.
• Asymptotic expansions provided insights into limiting behaviors.
• Comparison with time-independent potentials was performed.

Conclusions:

• Synchronization of Langevin dynamics is possible in time-dependent potentials and extends to nonequilibrium systems.
• The study provides a quantitative measure of synchronization across different physical regimes.
• The findings offer a deeper understanding of particle dynamics and synchronization phenomena.