Particle dynamics in a symmetrically driven underdamped inhomogeneous periodic potential system.

Area of Science:

• Statistical Mechanics
• Nonlinear Dynamics
• Condensed Matter Physics

Background:

• Investigating particle behavior in periodic potentials is crucial for understanding complex systems.
• Spatially inhomogeneous friction can lead to unique dynamical phenomena.
• The interplay between periodic potentials, driving forces, and friction is not fully understood.

Purpose of the Study:

• To numerically solve the underdamped Langevin equation for a particle in a sinusoidal potential.
• To analyze particle trajectories under a temporally sinusoidal force with spatially periodic friction.
• To investigate the emergence of stochastic resonance and ratchet effects in this system.

Main Methods:

• Numerical solution of the underdamped Langevin equation.
• Simulation of particle trajectories with varying system parameters (mean friction, driving field period).
• Analysis of trajectory amplitudes and phase lags relative to the applied field.

Main Results:

• Two distinct periodic trajectories (large amplitude/lag, small amplitude/lag) emerge at low noise.
• The system effectively behaves as a bistable system due to the periodic potential and friction.
• Stochastic resonance and ratchet effects are observed simultaneously, explained by the two trajectory states.

Conclusions:

• Spatially inhomogeneous friction in a periodic potential can induce bistable dynamics.
• The observed stochastic resonance and ratchet effects are directly linked to the distinct trajectory types.
• This work provides a unified framework for understanding these phenomena in driven dissipative systems.