Controlling activated processes of nonadiabatically, periodically driven dynamical systems: a multiple scale...

Area of Science:

• Non-equilibrium statistical mechanics
• Soft condensed matter physics

Background:

• Understanding escape rates from metastable states is crucial for many physical and chemical processes.
• Brownian motion in periodically driven systems presents complex dynamics, often defying intuitive adiabatic approximations.

Purpose of the Study:

• To determine the escape rate of Brownian particles from a metastable state under periodic external perturbation.
• To investigate the influence of driving frequency (ω) and amplitude on the escape dynamics.

Main Methods:

• Development of a multiple scale perturbation theory ('Kapitza window') to derive an effective time-independent potential.
• Expansion of the potential in orders of 1/ω up to ω(-3).
• Calculation of escape rates using the derived effective potential in the moderate-to-large damping limit.

Main Results:

• The derived time-independent potential accurately models the system's dynamics.
• High driving frequencies (large ω) with moderate-to-large damping impede particle escape.
• High amplitude of the periodic driving force significantly increases the escape rate.

Conclusions:

• The 'Kapitza window' provides a powerful theoretical framework for analyzing driven non-equilibrium systems.
• The interplay between driving frequency, amplitude, and damping critically affects barrier crossing dynamics.
• Theoretical predictions show good agreement with numerical simulations.