Self-propulsion and crossing statistics under random initial conditions

Area of Science:

• Physics
• Statistical Mechanics
• Soft Matter Physics

Background:

• Self-propelled particles exhibit complex behaviors, including barrier crossing.
• Rayleigh friction influences particle dynamics and energy dissipation.
• Wave-particle entities can interact with obstacles and overcome potential barriers.

Purpose of the Study:

• To investigate energy barrier crossing in self-propelled particles with Rayleigh friction.
• To explain the phenomenon of macroscopic tunneling observed in wave-particle systems.
• To rationalize experimental findings on droplet-obstacle interactions.

Main Methods:

• Analysis of particle dynamics under external force fields.
• Identification of saddle point transitions in velocity-flow phase space.
• Development of a probability distribution for barrier crossing based on initial conditions.

Main Results:

• A sharp transition in external force dramatically increases particle amplitude.
• Self-propulsion is sufficient to overcome high-energy barriers.
• A derived probability distribution for barrier crossing matches experimental data, resembling a Boltzmann exponential law.

Conclusions:

• The study reveals a mechanism for macroscopic tunneling in self-propelled systems.
• The findings provide a theoretical framework for understanding wave-particle entity interactions with obstacles.
• The probability of barrier crossing is analogous to that in Hamiltonian systems.