Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions

Area of Science:

• Physics
• Statistical Mechanics
• Soft Matter Physics

Background:

• Active matter systems exhibit self-propulsion, often involving complex driving mechanisms.
• Spontaneous symmetry breaking in propulsion direction is a key phenomenon in active matter.
• Understanding the dynamics of active objects under stochastic forces is crucial for predicting their behavior.

Purpose of the Study:

• To investigate the propulsion dynamics of passive objects driven by active forces with spontaneous symmetry breaking.
• To analyze the influence of stochastic forces on reversing propulsion direction.
• To model and understand the resulting velocity distributions and spatial statistics.

Main Methods:

• Formal mapping of the system to stochastic motion with a negative friction parameter.
• Calculation of diffusion coefficients using analogies to quantum mechanics (harmonic oscillator with delta-potential).
• Inclusion of constant active forcing magnitude and inertial effects.

Main Results:

• Observed ditched or double-peaked velocity distributions.
• Spatial statistics show outward propagating maxima from initially concentrated arrangements.
• The system exhibits behavior analogous to Coulomb friction but with a negative friction coefficient.

Conclusions:

• Active driving with stochastic direction reversal leads to unique emergent behaviors in passive objects.
• The theoretical framework provides insights into phenomena observed in self-propelled droplets, bacteria, and vibrated hoppers.
• The study highlights the importance of symmetry breaking and stochastic forces in active matter dynamics.