Dynamical phase transition in the first-passage probability of a Brownian motion

Area of Science:

• Statistical Physics
• Soft Matter Physics
• Physical Chemistry

Background:

• First-passage time distribution (FPTD) is crucial for understanding diffusion processes.
• Particle diffusion is often influenced by initial conditions and target proximity.
• Characterizing transitions in stochastic processes is key to fundamental physics.

Purpose of the Study:

• To investigate the first-passage time distribution (FPTD) for a diffusing particle with a distribution of initial positions.
• To identify and characterize a dynamical phase transition in the averaged FPTD.
• To explore the robustness and universality of this transition across different conditions.

Main Methods:

• Theoretical analysis of FPTD for a 1D freely diffusing particle.
• Averaging FPTD over initial positions drawn from a normalized distribution of finite width.
• Experimental validation using Brownian beads diffusing from an optical trap.

Main Results:

• A sharp dynamical phase transition was observed in the averaged FPTD.
• The transition shifts the FPTD structure from two-peak to single-peak as a parameter b (L/σ) decreases below a critical value (b_c).
• The transition arises from the competition between two timescales: σ²/D and L²/D, where D is the diffusion coefficient.

Conclusions:

• The observed dynamical phase transition is robust and occurs for various initial conditions, dimensions, and diffusion models.
• The findings provide fundamental insights into diffusion dynamics influenced by initial state distributions.
• The study bridges theoretical predictions with experimental observations in a well-controlled system.