First-passage-time distribution in a moving parabolic potential with spatial roughness.

Area of Science:

• Statistical Physics
• Nonlinear Dynamics
• Computational Physics

Background:

• First-passage-time distribution (FPTD) is crucial in various physical processes.
• Rough potentials introduce complexities not fully captured by standard theories.
• Existing methods like Kramers theory have limitations in certain parameter regimes.

Purpose of the Study:

• To investigate FPTD in time-dependent parabolic potentials with roughness.
• To compare the efficacy of Kramers theory and a novel integral equation-based method.
• To develop an improved analytical approach for FPTD calculations.

Main Methods:

• Spatially averaging rough potentials to derive effective smooth potentials and diffusion coefficients.
• Applying Kramers theory to obtain Kramers approximations (KAs) for FPTD.
• Developing and applying a probability asymptotic approximation (PAA) using an integral equation and transient PDF.

Main Results:

• Kramers approximations (KA) are accurate for high barriers and small forces but limited otherwise.
• The proposed probability asymptotic approximation (PAA) accurately predicts FPTD even for large external forces and low barriers.
• PAA shows good agreement with numerical simulations for rough potentials and low barriers.
• PAA extends the applicability to ultrafast varying potentials and short exiting times.

Conclusions:

• KA and PAA are complementary methods for determining FPTD across various barrier heights and external forces.
• PAA provides a significant analytical extension to KA, particularly for challenging parameter ranges.
• PAA is effective for mean first-passage time (MFPT) calculations across almost all external forces, unlike KA.