Survival of interacting diffusing particles inside a domain with absorbing boundary.

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Mathematical Physics

Background:

• Diffusive particle systems in confined domains are fundamental in statistical mechanics.
• Particle absorption at boundaries introduces non-equilibrium dynamics.
• Understanding absorption probabilities is crucial for modeling transport phenomena.

Purpose of the Study:

• To evaluate the probability of zero particle absorption in a diffusive gas within a d-dimensional domain over a long time T.
• To determine the behavior of this probability for interacting diffusive gases.
• To analyze the underlying density profiles and their implications.

Main Methods:

• Macroscopic fluctuation theory (MFT) was employed to analyze the system.
• The study focused on the probability P of no particle absorption.
• Analytical and numerical methods were used to derive results, particularly for the simple symmetric exclusion process (SSEP).

Main Results:

• The probability P decays exponentially with time T for a broad class of interacting diffusive gases.
• For d=1, the stationary gas density profile and P were found analytically.
• In higher dimensions, for the SSEP, -lnP scales as D_{0}TL^{d-2}s(n_{0}), where D_{0} is diffusivity, L is system size, and s(n_{0}) is a calculated rescaled action.

Conclusions:

• The probability of zero absorption events in diffusive particle systems exhibits exponential decay with time.
• The study provides a framework for understanding non-equilibrium boundary phenomena in statistical physics.
• The derived scaling law and rescaled action offer quantitative insights into particle transport and absorption in confined systems.