Standard and fractional Ornstein-Uhlenbeck process on a growing domain

Area of Science:

• Statistical Physics
• Non-equilibrium Systems
• Complex Systems

Background:

• Studying particle diffusion in harmonic potentials is crucial for understanding confined systems.
• The Ornstein-Uhlenbeck process models Brownian motion with a restoring force.
• Subdiffusive processes, like continuous-time random walks (CTRWs), exhibit anomalous diffusion behaviors.

Purpose of the Study:

• To investigate the impact of uniformly growing or contracting domains on normal diffusive and subdiffusive processes.
• To analyze the interplay between domain dynamics, harmonic potential, and particle diffusion.
• To compare the behavior of Brownian diffusion and subdiffusive CTRWs under these conditions.

Main Methods:

• Utilized a fractional Fokker-Planck equation applicable to both Brownian diffusion and subdiffusive CTRWs.
• Employed analytical derivations and numerical simulations to study particle distributions.
• Validated findings through random walk simulations.

Main Results:

• Particle random walk properties exhibit high sensitivity to the domain growth rate.
• Growing/contracting domains can break the confinement typically observed in static harmonic potentials.
• Subdiffusive CTRWs show distinct breakdown behaviors compared to Brownian diffusion, with power-law growth affecting CTRWs more readily than exponential growth affects Brownian motion.

Conclusions:

• The dynamics of diffusing particles are strongly influenced by the rate and nature of domain expansion or contraction.
• Differences in diffusion mechanisms (Brownian vs. subdiffusive) lead to qualitatively different responses to domain dynamics.
• The study reveals counterintuitive effects, highlighting the complexity of non-equilibrium diffusion in dynamic environments.