Mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent...

Area of Science:

• Physics
• Statistical Mechanics
• Surface Science

Background:

• Surface growth processes exhibit complex dynamics.
• Persistent large deviations are crucial for understanding system behavior.
• Edwards-Wilkinson dynamics and Mullins-Herring universality class are key models.

Purpose of the Study:

• To investigate the relationship between spatial and temporal persistent large deviations.
• To validate theoretical predictions for spatial persistent large deviations exponents using numerical simulations.
• To explore deviations in discrete models within the Mullins-Herring universality class.

Main Methods:

• Isomorphic mapping of spatial persistent large deviations probability (Px(x,s)) to temporal persistent large deviations probability (Pt(t,s)).
• Numerical simulations of surface growth processes governed by Edwards-Wilkinson dynamics.
• Numerical simulations of spatial persistence probability for a discrete Mullins-Herring model.

Main Results:

• The infinite family of spatial persistent large deviations exponents (thetax(s)) agrees with theoretical predictions.
• Numerical measurements of thetat(s) for temporal random walks confirm the agreement.
• Discrete Mullins-Herring model simulations show poor agreement with theory, attributed to finite-size corrections.

Conclusions:

• The theoretical framework connecting spatial and temporal persistent large deviations is robust for continuum models.
• Finite-size corrections significantly impact the accuracy of discrete model simulations, hindering asymptotic behavior observation.
• Further research may be needed to refine discrete models or simulation techniques to overcome finite-size limitations.