Maximal- and minimal-height distributions of fluctuating interfaces

Area of Science:

• Surface growth phenomena
• Nonlinear dynamics
• Statistical physics

Background:

• Interface growth models like Kardar-Parisi-Zhang (KPZ) and Villain-Lai-Das Sarma (VLDS) are crucial in understanding various physical systems.
• Understanding the statistical properties of interface heights is key to characterizing growth dynamics.

Purpose of the Study:

• To investigate and differentiate the maximal- and minimal-height distributions (MAHD, MIHD) for 2D interfaces governed by KPZ and VLDS equations.
• To explore the universality and dependence of these distributions on the nonlinear terms and model parameters.

Main Methods:

• Analytical investigation of nonlinear growth equations (KPZ and VLDS).
• Numerical simulations of lattice models belonging to KPZ and VLDS universality classes.
• Introduction and analysis of a simple, exactly solvable deposition-erosion model.

Main Results:

• Maximal- and minimal-height distributions are distinct for KPZ and VLDS classes.
• Two universal curves describe MAHD and MIHD, dependent on the sign of the nonlinear term.
• The asymmetry of local height distributions explains the difference between MAHD and MIHD.
• Average extremal heights exhibit scaling behavior consistent with average roughness.
• Generalized Gumbel distributions do not adequately fit the observed MAHD and MIHD.

Conclusions:

• The study reveals fundamental differences in height distributions for distinct interface growth models.
• The findings highlight the role of nonlinear dynamics and local height asymmetry in shaping interface morphology.
• The proposed deposition-erosion model serves as a valuable tool for illustrating these growth characteristics.