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Beyond the Wigner distribution: Schrödinger equations and terrace width distributions
Howard L Richards1, T L Einstein
1Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA. Howard.Richards@tamu-commerce.edu
Summary
The generalized Wigner distribution accurately models terrace width distributions on vicinal surfaces. A new phenomenological model explains this distribution and allows extraction of step-step interactions from experimental data.
Area of Science:
- Surface science
- Statistical mechanics
- Condensed matter physics
Background:
- The generalized Wigner distribution is a known approximation for terrace width distribution (TWD) on vicinal surfaces.
- This approximation is effective for specific step-step interactions (perpendicular to step direction, inverse square decay).
Purpose of the Study:
- To derive the generalized Wigner distribution from a phenomenological model.
- To explore generalizations for various step-step interactions.
- To enable extraction of step-step interactions from experimental TWDs.
Main Methods:
- Development of a phenomenological model involving direct and pressure-mediated step-step interactions.
- Generalization of the model to accommodate diverse step-step interaction potentials.
- Comparison of model predictions with numerical transfer-matrix and Monte Carlo simulations.
Main Results:
- The generalized Wigner distribution can be derived from a plausible phenomenological model.
- The model shows good agreement with TWDs from numerical simulations for various interactions.
- The phenomenological approach provides a method to extract step-step interaction parameters from experimental TWDs.
Conclusions:
- The phenomenological model provides a theoretical basis for the generalized Wigner distribution in TWD.
- This approach offers a powerful tool for analyzing and understanding step-step interactions on surfaces.
- The method is applicable to experimental data, facilitating the study of surface dynamics.