2003/06/12 by T. L. Einstein · 2 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1007/s00023-003-0964-4
published as Ann. Henri Poincare' 4, Suppl. 2, S811-S824 (2003) · 7 pages, 2 figures; based on talk presented at TH-2002, UNESCO, Paris, July 2002; to be published in Ann. Henri Poincare'
arxiv created 2003/06/12 · openalex publication_date 2003/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation <ℓ> on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped onto the world lines of spinless fermions in 1+1D using the Calogero-Sutherland model. The strength of the ("instantaneous", inverse-square) elastic repulsion between steps, in dimensionless form, is β(β-2)/4. The distribution of spacings s< ℓ> between neighboring steps (analogous to the normalized spacings of energy levels) is well described by a \it "generalized" Wigner surmise: pβ(0,s) ≈ a sβexp(-b s2). The value of β is taken to best fit the data; typically 2 ≤ β≤ 10. The procedure is superior to conventional Gaussian and mean-field approaches, and progress is being made on formal justification. Furthermore, the theoretically simpler step-step distribution function can be measured and analyzed based on exact results. Formal results and applications to experiments on metals and semiconductors are summarized, along with open questions. (conference abstract)