Rigorous Bound on the Integrated Density of States of a Three-Dimensional Random Alloy | Zendy

A. B. Harris | Zendy

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Rigorous Bound on the Integrated Density of States of a Three-Dimensional Random Alloy

Author(s) -

A. B. Harris

Publication year - 1973

Publication title -

physical review. b, solid state

Language(s) - English

Resource type - Journals

ISSN - 0556-2805

DOI - 10.1103/physrevb.8.3661

Subject(s) - physics , hamiltonian (control theory) , combinatorics , energy (signal processing) , lattice (music) , mathematical physics , condensed matter physics , quantum mechanics , mathematics , mathematical optimization , acoustics

We study the lattice model of a random alloy whose Hamiltonian is H=−Σr,δt a†rar+δ + Σrεra†rar, where δ are nearest-neighbor vectors and εr is a random site-diagonal energy uniformly distributed over the interval 0≤εr≤W. We prove that the integrated density of states per site N−1Z(E) satisfies the inequality, N−1Z(E)≤C1e−C2/E, where C1 and C2 are constants.

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