On the density of states of periodic media in the large coupling limit

Leonid Friedlander

doi:10.1081/PDE-120002790

On the density of states of periodic media in the large coupling limit

Leonid Friedlander

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

Let Ω₀ be a domain in the cube (0, 2π)ⁿ, and let χ_τ(x) be a function that equals 1 inside Ω₀, equals τ in (0, 2π)ⁿ/Ω₀, and that is extended periodically to Rⁿ. It is known that, in the limit τ → ∞, the spectrum of the operator - ∇χ_τ(x)∇ exhibits the band-gap structure. We establish the asymptotic behavior of the density of states function in the bands.

Original language	English (US)
Pages (from-to)	355-380
Number of pages	26
Journal	Communications in Partial Differential Equations
Volume	27
Issue number	1-2
DOIs	https://doi.org/10.1081/PDE-120002790
State	Published - 2002

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1081/PDE-120002790

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abstract = "Let Ω0 be a domain in the cube (0, 2π)n, and let χτ(x) be a function that equals 1 inside Ω0, equals τ in (0, 2π)n/Ω0, and that is extended periodically to Rn. It is known that, in the limit τ → ∞, the spectrum of the operator - ∇χτ(x)∇ exhibits the band-gap structure. We establish the asymptotic behavior of the density of states function in the bands.",

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AB - Let Ω0 be a domain in the cube (0, 2π)n, and let χτ(x) be a function that equals 1 inside Ω0, equals τ in (0, 2π)n/Ω0, and that is extended periodically to Rn. It is known that, in the limit τ → ∞, the spectrum of the operator - ∇χτ(x)∇ exhibits the band-gap structure. We establish the asymptotic behavior of the density of states function in the bands.

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ER -

On the density of states of periodic media in the large coupling limit

Abstract

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