Edge states for second order elliptic operators in a channel

David Gontier

doi:10.4171/JST/430

Edge states for second order elliptic operators in a channel

David Gontier

Université Paris Dauphine

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

Abstract

We present a general framework to study edge states for second order elliptic operators in a half channel. We associate an integer valued index to some bulk materials, and we prove that, for any junction between two such materials, localized states must appear at the boundary whenever the indices differ.

Original language	English
Pages (from-to)	1155-1202
Number of pages	48
Journal	Journal of Spectral Theory
Volume	12
Issue number	3
DOIs	https://doi.org/10.4171/JST/430
Publication status	Published - 1 Jan 2022
Externally published	Yes

Keywords

charge pumping
Dislocations
Lagrangian planes
Maslov index
spectral flow

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title = "Edge states for second order elliptic operators in a channel",

abstract = "We present a general framework to study edge states for second order elliptic operators in a half channel. We associate an integer valued index to some bulk materials, and we prove that, for any junction between two such materials, localized states must appear at the boundary whenever the indices differ.",

keywords = "charge pumping, Dislocations, Lagrangian planes, Maslov index, spectral flow",

author = "David Gontier",

note = "Publisher Copyright: {\textcopyright} 2023 European Mathematical Society.",

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doi = "10.4171/JST/430",

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AB - We present a general framework to study edge states for second order elliptic operators in a half channel. We associate an integer valued index to some bulk materials, and we prove that, for any junction between two such materials, localized states must appear at the boundary whenever the indices differ.

KW - charge pumping

KW - Dislocations

KW - Lagrangian planes

KW - Maslov index

KW - spectral flow

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JO - Journal of Spectral Theory

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Edge states for second order elliptic operators in a channel

Abstract

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