On the skeleton method and an application to a quantum scissor

Horia Cornean; P. Duclos; B. Ricaud

On the skeleton method and an application to a quantum scissor

Horia Cornean, P. Duclos, B. Ricaud

Institut for Matematiske Fag

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

Abstract

In the spectral analysis of few one dimensional quantum particles interacting through delta potentials it is well known that one can recast the problem into the spectral analysis of an integral operator (the skeleton) living on the submanifold which supports the delta interactions. We shall present several tools which allow direct insight into the spectral structure of this skeleton. We shall illustrate the method on a model of a two dimensional quantum particle interacting with two infinitely long straight wires which cross one anonter at angle \theta: the quantum scissor.

Originalsprog	Engelsk
Titel	Proceedings of Symposia in Pure Mathematics : Analysis on Graphs and Its Applications
Redaktører	Pavel Exner, Jonathan P. Keating, Peter Kuchment, Toshikazu Sunada, Alexander Teplyaev
Antal sider	16
Vol/bind	77
Forlag	American Mathematical Society
Publikationsdato	2008
Sider	657-672
ISBN (Trykt)	9780821844717
Status	Udgivet - 2008
Begivenhed	Symposia in Pure Mathematics - Analysis on Graphs and Its Applications. (An Isaac Newton Institute Programme) - Cambridge, Storbritannien Varighed: 8 jan. 2007 → 29 jun. 2007

Konference

Konference	Symposia in Pure Mathematics - Analysis on Graphs and Its Applications. (An Isaac Newton Institute Programme)
Land/Område	Storbritannien
By	Cambridge
Periode	08/01/2007 → 29/06/2007

AUB Link

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Citationsformater

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title = "On the skeleton method and an application to a quantum scissor",

abstract = "In the spectral analysis of few one dimensional quantum particles interacting through delta potentials it is well known that one can recast the problem into the spectral analysis of an integral operator (the skeleton) living on the submanifold which supports the delta interactions. We shall present several tools which allow direct insight into the spectral structure of this skeleton. We shall illustrate the method on a model of a two dimensional quantum particle interacting with two infinitely long straight wires which cross one anonter at angle \theta: the quantum scissor.",

author = "Horia Cornean and P. Duclos and B. Ricaud",

year = "2008",

language = "English",

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editor = "Pavel Exner and Keating, {Jonathan P.} and Peter Kuchment and Toshikazu Sunada and Alexander Teplyaev",

booktitle = "Proceedings of Symposia in Pure Mathematics",

publisher = "American Mathematical Society",

address = "United States",

note = "Symposia in Pure Mathematics - Analysis on Graphs and Its Applications. (An Isaac Newton Institute Programme) ; Conference date: 08-01-2007 Through 29-06-2007",

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Cornean, H, Duclos, P & Ricaud, B 2008, On the skeleton method and an application to a quantum scissor. i P Exner, JP Keating, P Kuchment, T Sunada & A Teplyaev (red), Proceedings of Symposia in Pure Mathematics: Analysis on Graphs and Its Applications. bind 77, American Mathematical Society, s. 657-672, Symposia in Pure Mathematics - Analysis on Graphs and Its Applications. (An Isaac Newton Institute Programme), Cambridge, Storbritannien, 08/01/2007.

On the skeleton method and an application to a quantum scissor. / Cornean, Horia; Duclos, P.; Ricaud, B.
Proceedings of Symposia in Pure Mathematics: Analysis on Graphs and Its Applications. red. / Pavel Exner; Jonathan P. Keating; Peter Kuchment; Toshikazu Sunada; Alexander Teplyaev. Bind 77 American Mathematical Society, 2008. s. 657-672.

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

TY - GEN

T1 - On the skeleton method and an application to a quantum scissor

AU - Cornean, Horia

AU - Duclos, P.

AU - Ricaud, B.

PY - 2008

Y1 - 2008

N2 - In the spectral analysis of few one dimensional quantum particles interacting through delta potentials it is well known that one can recast the problem into the spectral analysis of an integral operator (the skeleton) living on the submanifold which supports the delta interactions. We shall present several tools which allow direct insight into the spectral structure of this skeleton. We shall illustrate the method on a model of a two dimensional quantum particle interacting with two infinitely long straight wires which cross one anonter at angle \theta: the quantum scissor.

AB - In the spectral analysis of few one dimensional quantum particles interacting through delta potentials it is well known that one can recast the problem into the spectral analysis of an integral operator (the skeleton) living on the submanifold which supports the delta interactions. We shall present several tools which allow direct insight into the spectral structure of this skeleton. We shall illustrate the method on a model of a two dimensional quantum particle interacting with two infinitely long straight wires which cross one anonter at angle \theta: the quantum scissor.

M3 - Article in proceeding

SN - 9780821844717

VL - 77

SP - 657

EP - 672

BT - Proceedings of Symposia in Pure Mathematics

A2 - Exner, Pavel

A2 - Keating, Jonathan P.

A2 - Kuchment, Peter

A2 - Sunada, Toshikazu

A2 - Teplyaev, Alexander

PB - American Mathematical Society

T2 - Symposia in Pure Mathematics - Analysis on Graphs and Its Applications. (An Isaac Newton Institute Programme)

Y2 - 8 January 2007 through 29 June 2007

ER -

On the skeleton method and an application to a quantum scissor

Abstract

Konference

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Citationsformater