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

Department of Mathematical Sciences

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › 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.

Original language	English
Title of host publication	Proceedings of Symposia in Pure Mathematics : Analysis on Graphs and Its Applications
Editors	Pavel Exner, Jonathan P. Keating, Peter Kuchment, Toshikazu Sunada, Alexander Teplyaev
Number of pages	16
Volume	77
Publisher	American Mathematical Society
Publication date	2008
Pages	657-672
ISBN (Print)	9780821844717
Publication status	Published - 2008
Event	Symposia in Pure Mathematics - Analysis on Graphs and Its Applications. (An Isaac Newton Institute Programme) - Cambridge, United Kingdom Duration: 8 Jan 2007 → 29 Jun 2007

Conference

Conference	Symposia in Pure Mathematics - Analysis on Graphs and Its Applications. (An Isaac Newton Institute Programme)
Country/Territory	United Kingdom
City	Cambridge
Period	08/01/2007 → 29/06/2007

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@inproceedings{21e4af607d6f11dd8b88000ea68e967b,

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",

isbn = "9780821844717",

volume = "77",

pages = "657--672",

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",

}

Cornean, H, Duclos, P & Ricaud, B 2008, On the skeleton method and an application to a quantum scissor. in P Exner, JP Keating, P Kuchment, T Sunada & A Teplyaev (eds), Proceedings of Symposia in Pure Mathematics: Analysis on Graphs and Its Applications. vol. 77, American Mathematical Society, pp. 657-672, Symposia in Pure Mathematics - Analysis on Graphs and Its Applications. (An Isaac Newton Institute Programme), Cambridge, United Kingdom, 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. ed. / Pavel Exner; Jonathan P. Keating; Peter Kuchment; Toshikazu Sunada; Alexander Teplyaev. Vol. 77 American Mathematical Society, 2008. p. 657-672.

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › 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

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