Star graphs and Seba billiards

G Berkolaiko; EB Bogomolny; JP Keating

Star graphs and Seba billiards

G Berkolaiko, EB Bogomolny, JP Keating

Research output: Contribution to journal › Article (Academic Journal) › peer-review

54 Citations (Scopus)

Abstract

We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding result for certain Seba billiards in the semiclassical limit. The reasons for this are discussed. The formula we derive is also shown to be equivalent to a series expansion for the form factor-the Fourier transform of the two-point correlation function-previously calculated using periodic orbit theory.

Translated title of the contribution	Star graphs and Seba billiards
Original language	English
Pages (from-to)	335 - 350
Journal	Journal of Physics A: Mathematical and General
Volume	34 (3)
Publication status	Published - 26 Jan 2001

Bibliographical note

Publisher: IOP Publishing Ltd
Other identifier: IDS number 400FR

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title = "Star graphs and Seba billiards",

abstract = "We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding result for certain Seba billiards in the semiclassical limit. The reasons for this are discussed. The formula we derive is also shown to be equivalent to a series expansion for the form factor-the Fourier transform of the two-point correlation function-previously calculated using periodic orbit theory.",

author = "G Berkolaiko and EB Bogomolny and JP Keating",

note = "Publisher: IOP Publishing Ltd Other identifier: IDS number 400FR",

year = "2001",

month = jan,

day = "26",

language = "English",

volume = "34 (3)",

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journal = "Journal of Physics A: Mathematical and General",

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publisher = "IOP Publishing",

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TY - JOUR

T1 - Star graphs and Seba billiards

AU - Berkolaiko, G

AU - Bogomolny, EB

AU - Keating, JP

N1 - Publisher: IOP Publishing Ltd Other identifier: IDS number 400FR

PY - 2001/1/26

Y1 - 2001/1/26

N2 - We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding result for certain Seba billiards in the semiclassical limit. The reasons for this are discussed. The formula we derive is also shown to be equivalent to a series expansion for the form factor-the Fourier transform of the two-point correlation function-previously calculated using periodic orbit theory.

AB - We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding result for certain Seba billiards in the semiclassical limit. The reasons for this are discussed. The formula we derive is also shown to be equivalent to a series expansion for the form factor-the Fourier transform of the two-point correlation function-previously calculated using periodic orbit theory.

M3 - Article (Academic Journal)

VL - 34 (3)

SP - 335

EP - 350

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

ER -