Manley-Rowe relations for an arbitrary discrete system

I. Y. Dodin; A. I. Zhmoginov; N. J. Fisch

doi:10.1016/j.physleta.2008.08.011

Manley-Rowe relations for an arbitrary discrete system

I. Y. Dodin
, A. I. Zhmoginov
, N. J. Fisch

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

12 Scopus citations

Abstract

Manley-Rowe relations are formulated for a discrete Hamiltonian system with an arbitrary number of resonances. Assuming that the resonances are defined as over(R, ̂) | ω 〉 = 0, where over(R, ̂) is an n × n integer matrix of rank r < n, and | ω 〉 ≡ (ω₁, ..., ω_n)^T is the frequency vector, the projection of the action vector | J 〉 on ker over(R, ̂) is an adiabatic invariant. Hence n - r independent integrals, from where the conventional Manley-Rowe relations for a single resonance follow as a particular case.

Original language	English (US)
Pages (from-to)	6094-6096
Number of pages	3
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	372
Issue number	39
DOIs	https://doi.org/10.1016/j.physleta.2008.08.011
State	Published - Sep 22 2008

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1016/j.physleta.2008.08.011

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title = "Manley-Rowe relations for an arbitrary discrete system",

abstract = "Manley-Rowe relations are formulated for a discrete Hamiltonian system with an arbitrary number of resonances. Assuming that the resonances are defined as over(R,{\^ }) | ω 〉 = 0, where over(R,{\^ }) is an n × n integer matrix of rank r < n, and | ω 〉 ≡ (ω1, ..., ωn)T is the frequency vector, the projection of the action vector | J 〉 on ker over(R,{\^ }) is an adiabatic invariant. Hence n - r independent integrals, from where the conventional Manley-Rowe relations for a single resonance follow as a particular case.",

author = "Dodin, \{I. Y.\} and Zhmoginov, \{A. I.\} and Fisch, \{N. J.\}",

note = "Funding Information: This work was supported by DOE Contract No. DEFG0205ER54838 and DE-AC02-76-CH03073, and by the NNSA under the SSAA Program through DOE Research Grant No. DE-FG52-04NA00139.",

year = "2008",

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doi = "10.1016/j.physleta.2008.08.011",

language = "English (US)",

volume = "372",

pages = "6094--6096",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

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publisher = "Elsevier B.V.",

number = "39",

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TY - JOUR

T1 - Manley-Rowe relations for an arbitrary discrete system

AU - Dodin, I. Y.

AU - Zhmoginov, A. I.

AU - Fisch, N. J.

N1 - Funding Information: This work was supported by DOE Contract No. DEFG0205ER54838 and DE-AC02-76-CH03073, and by the NNSA under the SSAA Program through DOE Research Grant No. DE-FG52-04NA00139.

PY - 2008/9/22

Y1 - 2008/9/22

N2 - Manley-Rowe relations are formulated for a discrete Hamiltonian system with an arbitrary number of resonances. Assuming that the resonances are defined as over(R, ̂) | ω 〉 = 0, where over(R, ̂) is an n × n integer matrix of rank r < n, and | ω 〉 ≡ (ω1, ..., ωn)T is the frequency vector, the projection of the action vector | J 〉 on ker over(R, ̂) is an adiabatic invariant. Hence n - r independent integrals, from where the conventional Manley-Rowe relations for a single resonance follow as a particular case.

AB - Manley-Rowe relations are formulated for a discrete Hamiltonian system with an arbitrary number of resonances. Assuming that the resonances are defined as over(R, ̂) | ω 〉 = 0, where over(R, ̂) is an n × n integer matrix of rank r < n, and | ω 〉 ≡ (ω1, ..., ωn)T is the frequency vector, the projection of the action vector | J 〉 on ker over(R, ̂) is an adiabatic invariant. Hence n - r independent integrals, from where the conventional Manley-Rowe relations for a single resonance follow as a particular case.

UR - https://www.scopus.com/pages/publications/50349094340

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U2 - 10.1016/j.physleta.2008.08.011

DO - 10.1016/j.physleta.2008.08.011

M3 - Article

AN - SCOPUS:50349094340

SN - 0375-9601

VL - 372

SP - 6094

EP - 6096

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 39

ER -

Manley-Rowe relations for an arbitrary discrete system

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