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 - http://www.scopus.com/inward/record.url?scp=50349094340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50349094340&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2008.08.011

DO - 10.1016/j.physleta.2008.08.011

M3 - Article

AN - SCOPUS:50349094340

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

SN - 0375-9601

IS - 39

ER -