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.
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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 -