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.
|Original language||English (US)|
|Number of pages||3|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|State||Published - Sep 22 2008|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)