### 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 〉 ≡ (ω_{1}, ..., 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) |
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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 | |

State | Published - Sep 22 2008 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Dodin, I. Y., Zhmoginov, A. I., & Fisch, N. J. (2008). Manley-Rowe relations for an arbitrary discrete system.

*Physics Letters, Section A: General, Atomic and Solid State Physics*,*372*(39), 6094-6096. https://doi.org/10.1016/j.physleta.2008.08.011