Nearly resonant multidimensional systems under a transient perturbative interaction.
We analyze the response of a classical system with N>or=2 internal degrees of freedom satisfying R<or=(N-1) approximated resonance conditions to an external perturbative transient interaction. Under certain assumptions on the system internal frequencies and on the coupling interaction, we show the precise N-R adiabatic invariants and obtain an estimate of the span of the domain defined by the intersecting resonances. The results are illustrated considering a system of three anharmonic oscillators transiently coupled by an explicitly time-dependent interaction, and applied to the low energy vibro-rotationally inelastic collisions between two diatomic molecules.
Ruiz
Antonia
A
Departamento de Física Fundamental y Experimental, Electrónica y Sistemas and IUdEA, Universidad de La Laguna, La Laguna, Spain.
Palao
José P
JP
Heller
Eric J
EJ