Study of the double non linear quantum resonances in diatomic molecules

We study the quantum dynamics of diatomic molecule driven by a circularly polarized resonant electric field. We look for a quantum effect due to classical chaos appearing due to the overlapping of nonlinear resonances associated to the vibrational and rotational motion. We solve the Schr\"odinger equation associated with the wave function expanded in term of proper stationary states, $|n>\otimes|lm>$ (vibrational$\otimes$angular momentum states). Looking for quantum-classic correspondence, we consider the Liouville dynamics in the two dimensional phase space defined by the coherent -like state of vibrational states, and it is found some similarities when the quantum dynamics is pictured in terms of number and phase operators.Comment: 15 pages, 4 figure

Damping-Antidamping Effect on Comets Motion

We make an observation about Galilean transformation on a 1-D mass variable systems which leads us to the right way to deal with mass variable systems. Then using this observation, we study two-bodies gravitational problem where the mass of one of the bodies varies and suffers a damping-antidamping effect due to star wind during its motion. For this system, a constant of motion, a Lagrangian and a Hamiltonian are given for the radial motion, and the period of the body is studied using the constant of motion of the system. Our theoretical results are applied to Halley's comet.Comment: 19 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:0910.468