Abstract



For nonlinear conservative Hamiltonian systems, the evolution of phase space as energy increases involve appearance of chains of islands corresponding to periodic orbits or classical resonances. For 2 degrees of freedom systems, we can characterize a resonance by means of its order of resonance !x:!y, where !i is the frequency for icoordinate. Then, as energy increases, we can observe a sequence of appearance of resonances !x1:!y1, !x2:!y2, !x3:!y3, . . . On the other hand, in quantum mechanics we can represent the correlation diagram of eigenenergies versus a system parameter, obtaining dierent avoided crossings or quantum resonances. For 2 degrees of freedom systems, we can characterize a resonance by means of its order of resonance !x:!y = ny:nx, where ni is the dierence between quantum numbers, for icoordinate, of both eigenstates involved in avoided crossing. In this context we have found, in a model of LiCN molecule, series of quantum resonances in the correlation diagram of eigenenergies versus Planck¿s constant. As energy (and ¯h) increases we observe the next sequence of appearance of series of resonances: 1:6, 2:14, 1:8, 2:18, 1:10, 1:10, 1:8. Moreover, we observe a similar sequence of appearance of classical resonances: 1:6, 1:7, 1:8, 1:9, 1:10, 1:10, 1:8 . . . This is a very interesting result that shows the importance of periodic orbits in quantumclassical correspondence. This result also shows the power of correlation diagram E¯h as a tool for understanding quantum chaos.  
International

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Entity

Universidades Politécnica y Autónoma de Madrid 
Entity Nationality

ESPAÑA 
Place

Madrid (España) 