Observatorio de I+D+i UPM

Memorias de investigación
Conferencias:
Quantum and classical resonances
Año:2008
Áreas de investigación
  • Electrónica
Datos
Descripción
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 i-coordinate. 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 di erent 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 di erence between quantum numbers, for i-coordinate, of both eigenstates involved in avoided crossing. In this context we have found, in a model of Li-CN 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 quantum-classical correspondence. This result also shows the power of correlation diagram E-¯h as a tool for understanding quantum chaos.
Internacional
Si
ISSN o ISBN
0
Entidad relacionada
Universidades Politécnica y Autónoma de Madrid
Nacionalidad Entidad
ESPAÑA
Lugar del congreso
Madrid (España)
Esta actividad pertenece a memorias de investigación
Participantes
  • Autor: Florentino Borondo (Universidad Autónoma de Madrid)
  • Autor: Rosa Maria Benito Zafrilla (UPM)
  • Autor: Francisco Javier Arranz Saiz (UPM)
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Grupo de Investigación: Grupo de Sistemas Complejos
  • Departamento: Física y Mecánica Fundamentales y Aplicada a la Ingeniería Agroforestal
  • Departamento: Ingeniería Rural
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