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2001 (1)
1Author    Jan WiersigRequires cookie*
 Title    Resonance Zones in Action Space  
 Abstract    The classical and quantum mechanics o f isolated, nonlinear resonances in integrable systems with N > 2 degrees of freedom is discussed in terms o f geometry in the space o f action vari­ ables. Energy surfaces and frequencies are calculated and graphically presented for invariant tori inside and outside the resonance zone. The quantum mechanical eigenvalues, computed in the sem iclassical WKB approximation, show a regular pattern when transformed into the action space o f the associated symmetry reduced system: eigenvalues inside the resonance zone are arranged on iV-dimensional cubic lattices, whereas those outside are, in general, non-periodically distributed. However, TV-dimensional triclinic (skewed) lattices exist locally. Both kinds o f lattices are joined smoothly across the classical separatrix surface. The statements are illustrated with the help o f two and three coupled rotors. The energy-level statistics of this system are found numerically to be in very good agreement with the Poisson distribution, despite o f the complex lattice structure. PACS: 03.65.Sq, 05.45.-a 
  Reference    Z. Naturforsch. 56a, 537—556 (2001); received June 23 2001 
  Published    2001 
  Keywords    Resonance Zones, Energy Surfaces, Action Space, Energy-level Statistics, Semiclassical Quantization 
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 TEI-XML for    default:Reihe_A/56/ZNA-2001-56a-0537.pdf 
 Identifier    ZNA-2001-56a-0537 
 Volume    56