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Abstract: One-dimensional isoperiodic classical systems have been first analyzed byAbel. Abel-s characterization can be extended for singular potentials andpotentials which are not defined on the whole real line. The standard shearequivalence of isoperiodic potentials can also be extended by using reflectionand inversion transformations. We provide a full characterization ofisoperiodic rational potentials showing that they are connected bytranslations, reflections or Joukowski transformations. Upon quantization manyof these isoperiodic systems fail to exhibit identical quantum energy spectra.This anomaly occurs at order Oh^2 because semiclassical corrections of energylevels of order Oh are identical for all isoperiodic systems. We analyzefamilies of systems where this quantum anomaly occurs and some special systemswhere the spectral identity is preserved by quantization. Conversely, we pointout the existence of isospectral quantum systems which do not correspond toisoperiodic classical systems.



Autor: M. Asorey, J.F. Carinena, G. Marmo, A. Perelomov

Fuente: https://arxiv.org/







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