Communications in Mathematical Physics

, Volume 176, Issue 1, pp 1–22 | Cite as

Double wells: Nevanlinna analyticity, distributional Borel sum and asymptotics

  • E. Caliceti
  • V. Grecchi
  • M. Maioli


We consider the energy levels of a Stark family, in the parameterj, of quartic double wells with perturbation parameterg:
$$H(g,j) = p^2 + x^2 (1 - gx)^2 - j\left( {gx - \frac{1}{2}} \right).$$
For non-evenj (and for the symmetric casej=0) we prove analyticity in the full Nevanlinna disk ℜg−2 >R−1 of theg2-plane, as predicted by Crutchfield. By means of an approximation we give a heuristic estimate of the asymptotic smallg behaviour, showing the relation between the avoided crossings and the failure of the usual perturbation series.


Neural Network Statistical Physic Energy Level Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • E. Caliceti
    • 1
  • V. Grecchi
    • 1
  • M. Maioli
    • 2
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaIntaly
  2. 2.Dipartimento di MatematicaUniversità di ModenaModenaItaly

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