Double well Stark effect: crossing and anticrossing of resonances

Article type: Research Article

Authors: Grecchi, Vincenzo | Martinez, Andre | Sacchetti, Andrea

Affiliations: Università di Bologna, Dipartimento di Matematica, Piazza di Porta S. Donato 5, I–40127 Bologna, Italy. E-mail: Grecchi@dm.unibo.it | Université de Paris-Nord, Département de Mathémathiques (CNRS, URA 742), Av. J.B. Clément, F-93430 Villetaneuse, France. E-mail: Martinez@math.univ-paris13.fr | Università di Modena, Dipartimento di Matematica, Via Campi 213/B, I–41100 Modena, Italy. E-mail: Sacchet@c220.unimo.it

Abstract: We consider the semiclassical Stark effect for a family of asymmetric unstable double well models and we study the crossing and anticrossing of the field dependent resonances in the complex field plane. We prove that a Bender-Wu type singularity crosses the real axis when the internal barrier is nearly twice “larger” than the external one and the beating period is close to the shorter life-time of the resonances. At this critical point we have the anticrossing-crossing transition and for larger instability we have the single well localization.

DOI: 10.3233/ASY-1996-13403

Journal: Asymptotic Analysis, vol. 13, no. 4, pp. 373-391, 1996