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July, 2020 Widths of highly excited resonances in multidimensional molecular predissociation
André MARTINEZ, Vania SORDONI
J. Math. Soc. Japan 72(3): 687-730 (July, 2020). DOI: 10.2969/jmsj/81538153

Abstract

We investigate the simple resonances of a 2 by 2 matrix of $n$-dimensional semiclassical Schrödinger operators that interact through a first order differential operator. We assume that one of the two (analytic) potentials admits a well with non empty interior, while the other one is non trapping and creates a barrier between the well and infinity. Under a condition on the resonant state inside the well, we find an optimal lower bound on the width of the resonance. The method of proof relies on Carleman estimates, microlocal propagation of the microsupport, and a refined study of a non involutive double characteristic problem in the framework of Sjöstrand's analytic microlocal theory.

Funding Statement

The authors were partly supported by Università di Bologna, Funds for Selected Research Topics.

Citation

Download Citation

André MARTINEZ. Vania SORDONI. "Widths of highly excited resonances in multidimensional molecular predissociation." J. Math. Soc. Japan 72 (3) 687 - 730, July, 2020. https://doi.org/10.2969/jmsj/81538153

Information

Received: 25 October 2018; Published: July, 2020
First available in Project Euclid: 25 November 2019

zbMATH: 07257207
MathSciNet: MR4125842
Digital Object Identifier: 10.2969/jmsj/81538153

Subjects:
Primary: 35P15
Secondary: 35C20, 35S99, 47A75

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 3 • July, 2020
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