Methods and Applications of Analysis

Volume 17 (2010)

Number 2

Semi-classical Analysis of a Conjoint Crossing of Three Symmetric Modes

Pages: 137 – 164

DOI: https://dx.doi.org/10.4310/MAA.2010.v17.n2.a1

Authors

Clotilde Fermanian Kammerer

Vidian Rousse

Abstract

In this article we focus on a semiclassical Schrödinger equation with matrix-valued potential presenting a symmetric conjoint crossing of three eigenvalues. The potential we consider is well-known in the chemical literature as a pseudo Jahn-Teller potential. We analyze the energy transfers which occur between the three modes in terms of Wigner measures.

Keywords

Semi-classical analysis, Born-Oppenheimer approximation, Schrödinger equation, Wigner measures, eigenvalue crossings

2010 Mathematics Subject Classification

Primary 35Q40. Secondary 35B27, 81Q20.

Published 1 January 2010