Semi-classical analysis of a conjoint crossing of three symmetric modes

TL;DR

This paper investigates the semiclassical Schrödinger equation with a symmetric three-mode crossing potential, analyzing energy transfer between modes using Wigner measures, relevant to chemical pseudo Jahn-Teller systems.

Contribution

It provides a detailed semiclassical analysis of energy transfer in a three-mode crossing scenario, a novel focus in the context of pseudo Jahn-Teller potentials.

Findings

Characterization of energy transfer mechanisms between modes.

Application of Wigner measures to analyze mode interactions.

Insights into the dynamics of symmetric three-mode crossings.

Abstract

In this article we focus on a semiclassical Schr\"odinger 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.