Lysianne Hari (Universit茅 Marie et Louis Pasteur)
Title: Propagation of coherent states and problems of conical intersections
Abstract:
In this talk, we will study the propagation of coherent states (or wavepackets) for a system of coupled Schr枚dinger equations, in the semi-classical limit.
These equations appear in Quantum Chemistry to describe large molecules - namely with a very small electronic mass / nucleus mass ratio (semi-classical parameter).
The coupling between these equations can generate interesting phenomena: the Born-Oppenheimer Approximation is not valid anymore and transitions between energy levels can occur.
Usually, these couplings are induced by a matrix-valued potential with "eigenvalue crossings": they are equal on some region of the phase space.
We will focus on a precise question about the stability of the solution. Consider an initial coherent state (one can think of a gaussian), well-localized in phase space, "living" in a chosen eigenspace of the potential (ie at some given energy level). Does the associated solution keep the same localization property at leading order and does it stay in the same eigenspace (adiabaticity) ?
Without technical details, we will study various situations for several types of crossings leading to transition phenomena.
Where: Pavillion Andr茅-Aisenstadt, room 5183, and by Zoom (see link below)
Join Zoom Meeting
Meeting ID: 895 2873 0384
Passcode: 077937