I defended my Ph.D. thesis at the University of Bordeaux on May 12th, 2017 under the supervision of Pr. Mouez Dimassi.

My Ph.D. thesis

Spectral Analysis of Systems of h-pseudodifferential Operators

Research Interests 

My research lies in the areas of Partial Differential Equations and Mathematical Physics, more specifically, in Semiclassical and Microlocal Analysis, Spectral theory, Scattering theory, and Quantum dynamics. I am mainly interested in the following topics:

• Semiclassical approximation of quantum dynamics: time evolution of quantum observables, correspondance principle, propagation of coherent states and wave packets.
• Spectral and scattering theory for quantum Hamiltonians: perturbation theory, asymptotic analysis of eigenvalues and resonances, trace formulas, spectral shift function, magnetic Hamiltonians.
• Energy-level crossings in quantum mechanics: systems of h-pseudodifferential operators, Born-Oppenheimer approximation, propagation through energy-level crossings.

Publications

1. Long time semiclassical Egorov theorem for h-pseudodifferential systems

Asymptotic Analysis, Vol 101 (2017), no. 1-2, 17-67.

2. Semiclassical Trace Formula and Spectral Shift Function for Systems via a Stationary Approach, with M. Dimassi and S. Fujiié.

International Mathematics Research Notices (2017).

Work in progress

• Lieb-Thirring inequalities and discrete spectrum in gaps for slowly varying perturbations of periodic Schrödinger operators, with M. Dimassi.