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
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.
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.