Spectral study of semiclassical Schrödinger operators with purely imaginary potential.

par Victor Arnaiz Solorzano (IMB - Université de Bordeaux)

lundi 20 avr. 2026, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

In this talk I will present new results concerning the asymptotic distribution of eigenvalues for some non-selfadjoint semiclassical Schrödinger operators with purely imaginary potential. Assuming different generalized Morse type conditions on the critical values of the potential, we establish localization of eigenvalues at the botton of the spectrum of such operators by comparison with suitable model operators. By the way, we obtain an existence theorem and and asymptotic formula of the eigenvalues for the model operator $-\partial_x^2 + i x^n$ on $L^2(\R)$ for any odd integer number $n \geq 3$, generalizing a classical theorem of Y. Sibuya in the case $n = 3$. This talk is based on joint works with J-F. Bony and L. Michel.