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arXiv · 2607.07301

Semiclassical Schrödinger operators with purely imaginary potential

Victor Arnaiz·Jean-Francois Bony·Laurent Michel
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Abstract

We consider Schrödinger operators with purely imaginary potential $P = - h^{2} Δ+ i V ( x )$ on a bounded domain. Assuming that near its critical points the potential $V$ can be approximated by an homogeneous polynomial, we show that in the limit $h \to 0$ the leftmost eigenvalues of $P$ are asymptotically given by the local model associated to the most degenerated critical points of $V$. We give applications of this result to the associated evolution problem including shear flows in fluid mechanics.

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Victor Arnaiz, Jean-Francois Bony, Laurent Michel. 2026-07-08. Semiclassical Schrödinger operators with purely imaginary potential. https://arxiv.org/abs/2607.07301

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