Nicolas Frantz

activity

20222026

collaborators

8 papers

math.AP2026

Edge State Propagation Near Multiple and Singular Interfaces

Nicolas Frantz, {É}ric Vacelet

We study the semiclassical propagation of edge-states for a two-dimensional Dirac operator with a spatially varying mass. The zero set of the mass models the interface between topo…

math.AP2026

Edge modes generated by intersection between 3 energy bands

Clotilde Fermanian Kammerer, Nicolas Frantz

In this contribution, we investigate 2-dimensional model problems of three coupled equations. We assume that the underlying Hamiltonian presents a symmetric intersection between th…

math-ph2026

The Spectral Shift Function for Non-Self-Adjoint Perturbations

Vincent Bruneau, Nicolas Frantz, François Nicoleau

This paper is devoted to the definition and analysis of the spectral shift function (SSF) associated with non-self-adjoint perturbations of self-adjoint operators. Motivated by app…

math-ph2025

Localization of the eigenfunctions of a Bloch-Torrey operator on the half-plane

Martin Averseng, Nicolas Frantz, Frédéric Hérau +1

We consider a non-self adjoint operator of the form $- h^{2} Δ + i (V (x) + α (x) y)$ on the upper half plane $y > 0$ with Dirichlet boundary conditions on ${y = 0}$ with $V \geq 0$ , $V$ …

math-ph2025

Semiclassical tunneling for some 1D Schrödinger operators with complex-valued potentials

Martin Averseng, Nicolas Frantz, Frédéric Hérau +1

We consider the non-selfadjoint, semiclassical Schrödinger operator $L (h) := - h^{2} \partial_{x}^{2} + e^{i α} V$ , where $α \in (- π, π)$ and $V : R \to R_{+}$ is even an…

math.AP2025

Long-time evolution of forced waves in the low viscosity regime

Nicolas Frantz, Michał Wrochna

We consider a model for internal waves described by a zero order pseudo-differential Hamiltonian $P$ damped by a second order viscosity term $i ν Q$ . Under Morse-Smale or similar we…

math-ph2023

Scattering theory for some non-self-adjoint operators

Nicolas Frantz

We consider a non-self-adjoint $H$ given as the perturbation of a self-adjoint operator $H_{0}$ . We suppose that $H$ is of the form $H = H_{0} + C W C$ where $C$ is a bounded, positive defin…

math.SP2022

Spectral decomposition of some non-self-adjoint operators

Jérémy Faupin, Nicolas Frantz

We consider non-self-adjoint operators in Hilbert spaces of the form $H = H_{0} + C W C$ , where $H_{0}$ is self-adjoint, $W$ is bounded and $C$ is a metric operator, $C$ bounded and relative…