Nicolas Frantz

collaborators

6 papers

math.AP2026

Edge State Propagation Near Multiple and Singular Interfaces

Nicolas Frantz, {Ã}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

Semiclassical tunneling for some 1D SchrÃ¶dinger operators with complex-valued potentials

Martin Averseng, Nicolas Frantz, FrÃ©dÃ©ric HÃ©rau +1

We consider the non-selfadjoint, semiclassical SchrÃ¶dinger operator $L (h) := - h^{2} \partial_{x}^{2} + e^{i I^\pm} V$ , where $I^\pm \in (- I ¨ , I ¨ )$ and $V : R \to R_{+}$ is ev…

math-ph2026

The Spectral Shift Function for Non-Self-Adjoint Perturbations

Vincent Bruneau, Nicolas Frantz, FranÃ§ois 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

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

math.AP2025

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

Nicolas Frantz, MichaÅ Wrochna

We consider a model for internal waves described by a zero order pseudo-differential Hamiltonian $P$ damped by a second order viscosity term $i I^½ Q$ . Under Morse-Smale or similar w…