This book is a synthesis of recent advances in the spectral theory of the magnetic
Schrödinger operator. It can be considered a catalog of concrete examples of magnetic …

We consider an extreme type-II superconducting wire with non-smooth cross section, ie with
one or more corners at the boundary, in the framework of the Ginzburg–Landau theory. We …

We complete the analysis of the band functions for two-dimensional magnetic Schrödinger
operators with piecewise constant magnetic fields. The discontinuity of the magnetic field …

For a bounded corner domain Ω, we consider the attractive Robin Laplacian in Ω with large
Robin parameter. Exploiting multiscale analysis and a recursive procedure, we have a …

We study the quasi-classical limit of the Pauli–Fierz model: the system is composed of
finitelymany non-relativistic charged particles interactingwith a bosonic radiation field. We …

This paper is mainly inspired by the conjecture about the existence of bound states for
magnetic Neumann Laplacians on planar wedges of any aperture Φ∈(0, π). So far, a proof …

Let Ω be a curvilinear polygon and Q Ω γ be the Laplacian in L 2 (Ω), Q Ω γ ψ=− Δ ψ, with the
Robin boundary condition∂ ν ψ= γ ψ, where∂ ν is the outer normal derivative and γ> 0. We …

In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger
operator with a δ-interaction supported on a cone whose cross section is the sphere of …

We define a Schrödinger operator on the half-space with a discontinuous magnetic field
having a piecewise-constant strength and a uniform direction. Motivated by applications in …

We study a Schrödinger operator in. R3+:={x∈ R3| x=(x1, x2, x3), x2> 0} with a magnetic
field admitting a piecewise constant strength and a uniform direction. We review some …