21 citations · 51 across the 9 of their papers we have counts for
12 papers
Counting Negative Eigenvalues for the Magnetic Pauli Operator
Søren Fournais, Rupert L. Frank, Magnus Goffeng +2
We study the Pauli operator in a two-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues remi…
Flux and symmetry effects on quantum tunneling
Bernard Helffer, Ayman Kachmar, Mikael Persson Sundqvist
Motivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitia…
Computing nodal deficiency with a refined Dirichlet-to-Neumann map
Gregory Berkolaiko, Graham Cox, Bernard Helffer +1
Recent work of the authors and their collaborators has uncovered fundamental connections between the Dirichlet-to-Neumann map, the spectral flow of a certain family of self-adjoint…
Spectral flow for pair compatible equipartitions
Bernard Helffer, Mikael Persson Sundqvist
We show that a recent spectral flow approach proposed by Berkolaiko-Cox-Marzuola for analyzing the nodal deficiency of the nodal partition associated to an eigenfunction can be ext…
On an integral identity
Alin Bostan, Fernando Chamizo, Mikael P. Sundqvist
We give three elementary proofs of a nice equality of definite integrals, which arises from the theory of bivariate hypergeometric functions, and has connections with irrationality…
Counterexample to strong diamagnetism for the magnetic Robin Laplacian
Ayman Kachmar, Mikael P. Sundqvist
We determine a counterexample to strong diamagnetism for the Laplace operator in the unit disc with a uniform magnetic field and Robin boundary condition. The example follows from…
On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator III: Magnetic fields that change sign
Bernard Helffer, Hynek Kovařík, Mikael P. Sundqvist
We consider the semi-classical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm-Kovařík-Po…
On nodal domains in Euclidean balls
Bernard Helffer, Mikael Persson Sundqvist
Å. Pleijel (1956) has proved that in the case of the Laplacian with Dirichlet condition, the equality in the Courant nodal theorem (Courant sharp situation) can only be true for a…
Nodal domains in the square---the Neumann case
Bernard Helffer, Mikael Persson Sundqvist
Å Pleijel has proved that in the case of the Laplacian on the square with Neumann condition, the equality in the Courant nodal theorem (Courant sharp situation) can only be true fo…
Clusters of eigenvalues for the magnetic Laplacian with Robin condition
Magnus Goffeng, Ayman Kachmar, Mikael Persson Sundqvist
We study the Schrödinger operator with a constant magnetic field in the exterior of a compact domain in euclidean space. Functions in the domain of the operator are subject to a bo…
Lack of diamagnetism and the Little-Parks effect
Søren Fournais, Mikael Persson Sundqvist
When a superconducting sample is submitted to a sufficiently strong external magnetic field, the superconductivity of the material is lost. In this paper we prove that this effect…
A uniqueness theorem for higher order anharmonic oscillators
Søren Fournais, Mikael Persson Sundqvist
We study for , the family of self-adjoint operators \[ -\frac{d^2}{dt^2}+\Bigl(\frac{t^{k+1}}{k+1}-α\Bigr)^2 \] in and show th…