6 papers
On shape optimization with large magnetic fields in two dimensions
Vladimir Lotoreichik, Léo Morin
This paper aims to show that, in the limit of strong magnetic fields, the optimal domains for eigenvalues of magnetic Laplacians tend to exhibit symmetry. We establish several asym…
The Flea on the Magnetic Elephant
Pavel Exner, Léo Morin
We investigate a two-dimensional magnetic Laplacian with two radially symmetric magnetic wells. Its spectral properties are determined by the tunneling between them. If the tunneli…
Tunneling between magnetic wells in two dimensions
Søren Fournais, Yannick Guedes Bonthonneau, Léo Morin +1
The two-dimensional magnetic Laplacian is considered. We calculate the leading term of the splitting between the first two eigenvalues of the operator in the semiclassical limit un…
Magnetic tunneling between disc-shaped obstacles
Søren Fournais, Léo Morin
In this paper we derive formulae for the semiclassical tunneling in the presence of a constant magnetic field in 2 dimensions. The `wells' in the problem are identical discs with N…
The free energy of dilute Bose gases at low temperatures interacting via strong potentials
S. Fournais, L. Junge, T. Girardot +3
We consider a dilute Bose gas in the thermodynamic limit and prove a lower bound on the free energy for low temperatures which is in agreement with the conjecture of Lee-Huang-Yang…
Tunneling effect between radial electric wells in a homogeneous magnetic field
Léo Morin
We establish a tunneling formula for a Schrödinger operator with symmetric double-well potential and homogeneous magnetic field, in dimension two. Each well is assumed to be radial…