相关论文: Low-energy eigenstates in a vanishing magnetic fie…

This article deals with the spectral analysis of the semiclassical Neumann magnetic Laplacian on a smooth bounded domain in dimension three. When the magnetic field is constant and in the semiclassical limit, we establish a four-term…

This article is devoted the semiclassical spectral analysis of the Neumann magnetic Laplacian on a smooth bounded domain in three dimensions. Under a generic assumption on the variable magnetic field (involving a localization of the…

This paper is devoted to the spectral analysis of the Neumann realization of the 2D magnetic Laplacian with semiclassical parameter h > 0 in the case when the magnetic field vanishes along a smooth curve which crosses itself inside a…

We consider a relativistic no-pair model of a hydrogenic atom in a classical, exterior magnetic field. First, we prove that the corresponding Hamiltonian is semi-bounded below, for all coupling constants less than or equal to the critical…

The magnetic Laplacian with a step magnetic field has been intensively studied during the last years. We adapt the construction introduced by Bonnaillie-No\"el, Fournais, Kachmar and Raymond to prove the existence of bound states of a new…

We consider the semiclassical magnetic Laplacian $\mathcal{L}_h$ on a Riemannian manifold, with a constant-rank and non-vanishing magnetic field $B$. Under the localization assumption that $B$ admits a unique and non-degenerate well, we…

This paper deals with semiclassical asymptotics of the three-dimensional magnetic Laplacian in presence of magnetic confinement. Using generic assumptions on the geometry of the confinement, we exhibit three semiclassical scales and their…

In this paper we are interested in the semi-classical estimates of the spectrum of the Neumann Laplacian in dimension 3. This work aims to present a complementary case to the one presented in the paper of Helffer and Morame in the case of…

We provide a precise description of the bottom of the spectrum in the semiclassical limit of a harmonic-type Schr\"odinger operator with an inverse square potential. By exploiting the connection between the eigenfunctions of these operators…

We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schr\"odinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value $b_0$ of the intensity of the magnetic field is strictly…

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$…

We consider a periodic magnetic Schr\"odinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a noncompact Riemannian manifold $M$ such that $H^1(M, {\mathbb R})=0$ endowed with a properly discontinuous cocompact…

We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of the bundle exhibits a cluster of low-energy states. We…

We consider a magnetic laplacian P(A) on the Poincar\'e half-plane, when the magnetic field dA is infinite at infinity such that P(A) has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues.

We consider a magnetic Schr\"odinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a two-dimensional Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the…

We study the energy minima of the fully-connected $m$-components vector spin glass model at zero temperature in an external magnetic field for $m\ge 3$. The model has a zero temperature transition from a paramagnetic phase at high field to…

This paper is concerned with spectrum properties of the magnetic Laplacian with a higher-order vanishing magnetic field in a bounded domain. We study the asymptotic behaviors of ground state energies for the Dirichlet Laplacian, the Neumann…

We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann ``windows'' of the same length the centers of which are $2l$ apart, and study the asymptotic behaviour of the discrete spectrum as $l\to\infty$.…

This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…

We consider the Bochner Laplacian on high tensor powers of a positive line bundle on a closed symplectic manifold (or, equivalently, the semiclassical magnetic Schr\"odinger operator with the non-degenerate magnetic field). We assume that…