In the past decade, the mathematics of superconductivity has been the subject of intense
study. This book examines in detail the nonlinear Ginzburg–Landau (GL) functional, the …

The x and Q 2 dependence of the single photon exchange cross section d 2 σ/dQ 2 dx and
the proton structure functions F 2 (x, Q 2) and R (x, Q 2) have been measured in deep …

Motivated by a recent paper by Montgomery [Mon], we give the asymptotic behavior, in the
semi-classical sense, of the ground state energy for the Schrödinger operator with a …

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 …

In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be
modified. The usual modification, based on “the minimal coupling principle” at the level of …

In this work, we prove a nonlocal Halanay inequality with an exact decay rate. This enables
us to analyze behavior of solutions to some classes of nonlocal ODEs and PDEs involving …

The even-dimensional Dirac and Schrödinger operators with a constant magnetic field of full
rank have purely essential spectrum consisting of isolated eigenvalues, so-called Landau …

We consider the Schrödinger operator with magnetic field,\begin {equation*} H=(\frac
{1}{i}\nabla-{\overset {\rightharpoonup}{a}}(x))^{2}+ V (x)\text {in}\mathbb {R}^{n}.\end …

Abstract We study the Bochner–Schrödinger operator H_ p= 1 p\varDelta^ L^ p ⊗ E+ VH p=
1 p Δ L p⊗ E+ V on high tensor powers of a positive line bundle L on a symplectic manifold …

Introduction to semi-classical methods for the Schrödinger operator with magnetic field Page 1
HAL Id: cel-00376427 https://cel.hal.science/cel-00376427 Submitted on 17 Apr 2009 HAL is a …