标题： 具有半经典应用的磁性阶梯下的三维薛定谔算子 显示英文标题

标题： A 3D-Schroedinger operator under magnetic steps with semiclassical applications

摘要： 我们在半空间上定义了一个薛定谔算子，该算子具有不连续的磁场，其强度是分段常数且方向均匀。 受超导理论应用的启发，我们研究了该算子谱的下确界。 我们给出了磁场强度和方向的充分条件，使得前述下确界成为半平面上约化模型算子的一个本征值。 我们使用半空间上的薛定谔算子来研究空间中有界区域中的一个新的半经典问题，考虑具有分段常数磁场的磁诺伊曼拉普拉斯算子。 然后我们精确地确定了半经典基态在磁场不连续跳跃处特定点附近的局域化。 显示英文摘要

摘要： We define a Schr\"odinger operator on the half-space with a discontinuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the infimum of the spectrum of the operator. We give sufficient conditions on the strength and the direction of the magnetic field such that the aforementioned infimum is an eigenvalue of a reduced model operator on the half-plane. We use the Schr\"odinger operator on the half-space to study a new semiclassical problem in bounded domains of the space, considering a magnetic Neumann Laplacian with a piecewise-constant magnetic field. We then make precise the localization of the semiclassical ground state near specific points at the discontinuity jump of the magnetic field.