Magnetic Wells in Dimension Three

Classical magnetic Lifshits tails in three space dimensions: impurity potentials with slow anisotropic decay

We determine the leading low-energy fall-off of the integrated density of states of a magnetic Schroedinger operator with repulsive Poissonian random potential in case its single impurity potential has a slow anisotropic decay at infinity. This so-called magnetic Lifshits tail is shown to coincide with the one of the corresponding classical integrated density of states.

On the asymptotic limit of the three dimensional Vlasov-Poisson system for large magnetic field : formal derivation

This paper establishes the long time asymptotic limit of the three dimensional Vlasov-Poisson equation with strong external magnetic field. The guiding center approximation is investigated in the three dimensional case with a non-constant magnetic field. In the long time asymptotic limit, the motion can be split in two parts : one stationary flow along the lines of the magnetic field and the guiding center motion in the orthogonal plane of the magnetic field where classical drift velocities are recovered. We discuss in particular the effect of nonconstant external magnetic fields.

Strong diamagnetism for the ball in three dimensions

In this paper we give a detailed asymptotic formula for the lowest eigenvalue of the magnetic Neumann Schrödinger operator in the ball in three dimensions with constant magnetic field, as the strength of the magnetic field tends to infinity. This asymptotic formula is used to prove that the eigenvalue is monotonically increasing for large values of the magnetic field.

恒定磁场下三维磁性狄利克雷拉普拉斯算子基态能量的优化

Optimizing the ground state energy of the three-dimensional magnetic Dirichlet Laplacian with constant magnetic field

针对固定体积三维区域中恒定磁场下磁性狄利克雷拉普拉斯算子基态能量极小化问题，通过柱形区域分析揭示几何约束（磁场增强时区域沿磁场方向特定速率伸长），结合数值结果验证预测并提出猜想。

On Three Imaginary-time Path Integral Formulas with Magnetic Fields in Relativistic Quantum Mechanics

Three magnetic relativistic Schrödinger operators are considered, corresponding to the classical relativistic Hamiltonian symbol with both magnetic vector and electric scalar potentials. Path integral representations for the solutions of their respective imaginary-time relativistic Schrödinger equations, i.e. heat equations are given in two ways. The one is by means of the probability path space measure coming from the Lévy process concerned, and the other is through time-sliced approximation with Chernoff's theorem.

Three charges on a plane in a magnetic field: Special trajectories

As a generalization and extension of JMP 54 (2013) 022901, the classical dynamics of three non-relativistic Coulomb charges $(e_1, m_1)$, $(e_2, m_2)$ and $(e_3, m_3)$ on the plane placed in a constant magnetic field perpendicular to the plane is considered. Special trajectories for which the distances between the charges remain unchanged are presented and their corresponding integrals of motion are indicated. For these special trajectories the number of integrals of motion is larger than the dimension of the configuration space and hence they can be called \emph{particularly superintegrable}.…