Confining quantum particles with a purely magnetic field

Quantum exotic: A repulsive and bottomless confining potential

On a simple model $V(x,y)=A\,x^2+B\,y^2+C\,x^2y^2+D\,(x^2y^4+x^4y^2)$ we demonstrate that even in a classically repulsive regime (i.e., at couplings which make the potential decreasing to $-\infty$ in some directions) quantum mechanics may still support the purely discrete spectrum of bound states. In our example, there exists a critical boundary of this domain of stability where a further increase of repulsion causes an explosive escape of particles in infinity.

径向磁阱之间的纯磁隧穿

Purely magnetic tunnelling between radial magnetic wells

本文研究二维磁拉普拉斯算子在具有两个对称径向阱的正磁场下的半经典谱，建立了最低两个特征值之间谱间隙的精确隧穿公式，并证明该间隙在半经典极限下指数级小但为正。

A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot

We discuss a geometric approach to confining a Dirac neutral particle with a permanent magnetic dipole moment interacting with external fields to a hard-wall confining potential in the Minkowski spacetime through noninertial effects. We discuss the behaviour of external fields induced by noninertial effects, and a case where relativistic bound states can be achieved in analogous way to having a Dirac particle confined to a quantum dot. We show that this confinement of a Dirac neutral particle analogous to a quantum dot arises from noninertial effects that give rise to the geometry of the manif…

On a neutral particle with a magnetic quadrupole moment in a uniform effective magnetic field

Quantum effects on a Landau-type system associated with a moving atom with a magnetic quadrupole moment subject to confining potentials are analysed. It is shown that the spectrum of energy of the Landau-type system can be modified, where the degeneracy of the energy levels can be broken. In three particular cases, it is shown that the analogue of the cyclotron frequency is modified, and the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum and by the parameters associated with confining poten…

Magnetic confinement at a boundary approximates specular reflection

We conjecture that for a plasma in a spatial domain with a boundary, the specular reflection effect of the boundary can be approximated by a large magnetic confinement field in the near-boundary region. In this paper, we verify this conjecture for the 1.5D relativistic Vlasov-Maxwell system (RVM) on a bounded domain $Ω= (0, 1)$ with an external confining magnetic field.

纯电和纯磁韦伊尔曲率张量的庞特里亚金类障碍

A Pontryagin class obstruction for purely electric and purely magnetic Weyl curvature tensors

研究纯电或纯磁韦伊尔曲率张量的洛伦兹度量存在性，通过庞特里亚金形式的乘积 vanish 推导 cohomological 障碍，关联到 Petrov 子类型和非退化脐超曲面的分类。