外均匀磁场中自旋为1的量子力学粒子的精确解

均匀磁场中自旋为1的量子力学粒子的精确解及其附加本征特性

Exact solutions for a quantum-mechanical particle with spin 1 and additional intrinsic characteristics in a homogeneous magnetic field

利用广义协变矩阵，构造了圆柱坐标系下自旋为1的粒子在均匀磁场作用下的10维Petiau-Duffin-Kemmer量子力学方程的精确解.三个线性独立类型的解决方案是分开的，在每种情况下的公式的能级已被发现。在类似的技术的量子力学方程的粒子与自旋1和额外的内在电磁特性-极化率，精确的解决方案被发现在存在外部均匀磁场。

Symmetries, constants of the motion and reduction of mechanical systems with external forces

This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding symmetries and conserved quantities. We particularize our results for the so-called Rayleigh dissipation, i.e., external forces that are derived from a dissipation function, and illustrate them with some examples. Moreover, we present a theory for the reduction of Lagrangian systems subjected to external forces which are invariant under the action of a Lie group.

Freezing of energy of a soliton in an external potential

In this paper we study the dynamics of a soliton in the generalized NLS with a small external potential $εV$ of Schwartz class. We prove that there exists an effective mechanical system describing the dynamics of the soliton and that, for any positive integer $r$, the energy of such a mechanical system is almost conserved up to times of order $ε^{-r}$. In the rotational invariant case we deduce that the true orbit of the soliton remains close to the mechanical one up to times of order $ε^{-r}$.

关于Lobachevsky空间中均匀磁场中Dirac方程的精确解

On exact solutions of the Dirac equation in a homogeneous magnetic field in the Lobachevsky space

在具有常负曲率的黎曼空间，双曲罗巴切夫斯基空间中，当存在类似于闵可夫斯基空间中均匀磁场的外磁场时，构造了自旋S=1/2粒子的量子力学Dirac方程的精确解.在Lobachevsky空间几何的基础上，得到了描述粒子在磁场中运动量子化的能级一般公式。

（2+1）维均匀和非均匀磁场诱导的费米子凝聚和真空电流密度

Fermion Condensate and Vacuum Current Density Induced by Homogeneous and Inhomogeneous Magnetic Fields in (2+1)-Dimensions

我们计算了（2+1）维空间中的凝聚态和外加静磁场诱导的真空电流密度。在微扰水平上，我们考虑沿一个直角坐标系指数衰减的磁场。在非微扰条件下，我们通过求解彩虹阶梯近似下的Schwinger-Dyson方程，得到了均匀磁场中的费米子传播子。在大通量的限制，我们观察到，这两个量，无论是微扰（非均匀）和非微扰（均匀），是成比例的外部场，与早期的预期。

黎曼球面空间中均匀磁场中Dirac方程的精确解

On exact solutions of the Dirac equation in a homogeneous magnetic field in the Riemann spherical space

在常正曲率空间、球面Riemann空间中，当存在类似于Minkowski空间中均匀磁场的外磁场时，构造了自旋S=1/2粒子的量子力学Dirac方程的精确解.在黎曼空间几何的背景下，得到了描述粒子在磁场中运动量子化的能级一般公式。