论文标题
在磁场中的二维时间依赖性各向异性谐波振荡器上
On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
论文作者
论文摘要
在磁场，Landau问题和非共同空间中的振荡器中有带电的谐波振荡器，在其哈密顿量中具有相同的数学结构。我们已经考虑了一个任意时间依赖性参数（有效质量和频率）的二维各向异性谐波振荡器（AHO），该参数位于任意时间依赖的磁场中。已经构建了一类二次不变的操作员（从刘易斯和里森菲尔德的意义上讲）。不变的运算符（$ \ hat {\ Mathcal {i}} $）已通过线性规范转换（组$ sp（4，\ Mathbb {r}）$简化为简化的代表性表单）。获得了由$ \ hat {\ Mathcal {i}} $组成的希尔伯特空间的正顺序基础。为了获得与系统相对应的时间相关的schrödinger方程的溶液，构建了几何和动态相位因子。已经证明了与我们系统相对应的两部分相干状态的Peres-Horodecki可分离性标准。
A Charged harmonic oscillator in a magnetic field, Landau problems, and an oscillator in a noncommutative space, share the same mathematical structure in their Hamiltonians. We have considered a two-dimensional anisotropic harmonic oscillator (AHO) with arbitrarily time-dependent parameters (effective mass and frequencies), placed in an arbitrarily time-dependent magnetic field. A class of quadratic invariant operators (in the sense of Lewis and Riesenfeld) have been constructed. The invariant operators ($\hat{\mathcal{I}}$) have been reduced to a simplified representative form by a linear canonical transformation (the group $Sp(4, \mathbb{R})$). An orthonormal basis of the Hilbert space consisting of the eigenvectors of $\hat{\mathcal{I}}$ is obtained. In order to obtain the solutions of the time-dependent Schrödinger equation corresponding to the system, both the geometric and dynamical phase-factors are constructed. Peres-Horodecki Separability Criterion for the bipartite coherent states corresponding to our system has been demonstrated.
