论文标题
多项式电势和两个维度的量子点
Polynomial potentials and coupled quantum dots in two and three dimensions
论文作者
论文摘要
Non-separable $D-$dimensional partial differential Schrödinger equations are considered at $D=2$ and $D=3$, with the even-parity local potentials $V(x,y,\ldots)$ which are polynomials of degree four (cusp catastrophe resembling case) and six (butterfly resembling case).假定它们的极端（即最小值和最大值）是通过合适的耦合常数临时参数化来定位的。然后，在模拟量子点的动态型制度中发现了可行的低谎言结合状态的非数字近似结构$ψ（x，y，\ ldots）$] $]，在$ v（x，y，y，\ ldots）$的单个最小值中，可以很好地分开量子点的耦合系统，并具有良好的潜力，并具有局部的潜力，并具有和平近似于和平的效果。然后在称为重新定位量子灾难的特定进化场景中发现可测量的特征（尤其是拓扑保护的概率密度分布）。
Non-separable $D-$dimensional partial differential Schrödinger equations are considered at $D=2$ and $D=3$, with the even-parity local potentials $V(x,y,\ldots)$ which are polynomials of degree four (cusp catastrophe resembling case) and six (butterfly resembling case). Their extremes (i.e., minima and maxima) are assumed pronounced, localized via a suitable ad hoc parametrization of the coupling constants. A non-numerical approximate construction of the low lying bound states $ψ(x,y,\ldots)$] is then found feasible in the dynamical regime simulating a coupled system of quantum dots in which the individual minima of $V(x,y,\ldots)$ are well separated, with the potential being locally approximated by the harmonic oscillator wells. The measurable characteristics (and, in particular, the topologically protected probability-density distributions) are then found bifurcating in a specific evolution scenario called a relocalization quantum catastrophe.
