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arXiv 2003.06501quant-ph
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二维和三维中的多项式势和耦合量子点

Polynomial potentials and coupled quantum dots in two and three dimensions

Miloslav Znojil

摘要:

在$D=2$和$D=3$上考虑了不可分的$D-$维偏微分薛定谔方程,其中偶宇称局部势$V(x,y,\ldots)$是四次多项式(尖点突变类情形)和六次多项式(蝴蝶类情形).其极端(即,最小值和最大值)被假定为明显的,通过耦合常数的适当的特别参数化而局部化。然后发现在模拟量子点耦合系统的动力学机制中,低束缚态[$ψ(x,y,\ldots)$ ]的非数值近似构造是可行的,其中$V(x,y,\ldots)$的各个极小值被很好地分离,势被谐振子阱局部近似。可测量的特征(特别是拓扑保护的概率密度分布),然后发现分叉在一个特定的演化场景称为重定位量子灾难。

英文摘要:

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). 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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