Polynomial potentials and coupled quantum dots in two and three dimensions

• URL: http://arxiv.org/abs/2003.06501v1
• Date: Fri, 13 Mar 2020 22:52:18 GMT
• Title: Polynomial potentials and coupled quantum dots in two and three dimensions
• Authors: Miloslav Znojil
• Abstract summary: Non-separable $D-$ partial differential Schr"odinger equations are considered at $D=2$ and $D$, with the even-parity local potentials $V(x,y,ldots)$. A non-numerical approximate construction of the low lying bound states $psi(x,y,ldots)$ is then found feasible in the dynamical regime.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-separable $D-$dimensional partial differential Schr\"{o}dinger 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 $\psi(x,y,\ldots)$] 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.

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