Relocalization switch in a triple quantum dot molecule in 2D
Miloslav Znojil
TL;DR
This work addresses relocalization (a quantum catastrophe) of probability density in a symmetric triple quantum dot molecule modeled in two dimensions. It builds a 2D bound-state framework using a three-parameter non-separable sextic potential $V(x,y)=r^6 - A^2 r^4 + (B^2 + C^2 y^2) r^2$ with $r^2=x^2+y^2$, where $A^2=3(\alpha^2+\beta^2)$, $B^2=3\alpha^2\gamma^2$, and $\gamma^2=\alpha^2+2\beta^2$, yielding three local minima at $r=0$ and at $(x,y)=(\pm \gamma,0)$ and barrier heights $V(\pm \alpha,0)=\alpha^4(\beta^2+\gamma^2)$. For large $\alpha,\beta$ the wells are well separated, allowing non-numerical insights into the low-lying spectra and the parameter-driven transition between central and off-central localization, with a sharp relocalization near $\alpha \approx \beta \gg 1$. The results extend quantum catastrophe analysis from 1D to a tractable 2D setting, offering a controllable mechanism for localization switching in quantum dot molecules and highlighting the role of tunneling between multiple minima in non-separable potentials.
Abstract
Tunneling between pronounced minima of a polynomial potential (simulating coupled quantum dots) can cause an abrupt quantum-catastrophic relocalization of density $|ψ(x,y, \ldots)|$. Non-numerical illustration is constructed, in 2D, using a non-separable sextic-oscillator model.