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The ground states of electrons in two vertically coupled quantum dots in thepresence of an external magnetic field have been studied within the densityfunctional theory. A phase diagram of the transition to the quantum Hall statein double quantum dots has been plotted for the Landau level filling factor$\nu = 1$. It has been shown that the quantum Hall state can be stable for azero tunnel splitting. The influence of the impurity potential on the stabilitycondition for the quantum Hall state has been analyzed.

The Stability of the Quantum Hall State at $\nu = 1$ in Bilayer Electron Systems