Neil F. Johnson — Page 9

arXiv1995

Entangled Electronic States in Multiple Quantum-Dot Systems

We present an analytically solvable model of $P$ colinear, two-dimensional quantum dots, each containing two electrons. Inter-dot coupling via the electron-electron interaction gives rise to sets of entangled ground states. These ground states have crystal-like inter-plane correlations and arise discontinously with increasing magnetic field. Their ranges and stabilities are found to depend on dot size ratios, and to increase with $P$.

cond-mat↗

arXiv1995

Analytic results for $N$ particles with $1/r^2$ interaction in two dimensions and an external magnetic field

The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $β/r^2$ in a two-dimensional parabolic potential $ω_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a $(2N-4)$-dimensional problem which is independent of $B$ and $ω_0$. An exact, infinite set of relative mode excitations are obtained for any $N$. The $N=3$ problem reduces to that of a ficticious particle in a two-dimensional, non-linear potential of strength $β$, subject to a ficticious magnetic field $B_{\rm fic}\propto J$, the relative angular momentum.

cond-mat↗