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

Abstract

The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $\beta /r^2$ in a two-dimensional parabolic potential ${\omega }_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a $(2N-4)$-dimensional problem which is independent of $B$ and ${\omega }_0$. 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 $\beta$, subject to a ficticious magnetic field $B_{\mathrm{fic}}\propto J$, the relative angular momentum.

To appear in Physical Review Letters (in press). RevTeX file. Two figures available from [email protected] or [email protected]

References in corpus (1)

• Addition Spectra of Quantum Dots in Strong Magnetic Fields

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