We have evaluated the angular-momentum-state occupation-number distribution functions for finite numbers of electrons in Laughlin states. For very small numbers of electrons the angular-momentum-state occupation numbers have been evaluated exactly while for larger numbers of electrons they have been obtained from Monte Carlo estimates of the one-particle density matrix. An exact relationship, valid for any number of electrons, has been derived for the ratio of the occupation numbers of the two outermost orbitals of the Laughlin droplet and is used to test the accuracy of the Monte Carlo calculations. We compare the occupation numbers near the outer edges of the droplets with predictions based on the chiral Luttinger-liquid picture of Laughlin state edges and discuss the surprisingly large oscillations in occupation numbers which occur for angular momenta far from the edge.
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Mitra et al. (1993) studied this question.
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