Generalizing the Quinn-Wojs Theorem on Distinct Multiplets of Composite Fermions
The combinatorial tool of generating functions for restricted partitions is used to generalize a quantum physics theorem relating distinct multiplets of different angular momenta in the composite Fermion model of the fractional quantum Hall effect. Specifically, if gℓ(N,M)gℓ(N,M) denotes the number of distinct multiplets of angular momentum ℓℓ and total angular momentum M, we prove that
where the sum is taken over all positive divisors of N and L(k)=kℓ-kN/2+3k/2-N+N/(2k)-1/2L(k)=kℓ-kN/2+3k/2-N+N/(2k)-1/2. The original Quinn–Wójs theorem results when k=1k=1 and it appears that this generalization will be useful in further investigations of nuclear shells modeling elementary particle interactions when the particles are clustered together.
Quinn, Jennifer J. and Tobiska, Josef M., "Generalizing the Quinn-Wojs Theorem on Distinct Multiplets of Composite Fermions" (2005). SIAS Faculty Publications. 214.