Asymptotic Gaussian law for noninteracting indistinguishable particles in random networks
Abstract For N indistinguishable bosons or fermions impinged on a M-port Haar-random unitary network the average probability to count n 1, … n r particles in a small number r ≪ N of binned-together output ports takes a Gaussian form as N ≫ 1. The discovered Gaussian asymptotic law is the well-known...
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| Format: | article |
| Langue: | EN |
| Publié: |
Nature Portfolio
2017
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| Accès en ligne: | https://doaj.org/article/e10c85d538e344e082b1e60d1e9133f7 |
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| Résumé: | Abstract For N indistinguishable bosons or fermions impinged on a M-port Haar-random unitary network the average probability to count n 1, … n r particles in a small number r ≪ N of binned-together output ports takes a Gaussian form as N ≫ 1. The discovered Gaussian asymptotic law is the well-known asymptotic law for distinguishable particles, governed by a multinomial distribution, modified by the quantum statistics with stronger effect for greater particle density N/M. Furthermore, it is shown that the same Gaussian law is the asymptotic form of the probability to count particles at the output bins of a fixed multiport with the averaging performed over all possible configurations of the particles in the input ports. In the limit N → ∞, the average counting probability for indistinguishable bosons, fermions, and distinguishable particles differs only at a non-vanishing particle density N/M and only for a singular binning K/M → 1, where K output ports belong to a single bin. |
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