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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 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.

SUBMITTER: Shchesnovich VS

PROVIDER: S-EPMC5428393 | biostudies-literature | 2017 Feb

REPOSITORIES: biostudies-literature

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Asymptotic Gaussian law for noninteracting indistinguishable particles in random networks.

Shchesnovich Valery S VS

Scientific reports 20170216 1

For N indistinguishable bosons or fermions impinged on a M-port Haar-random unitary network the average probability to count n <sub>1</sub>, … n <sub>r</sub> 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 ...[more]

PMID: 28194000

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