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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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