title: 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 n1, … nrparticles 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.
authors.affiliation: Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, SP, 09210-170, Brazil. valery@ufabc.edu.br.
authors.forename: Valery S
authors.identifier: 0000-0002-6294-4993
authors.initials: VS
authors.lastname: Shchesnovich