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Springer eBooks

Manifestations of Bose and Fermi Statistics on the Quantum Distribution Function for Systems of Spin-0 and Spin-1/2 Particles

Robert F. O’Connell, Eugene Paul Wigner

Published Jan 1, 1997• 0 citations
Publisher
DOI
10.1007/978-3-642-59033-7_29

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In this paper, we show two kinds of entangled many body systems with special statistic properties. Firstly, an entangled fermions system with a pairwise entanglement between every two particles in the lowest energy energy level obeys the fractional statistics. As a check, for particle number N=2, N=3 and N=4, considering that any two fermions in the lowest Landau level are entangled in a proper way, the Laughlin wave function can be derived. The results reveals the explicit entanglement pattern of the Laughlin states. Secondly, we noticed that both Bose-Einstein statistics and Fermi-Dirac distributions are derived from computing the partial function of a free quantum many body system in a certain ensemble without considering entanglement. We extend the computation of the partial function to an entangled quantum many body system without interaction, in this system we assume that every particle in energy level εiε_iεi​ is entangled with a particle in the energy level εi+1ε_{i+1}εi+1​ (i=1,3,5,...i=1,3,5,...i=1,3,5,...) and also every particle in energy level εi+1ε_i+1εi​+1 is entangled with a particle in the energy level εiε_{i}εi​ (i=1,3,5,...i=1,3,5,...i=1,3,5,...), which indicates that the two energy level have the same number of particles. In the entangled system, we find that the partial function will be changed. As a results, both the Bose-Einstein Statics and the Fermi-Dirac distributions will be modified at finite temperature.