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arXiv:0901.1709 · Europhysics Letters (EPL)

Pair distribution function of one-dimensional “hard-sphere” Fermi and Bose systems

Bo-Bo Wei, Chen-Ning Yang

Published Jul 1, 2009• 1 citation
arXivHTMLPDF

Abstract

The pair distributions of one-dimensional "hard-sphere" fermion and boson systems are exactly evaluated by using gap variables.
DOI
10.1209/0295-5075/87/10005

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The pair distribution function for a hard sphere Bose system has been calculated by using a method in which the hard sphere potential is replaced by the so-called pseudo-potential. The problem is carried through using the quasi-particle formalism of Bogoliubov. In this calculation one considers a system of bosons interacting via the pseudo-potential which can be regarded as a weak interaction when the system is very dilute. The Hamiltonian of the system is diagonalized by means of a canonical transformation which has the effect of separating the energy into two parts, one of which is the ground state energy and the other corresponds to an ideal Bose gas composed of ``elementary excitations'' or ``quasi-particles.'' This formalism is applied to the calculation of the pair distribution function. This quantity is calculated by averaging over a grand canonical ensemble constructed with the total number of elementary excitations. A result which is seen to be valid both for the condensed and gaseous phases of the system and also for any distance r between the particles is obtained. A discussion of the difference between these results and the ones obtained in a previous calculation and a comparison between both results and the experimental ones is also given.