Analogues between a quantum many body problem and the log-gas

Abstract

The ground state wavefunction of a t-component quantum system in one dimension interacting via the 1/r2 potential is interpreted as the Boltzmann probability factor of a t-component log-gas. This allows predictions regarding the asymptotic behaviour of the ground state correlations and density matrix to be made. Using the results of an exact calculation of a two-component log-gas, exact results are obtained for the quantum system in the case t=2.