A constant term identity and its relationship to the log-gas and some quantum many body systems

Abstract

The excess chemical potential of an impurity charge in the one-component log-gas on a line in periodic boundary conditions is calculated by using an identity for the constant term in the Laurent expansion of a certain multivariable function. The coefficient of the leading term in the large separation expansion of the ground state one-particle density matrix for the one-dimensional quantum many body system with the 1/r2 potential can be expressed in terms of this excess chemical potential and thus evaluated explicitly. © 1992.