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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/ r 2 potential can be expressed in terms of this excess chemical potential and thus evaluated explicitly.
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