SOLVING 1D PLASMAS AND 2D BOUNDARY-PROBLEMS USING JACK POLYNOMIALS AND FUNCTIONAL RELATIONS

The general one-dimensional ''log-sine'' gas is defined by restricting the positive and negative charges of a two-dimensional Coulomb gas to live on a circle. Depending on charge constraints, this problem is eq uivalent to different boundary field theories. We study the electrical ly neutral case, which is equivalent to a two-dimensional free boson w ith an impurity cosine potential. We use two different methods: a pert urbative one based on Jack symmetric functions, and a non-perturbative one based on the thermodynamic Bethe ansatz and functional relations. The first method allows us to find an explicit series expression for all coefficients in the virial expansion of the free energy and the ex perimentally measurable conductance. Some results for correlation func tions are also presented. The second method gives an expression for th e full free energy, which yields a surprising fluctuation-dissipation relation between the conductance and the free energy.