Mapping of the Calogero-Sutherland Model to the Gaussian Model

where d(x) = |(L/π) sin[πx/L]| and L is the systems size. At the special values λ = 1/2, 1 and 2, the CSM describes statistics of eigenvalues of random matrices belonging to one of the three Dyson’s ensembles. Recently these special cases were intensely studied in connection with the theory of universal spectral correlations in random systems [1]. The spectrum of CSM was obtained by the so-called Asymptotic Bethe Ansatz [2] and turns out to be very simple due to the fact that CSM has a trivial twoparticle scattering phase equal to φ(k1, k2) = π(λ − 1)sign(k1 − k2). As a consequence the CSM can be thought of as an ideal gas of excitations obeying the fractional exclusion principle formulated in Ref.[3]. It is not surprising that a theory with such a simple S-matrix has particularly simple correlation functions. The exact expression for the density-density