ON THE LARGE N LIMIT IN A MODEL WITH THE COLLECTIVE VARIABLE

Razvan Gurău

Abraham Klein

We describe a new form of the generalized density matrix theory which is free of the defects of the previous formulation. The application of the Wigner transform provides an economical derivation of time-dependent Hartree-Fock as the semi-classical limit. From this framework, we seek to illuminate some open questions in the theory of large amplitude collective motion, and to provide, thereby, a mathematically complete theory of the phenomenon.

Hideaki Hiro-Oka, Hisakazu Minakata

We present a large-N collective field formalism for anyons in external magnetic fields interacting with an arbitrary two-body potential. We discuss how the Landau levels are reproduced in our framework. We apply it to the soluble model for anyons proposed by Girvin et al., and obtain the dispersion relation of the collective modes for arbitrary statistical parameters.

Luigi Accardi, Yun Gang Lu

Branislav Jurčo

We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brézin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal polynomials and saddle point approximation. Large-N limit of the matrix model corresponds to the thermodynamic limit of the integrable system. In this limit (functional) Bethe ansatz is the same as the generating function for correlators of the matrix models.

Luigi Accardi, A. Frigerio, Yun Gang Lu