Dipoles at $\nu =1$

Abstract

We consider the problem of Bosonic particles interacting repulsively in a strong magnetic field at the filling factor $\nu =1.$ We project the system in the Lowest Landau Level and map the dynamics into an interacting Fermion system. We study the resulting Hamiltonian in the Hartree--Fock approximation in the case of a $\delta $ repulsive potential. The physical picture which emerges is in agreement with the proposal of N. Read that the composite Fermions behave as a gas of dipoles. We argue that the consequence of this is that the composite Fermions interact with screened short range interactions. We develop a Landau theory which we also expect to describe the physical $\nu =1/2$ Fermionic state. The Form factor, the effective mass and the conductivity are analised in this model.