LEVEL SPACING STATISTICS OF BIDIMENSIONAL FERMI LIQUIDS .2. LANDAU FIXED-POINT AND QUANTUM CHAOS

We investigate the presence of quantum chaos in the spectrum of the bi dimensional Fermi liquid by means of analytical and numerical methods. This model is integrable in a certain limit by bosonization of the Fe rmi surface. We study the effect on the level statistics of the moment um cut-off lambda present in the bidimensional bosonization procedure. We first analyse the level spacing statistics in the lambda-restricte d Hilbert space in one dimension. With g(2) and g(4) interactions, the level statistics are found to be Poissonian at low energies, and G.O. E. at higher energies, for a given cut-off lambda. In order to study t his cross-over, a finite temperature is introduced as a way of focussi ng, for a large inverse temperature beta, on the low energy many-body states, and driving the statistics from G.O.E. to Poissonian. As far a s two dimensions are concerned, we diagonalize the Fermi liquid Hamilt onian with a small number of orbitals. The level spacing statistics ar e found to be Poissonian in the lambda-restricted Hilbert space, provi ded the diagonal elements are of the same order of magnitude as the of f-diagonal matrix elements of the Hamiltonian.