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We investigate the presence of quantum chaos in the spectrum of the bidimensional Fermi liquid by means of analytical and numerical methods. This model is integrable in a certain limit by bosonization of the Fermi surface. We study the effect on the level statistics of the momentum cut-off Λ present in the bidimensional bosonization procedure. We first analyse the level spacing statistics in the Λ-restricted Hilbert space in one dimension. With g2 and g4 interactions, the level statistics are found to be Poissonian at low energies, and G.O.E. at higher energies, for a given cut-off Λ. In order to study this cross-over, a finite temperature is introduced as a way of focussing, for a large inverse temperature β, on the low energy many-body states, and driving the statistics from G.O.E. to Poissonian. As far as two dimensions are concerned, we diagonalize the Fermi liquid Hamiltonian with a small number of orbitals. The level spacing statistics are found to be Poissonian in the Λ-restricted Hilbert space, provided the diagonal elements are of the same order of magnitude as the off-diagonal matrix elements of the Hamiltonian

Level Spacing Statistics of Bidimensional Fermi Liquids. II. Landau Fixed Point and Quantum Chaos