SIMPLE-MODEL FOR QUANTUM CHAOS

A simple second-quantized model exhibiting quantum chaos is introduced. Experimentally, this model could be realized as a triplet excitation of a molecule. Numerically, it requires only a minimal amount of computer time. Two cases of this model with and without inversion symmetry are discussed. The level spacing distribution of the case without inversion symmetry shows an especially close resemblance to the Wigner distribution. A related classical billiard model on a 1/r-potential-energy surface is presented as a continuum extension of our model. The real-space representation of the Hamiltonian shows a self-similarity, whose fractal dimension is calculated to be 1.5.