Correlation decay in quantum chaotic billiards with bulk or surface disorder

We study the decay properties of correlation functions in quantum billiards with surface or bulk disorder. The quantum system is modeled by means of a tight-binding Hamiltonian with diagonal disorder, solved on L x L clusters of the square lattice. The correlation function is calculated by launching the system at t = 0 into a wave function of the regular (clean) system and following its time evolution. The results show that the correlation functi on decays exponentially with a characteristic correlation time (inverse of the Lyapunov exponent lambda). For small enough disorder the Lyapunov expon ent is approximately given by the imaginary part of the self-energy induced by disorder. On the other hand, if the scaling of the Lyapunov exponent wi th L is investigated by keeping constant l/L, where I is the mean free path , the results show that lambda proportional to 1/L. [S1063-651X(99)00607-8] .