Louis E, Vergés J A, Cuevas E
Departamento de Física Aplicada, Universidad de Alicante, Apartado 99, E-03080 Alicante, Spain.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jul;60(1):391-7. doi: 10.1103/physreve.60.391.
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 LxL 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 function decays exponentially with a characteristic correlation time (inverse of the Lyapunov exponent lambda). For small enough disorder the Lyapunov exponent 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 with L is investigated by keeping constant l/L, where l is the mean free path, the results show that lambda is proportional to 1/L.
