Lyapunov exponents and poles in a non Hermitian dynamics

By means of expressing volumes in phase space in terms of traces of quantum operators, a relationship between the poles of the scattering matrix and the Lyapunov exponents in a non Hermitian quantum dynamics, is presented. We illustrate the formalism by characterizing the behavior of the Gamow model whose dissipative decay time, measured by its decoherence time, is found to be inversely proportional to the Lyapunov exponents of the unstable periodic orbits. The results are in agreement with those obtained by means of the semiclassical periodic-orbit approach in quantum resonances theory but using a simpler mathematics.