  By means of expressing volumes in phase space in terms of traces of quantum
operators, a relationship between the Hamiltonian poles 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.
