Non exponential quasiparticle decay and phase relaxation in low dimensional conductors

We show that in low dimensional disordered conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In the quasi-one dimensional case, both behave at small time as $e^{- (t/\tau_{in})^{3/2}}$ where the inelastic time $\tau_{in}$, identical for both processes, is a power $T^{2/3}$ of the temperature. This result implies the existence of an unusual distribution of relaxation times that we obtain.