Aging effects in the quantum dynamics of a dissipative free particle: non-ohmic case

We report new results related to the two-time dynamics of the coordinate of a quantum free particle, damped through its interaction with a fractal thermal bath (non-ohmic coupling $\sim {\omega }^{\delta }$ with $0<\delta <1$ or $1<\delta <2)$. When the particle is localized, its position does not age. When it undergoes anomalous diffusion, only its displacement may be defined. It is shown to be an aging variable. The finite temperature aging regime is self-similar. It is described by a scaling function of the ratio $t_w\mathrm{/}\tau$ of the waiting time to the observation time, as characterized by an exponent directly linked to $\delta$.