Decoherence without classicality in the resonant quantum kicked rotor

We study the quantum kicked rotor in resonance subjected to a unitary noise defined through Kraus operators. We show that this type of decoherence does not, in general, lead to the classical diffusive behavior. We find exact analytical expressions for the density matrix and the variance in the primary resonances. The variance does not loose its ballistic behavior; however, the coherence decays as a power law. The secondary resonances are treated numerically, obtaining a power-law decay for the variance and an exponential-law decay for the coherence.

Figure 1

The coherence $C\left(n\right)$ as a function of the dimensionless time $n$ in log-log scales for $\Delta \kappa =1000$. The coherence was calculated, from top to bottom, for $\alpha =0.1$, $\alpha =0.2$, $\alpha =0.3$, and $\alpha =0.5$. The straight stretches with slopes of $-0.5$ show a power-law behavior $C\left(n\right)\sim \frac{1}{\sqrt{n}}$.

Figure 2

The coherence $C\left(n\right)$ as a function of the dimensionless time $n$ for $\alpha =0.1$ in log-log scales. For large $n$ the curve satisfy a power law $C\left(n\right)\sim n^{-\gamma }$. The parameters of the curves, from top to bottom, are (1) $\Delta \kappa =0.2$ and $\gamma =0.36$, (2) $\Delta \kappa =0.3$ and $\gamma =0.37$, (3) $\Delta \kappa =1$ and $\gamma =0.4$, and (4) $\Delta \kappa =10$ and $\gamma =0.47$.

Figure 3

The standard deviation $\sigma \left(n\right)$ as a function of the dimensionless time $n$. The parameters are ${\kappa }_1=0.1$, ${\kappa }_2=0.2$, and $p/q=1/3$ in all cases. Dashed line $\alpha =0.1$ $\left(c=1.2\right)$, thick line $\alpha =0.2$ $\left(c=1.0\right)$, and thin line $\alpha =0.5$ $\left(c=0.9\right)$.