Quantum-classical transition and quantum activation of ratchet currents in the parameter space

The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero-temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed based on quantum, semiclassical, and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.

Figure 1

The parameter spaces showing the (a) $C_Q$, (b) $C_S$, for ${\hslash }_{\text{eff}}=0.082$, and (c) $C_C$ for $T_{\text{eff}}=0.082$. Red (green) to yellow (white) colors are related to increasing negative (positive) currents [marked with ($-$) and ($+$) for the printed grayscale]. Note the black boundaries delimiting positive and negative currents. In (d) we have the $C_C$ for $T_{\text{eff}}=0$ with black colors related to close to zero currents; green to blue colors (light to dark gray) are related to increasing positive currents while red, yellow to purple (white to light gray) colors related to increasing negative currents. Letters denote the chaotic background $A$ and the ISSs $B_1,B_2,C_{-1}$, and $F$.

Figure 2

Plotted is (a) $\left|C_S\right|-\left|C_Q\right|$ and (b) $\left|C_C\right|-\left|C_Q\right|$ (for $T_{\mathrm{eff}}=0.082$) from the data of Fig. 1 [Symbols ($-$)/($+$) to identify the negative and positive currents in printed grayscale].

Figure 3

Plotted is $\mathcal{D}(\tilde{p},p)$ for (a) ${\hslash }_{\text{eff}}=0.0001$ and (b) ${\hslash }_{\text{eff}}=0.082$, and the activation and suppression $\delta \left({\hslash }_{\text{eff}}\right)$ for (c) ${\hslash }_{\text{eff}}=0.01$ and (d) ${\hslash }_{\text{eff}}=0.082$.