Environmental stability of quantum chaotic ratchets

The transitory and stationary behavior of a quantum chaotic ratchet consisting of a biharmonic potential under the effect of different drivings in contact with a thermal environment is studied. For weak forcing and finite $\hslash$, we identify a strong dependence of the current on the structure of the chaotic region. Moreover, we have determined the robustness of the current against thermal fluctuations in the very weak coupling regime. In the case of strong forcing, the current is determined by the shape of a chaotic attractor. In both cases the temperature quickly stabilizes the ratchet, but in the latter it also destroys the asymmetry responsible for the current generation. Finally, applications to isomerization reactions are discussed.

Figure 1

Classical (contour lines) and quantum (gray scale density plot) phase space distributions for $t=50$ (in units of the period of the forcing). In the upper row $F=0.02$ and in the lower one $F=0.05$. We display the cases (from left to right) for $T=0$, $T=0.01$, and $T=0.1$. In all cases $\Gamma ={10}^{-4}$ and $\hslash =0.041$.

Figure 2

Quantum current as a function of time $t$ (in units of the period of the forcing) for the cases shown in Fig. 1. In panel (a) $F=0.02$ and in (b) $F=0.05$. Blue dot-dashed lines correspond to $T=0$, orange dashed lines to $T=0.01$, and black solid lines to $T=0.1$. In all cases $\Gamma ={10}^{-4}$ and $\hslash =0.041$.

Figure 3

Classical (contour lines) and quantum (gray scale density plot) phase space distributions for $t=50$ (in units of the period of the forcing). From left to right and top to bottom we show the results corresponding to $T=0$, $T=0.001$, $T=0.01,$ and $T=0.1$, respectively. In all cases $F=2.5$, $\Gamma =0.05,$ and $\hslash =0.041$.

Figure 4

Classical (thin lines with symbols) and quantum current as a function of time $t$ (in units of the period of the forcing) for some of the cases shown in Fig. 3. Blue dot-dashed lines (and circles for the classical case) correspond to $T=0$, orange dashed lines (and squares for the classical case) to $T=0.01$, and black solid lines (and diamonds for the classical case) to $T=0.1$. In all cases $F=2.5$, $\Gamma =0.05,$ and $\hslash =0.041$. In the inset we show the stabilization region enlarged for the sake of clarity.

Figure 5

Classical (left panel) and quantum (right panel) phase space distributions at time $t=50$ corresponding to $T=0$. In all cases $F=2.5$, $\Gamma =0.05$ and $\hslash \simeq 0.0015$.