Weak localization of the open kicked rotator

We present a numerical calculation of the weak localization peak in the magnetoconductance for a stroboscopic model of a chaotic quantum dot. The magnitude of the peak is close to the universal prediction of random-matrix theory. The width depends on the classical dynamics, but this dependence can be accounted for by a single parameter: the level curvature around zero magnetic field of the closed system.

Figure 1

The critical value ${\gamma }_c$ of the TRS-breaking parameter in the closed three-kick model is presented for different system sizes at fixed $K$. The parity-breaking parameter is $q=0.2$. The solid line shows the large-$K$ limit (3.8). The dashed lines are averages over $M$ of the numerical data.

Figure 2

Same as Fig. 1, but now for the closed one-kick model. The parity-breaking parameter is $\varphi =0.2\pi$. The solid line shows the large-$K$ limit (3.9).

Figure 3

Dependence of the average conductance on the TRS-breaking parameter $\gamma$. The three-kick model is characterized by $K=7.5$, $q=0.2$, and ${\tau }_D=M∕2N=25$. The dotted line shows the RMT prediction (3.11), with ${\gamma }_c$ calculated from the mean level curvatures (Fig. 1).

Figure 4

Same as Fig. 3, but for $K=41$.

Figure 5

Dependence of the crossover parameter ${\gamma }^{*}$ on the system size. The data are obtained by fitting the Lorentzian (4.1) to the numerical data of Figs. 3, 4. The solid line shows the large $K$ limit (3.8). The dotted lines are the RMT prediction for $K=7.5$ and $K=41$, using ${\gamma }_c$ found from the level curvatures in the closed model (Fig. 1).

Figure 6

Dependence of the ratio ${\gamma }^{*}∕{\gamma }_{\mathrm{RMT}}^{*}$ for the three-kick model and the ratio ${\delta }^{*}∕{\delta }_{\mathrm{RMT}}^{*}$ for the one-kick model on the dwell time ${\tau }_D$. Data points for a given dwell time are obtained by averaging over system sizes in the range from $200$ to $1000$.

Figure 7

Dependence of the amplitude of the weak localization peak $\delta G\left(0\right)$ (averaged over several system sizes) on the dwell time ${\tau }_D$. Dashed lines show a linear dependence on $1∕{\tau }_D$, extrapolated to the RMT value $\mid \delta G\left(0\right)\mid =1∕4$.

Figure 8

Dependence of $\delta G\left(0\right)$ on the system size $M$ for several dwell times. Dashed lines show averages over system size.