Figure 1

(a) Measured MR for the 7-dot array ($T=10\mathrm{mK}$). Arrows: positions of the resonant maxima and minima expressed by the values of ${\omega }_{+}/{\omega }_{-}$. Inset shows a micrograph of the 7-dot array. (b) Upper row: classically calculated trajectories for certain initial conditions in the entrance constriction. Lower row: QM density probabilities (yellow: highest, black: lowest probability). According to the actual dot shape we chose ${\omega }_{x,d}=1.06\times {10}^{12}{\mathrm{s}}^{-1}$, ${\omega }_y=0.85\times {10}^{12}{\mathrm{s}}^{-1}$, ${\omega }_{x,c}=2.16\times {10}^{12}{\mathrm{s}}^{-1}$; extension in $x$ direction: $0.32\mu \mathrm{m}$ (dot region), $0.076\mu \mathrm{m}$ (constriction region).Reuse & Permissions

Figure 2

$\mathrm{PS}\mathrm{\text{−}}{H}^P$ representations for different ratios of ${\omega }_{+}/{\omega }_{-}$: white dots represent the PS, color plots the $H^P$ (red: high, blue: low QM phase-space probability). (a) ${\omega }_{+}/{\omega }_{-}=1.6269$. The PS shows two types of KAM islands symbolized by (1) and (2) and a “sticky layer” (light gray) around them. The type-2 KAM islands in each dot have highest phase-space probability. (b) ${\omega }_{+}/{\omega }_{-}=2.0000$. The large white dots, in the regions where the chaotic sea has been drained, correspond to different periodic orbits. The red triangle (first dot, highest probability) represents a backscattered orbit [same initial condition as in Fig. 1b at ${\omega }_{+}/{\omega }_{-}=2.0000$]. (c) ${\omega }_{+}/{\omega }_{-}=3.0000$. Large white dots: as in (b). The phase-space probability (for $v_y>0$) is concentrated at the left transition between dot and constriction (symmetric with respect to the middle of the constriction if $v_y<0$ data are included). The red rectangle indicates the size of $\hslash$, i.e., the QM uncertainty. (d) Probability density for ${\omega }_{+}/{\omega }_{-}=3.0000$ (red: highest, blue: lowest probability).Reuse & Permissions

Figure 3

Phase space of the 7-dot array for ${\omega }_{+}/{\omega }_{-}=1.6269$ ($B\approx 0.16\mathrm{T}$). (a) Magnification of the two types of KAM islands in a two-dimensional ($v_{x,}x$) PS symbolized by (1) and (2) and a “sticky layer” (light gray) around them. $v_F=2.1\times {10}^5\mathrm{m}/\mathrm{s}$. (b) Left panel: trajectories at the center of the two KAM islands attributed to the pure ${\omega }_{+}$ (1) and pure ${\omega }_{-}$ (2) mode, showing two different circulations. Right panel: probability current density (red: current flow to the right, blue: current flow to the left).Reuse & Permissions