Figure 1

Surface of section of unperturbed (regular) system (left) and of the perturbed system with mixed regular chaotic dynamics (right).Reuse & Permissions

Figure 2

(a) The surface of section (SOS) for the distorted quadrupole billiard (main picture, upper half of SOS is shown), the shape of a billiard with bow-tie orbit shown (left inset) and the enlarged bow-tie island (right inset). The area of the red ellipse corresponds to the area used to calculate the analytical curve in panel (b); (b) Comparison between the mean level splitting the bow-tie modes in distorted quadrupole billiard (dots) and Eq. (4) (red line) (note that in optical resonators [10] ${\hslash }_{\mathrm{e}\mathrm{f}\mathrm{f}}=1/kR$); (c) SOS for the system of cold atoms in periodic laser field [12]. Arrows show the position of the symmetry-related regular states; (d) Comparison between the CAT-splittings between symmetry-related states in the system in (c) [12] (black lines) and our theory (red line).Reuse & Permissions

Figure 3

(a) Comparison between the level splitting (normalized to the median [5]) distribution for random matrix simulated data (red curve), Eq. (8) (green curve), and Cauchy distribution (blue curve). (b) Comparison between the level splitting distribution for the bow-tie orbit in quadrupole billiard for $kR=50$ with symmetric (pink curve) and asymmetric (red curve) distortion $\delta r$, analytical prediction given by Eq. (8) (green curve) and Cauchy distribution given by Eq. (6) (blue curve).Reuse & Permissions

Figure 4

Comparison between the nearest neighbor spacing distribution in the deformed elliptical microresonator for $kR\simeq 75$ (green), best fit Berry-Robnik distribution (blue) and our analytical result (red); the inset shows the limit of small spacing in more detail.Reuse & Permissions