Classical and Quantum Mixed-Type Lemon Billiards without Stickiness

The boundary of the lemon billiards is defined by intersection two circles equal unit radius with distance $2B$ between their centers, as introduced Heller and Tomsovic in Phys. Today {\bf 46} 38 (1993). This paper a continuation our recent on classical quantum ergodic billiard ($B=0.5$) strong stickiness effects published Rev. E 103} 012204 (2021). Here we study billiards, for cases $B=0.42,\;0.55,\; 0.6$, which are mixed-type without regions thus serve ideal examples systems simple divided phase space. portraits show structure one large chaotic sea uniform chaoticity (no regions) surrounding regular island almost no further substructure, being entirely covered invariant tori. smooth, except few points. transport time estimated to be very short (just collisions), therefore localization eigenstates rather weak. states characterized following {\em universal} properties regions:(i) Using Poincar\'e-Husimi (PH) functions separated ones ones. eigenenergies obey Poissonian statistics, while exhibit Brody distribution various values level repulsion exponent $\beta$, its value depending strength eigenstates. Consequently, total spectrum well described Berry-Robnik-Brody (BRB) distribution.