Action-Quantized Scar Multiplets and Dissipative Cat States from Fractal Period-Locking in the Open Quantum Baker Map

We open the quantum baker map with a position window of width $w$ and center $q_c$. Classical pruning tiles the $(q_c,w)$ plane into diamonds where the $T$ leading resonances form root-of-unity multiplets. At $w=1/2$ one periodic orbit survives for almost every $q_c$, and the multiplets are quantize