 The first two questions focus on different directions of research, both related to what is known as semi-classical mechanics. In the first, investigation starts with a classical chaotic system and seeks to quantize it to study its quantum behavior. To quantize a classical model, one replaces functions in the equations of motion with their corresponding quantum operators. Here, there are various results demonstrating that strongly ergodic classical billiards, when quantized, exhibit quantum ergodicity. But this is not the same as showing that a classical chaotic system, when quantized, exhibits chaotic behavior. There are no examples of the latter due to the reasons listed at the beginning of this subsection.