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Quantum chaos comes from the classical chaos. unfortunately, the concept of trajectory is forbidden in quantum theory. So it is very difficult to define the quantum chaos.

Now many works use lots of methods to define it, for example, Random-Matrix theory, Level repulsion, and so on.

Now I have a question.

1. For a classical chaotic system, what phenomenon can we detect in the experiment, and then we can say it is chaos?

2. There are lots of definitions of quantum chaos. I don't know which one is most popular? Similarly, what phenomenon can we detect in the experiment, and then we can say it is chaos?

Thank you!