I read several books and papers on quantum chaos, to my understanding they all emphases that the quantum chaos does not really exist because the linearity of the Schrodinger equation. Some works were done on the so-called quantum kicked rotors which was used as a quantum counterpart for the classical chaos. The model is quantum however the way they study the rotors are quasi-classical. It just look like to study a classical but quantized map and come to the conclusion that the chaos is what they called 'quantum chaos'. Does it really make sense? Also, someone study the so-called chaos-assist turnelling based on the classical-quantized map, as we all know, in the classical case, no turnelling occurs, so if we start the motion in any stable orbit in the phase space, it not possible to jump into the chaotic area with external force. But they said the turnelling is possible because the model is quantum. Again, it is so confusing because
- they use a classical map to study the quantum model
- the map is classical but they consider it should work for quantum case
- they called quasi-classical method but apply the quantum characteristic without any reason?