# Is that true that real quantum chaos doesn't exist?

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

1. they use a classical map to study the quantum model
2. the map is classical but they consider it should work for quantum case
3. they called quasi-classical method but apply the quantum characteristic without any reason?
• Quantum chaos is the study of the quantum behavior of classically chaotic systems. It addresses the question of what are the signatures of classical chaos in the spectra and wave functions of quantum systems – Thomas Feb 19 '13 at 18:36
• Also, just because Schrodinger's equation is linear in the wave function doesn't mean that the potential need be linear as you add more particles. – Jerry Schirmer Feb 19 '13 at 18:47
• Thanks for the comment. That's also confusing to me, in the quantum language if the potential is nonlinear so why equation is still claimed as linear? It is always hard for me to distinguish the classical and quantum case – user1285419 Feb 19 '13 at 19:10
• Linear in this case means that the equation is linear with respect to the wave function (in the sense of linear function: en.wikipedia.org/wiki/Linear_function ). Specifically, superposition results in an answer that is the sum of the answers that would be given by the component parts. However, if the potential is understood to depend on the wavefunction, then this no longer holds. Even the simple three particle system is wicked tricky. – KDN Feb 20 '13 at 1:16
• There are systems that exhibit quantum chaos but are classically regular. You can't avoid having different definitions of chaos in the two cases. – JohnS Apr 12 '18 at 21:41