Abstract
In the previous chapter, I classified Hamiltonians H and Floquet operators F by their groups of canonical transformations. Now I propose to show that orthogonal, unitary, and symplectic canonical transformations correspond to level repulsion of, respectively, linear, quadratic, and quartic degree [48, 49]. The different canonical groups are thus interesting not only from a mathematical point of view but also have distinct measurable consequences. It is a fascinating feature of quantum mechanics that different behavior under time reversal actually becomes observable experimentally. The origin of this phenomenon lies in the antilinearity of the quantum mechanical time-reversal operator — a property alien to classical mechanics.
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Haake, F. (2001). Level Repulsion. In: Quantum Signatures of Chaos. Springer Series in Synergetics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04506-0_3
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