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Quantum and Classical Manifestation of Hamiltonian Monodromy
Chen, Chen
Chen, Chen
Abstract
Integrable Hamiltonian systems are said to display nontrivial monodromy if fundamental action-angle loops defined on phase-space tori change their topological structure when the system is carried around a circuit. It was shown in earlier work that this topological change can be seen in families of trajectories of noninteracting particles; however, that work required use of a very abstract flow in phase space. In this dissertation, we show that the same topological change can occur as a result of application of ordinary forces. We also show how this dynamical phenomenon could be observed experimentally in cold atom systems. Almost everything that happens in classical mechanics also shows up in quantum mechanics when we know where to look for it. In the latter half of the dissertation, we show a corresponding change in quantum wave functions: these wave functions change their topological structure in the same way that the action and angle loops change. Also the probability current associated with this wave function follows the angle loop, changing its winding number from 0 to -1.
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2017-06-14
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Physics
DOI
http://dx.doi.org/doi:10.21220/S2X675