Abstract
Nonlinear dynamical systems with only one space dimension can undergo a transition to chaos if they are driven by a time-periodic force. In this chapter, we focus on the dynamics of quantum systems with time-periodic Hamiltonians as they undergo a transition from a regime in which they exhibit integrable-like behavior to a regime where they exhibit the manifestations of chaos. Time-periodic systems have discrete time-translation invariance, and their dynamics is constrained by conservation laws. For such systems, the Floquet energy (also called quasienergy) is a constant of the motion even in the presence of a transition to chaos in the underlying classical phase space. For intense time-periodic fields, the Floquet states appear to describe coherent photon structures that result from the interaction between the driving field and the nonlinear forces of the driven system.
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Reichl, L.E. (2004). Time-Periodic Systems. In: The Transition to Chaos. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4350-0_9
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DOI: https://doi.org/10.1007/978-1-4757-4350-0_9
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