Journal
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
Volume 71, Issue 10, Pages 897-907Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/zna-2016-0079
Keywords
Driven Quantum Systems; Floquet Theory; Quasi-Periodicity; Reducibility
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Funding
- European Research Council within project ODYCQUENT [259264]
- [2014-SGR-00504]
- [MTM2015-65715-P]
- European Research Council (ERC) [259264] Funding Source: European Research Council (ERC)
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Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasi-periodically driven quantum systems can be treated with generalisations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalisation of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.
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