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Nonequilibrium Quantum Dynamics of Many-Body Systems

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Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that takes them out of equilibrium; on the Hamiltonian, whether it is integrable or chaotic; and on the onset of multifractal eigenstates that occurs in the vicinity of the transition to a many-body localized phase. We unveil different behaviors at different time scales. We also discuss how information about the spectrum of a many-body quantum system can be extracted by the sole analysis of its time evolution, giving particular attention to the so-called correlation hole. This approach is useful for experiments that routinely study dynamics, but have limited or no direct access to spectroscopy, as experiments with cold atoms and trapped ions.

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Acknowledgements

LFS was supported by the NSF grant No. DMR-1603418. EJTH acknowledges funding from PRODEP-SEP and Proyectos VIEP-BUAP, Mexico.

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Authors and Affiliations

  1. Department of Physics, Yeshiva University, New York, NY, 10016, USA

    Lea F. Santos

  2. Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apt. Postal J-48, Puebla, 72570, Puebla, Mexico

    E. Jonathan Torres-Herrera

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  1. Lea F. Santos
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  2. E. Jonathan Torres-Herrera
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Correspondence to Lea F. Santos .

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Editors and Affiliations

  1. Stern College for Women, Yeshiva University, New York, New York, USA

    Mark Edelman

  2. INPE/LAC, Instituto Nacional de Pesquisas Espaciai, São José dos Campos, São Paulo, Brazil

    Elbert E. N. Macau

  3. Departamento de Fisica, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain

    Miguel A. F. Sanjuan

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Santos, L.F., Torres-Herrera, E.J. (2018). Nonequilibrium Quantum Dynamics of Many-Body Systems. In: Edelman, M., Macau, E., Sanjuan, M. (eds) Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-68109-2_12

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