Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2

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dc.AffiliationOctober University for modern sciences and Arts (MSA)
dc.contributor.authorV. Fine, Boris
dc.contributor.authorA. Elsayed, Tarek
dc.contributor.authorM. Kropf, Chahan
dc.contributor.authorS. de Wijn, Astrid
dc.date.accessioned2020-02-26T09:16:17Z
dc.date.available2020-02-26T09:16:17Z
dc.date.issued2014
dc.descriptionMSA Google Scholaren_US
dc.description.abstractWe show that macroscopic nonintegrable lattices of spins 1/2, which are often considered to be chaotic, do not exhibit the basic property of classical chaotic systems, namely, exponential sensitivity to small perturbations. We compare chaotic lattices of classical spins and nonintegrable lattices of spins 1/2 in terms of their magnetization responses to imperfect reversal of spin dynamics known as Loschmidt echo. In the classical case, magnetization exhibits exponential sensitivity to small perturbations of Loschmidt echoes, which is characterized by twice the value of the largest Lyapunov exponent of the system. In the case of spins 1/2, magnetization is only power-law sensitive to small perturbations. Our findings imply that it is impossible to define Lyapunov exponents for lattices of spins 1/2 even in the macroscopic limit. At the same time, the above absence of exponential sensitivity to small perturbations is an encouraging news for the efforts to create quantum simulators. The power-law sensitivity of spin 1/2 lattices to small perturbations is predicted to be measurable in nuclear magnetic resonance experiments.en_US
dc.description.sponsorshipAmerican Physical Societyen_US
dc.description.urihttps://www.scimagojr.com/journalsearch.php?q=21100855841&tip=sid&clean=0
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dc.identifier.urihttps://t.ly/JXke5
dc.language.isoenen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.ispartofseriesPhysical Review E;Volume 89 Issue 1 page: 1-12
dc.subjectUniversity of Exponential sensitivityen_US
dc.titleAbsence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2en_US
dc.typeArticleen_US

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