Numerical Studies of Quantum Chaos in Various Dynamical Systems

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dc.contributor.advisorGalitski, Victoren_US
dc.contributor.authorRozenbaum, Efimen_US
dc.contributor.departmentPhysicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2020-07-10T05:34:33Z
dc.date.available2020-07-10T05:34:33Z
dc.date.issued2020en_US
dc.description.abstractWe study two classes of quantum phenomena associated with classical chaos in a variety of quantum models: (i) dynamical localization and its extension and generalization to interacting few- and many-body systems and (ii) quantum exponential divergences in high-order correlators and other diagnostics of quantum chaos. Dynamical localization (DL) is a subtle phenomenon related to Anderson localization. It hinges on quantum interference and is typically destroyed in presence of interactions. DL often manifests as a failure of a driven system to heat up, violating the foundations of statistical physics. Kicked rotor (KR) is a prototypical chaotic classical model that exhibits linear energy growth with time. The quantum kicked rotor (QKR) features DL instead: its energy saturates. Multiple attempts of many-body generalizations faced difficulties in preserving DL. Recently, DL was shown in a special integrable many-body model. We study non-integrable models of few- and many-body QKR-like systems and provide direct evidence that DL can persist there. In addition, we show how a novel related concept of localization landscape can be applied to study transport in rippled channels. Out-of-time-ordered correlator (OTOC) was proposed as an indicator of quantum chaos, since in the semiclassical limit, this correlator's possible exponential growth rate (CGR) resembles the classical Lyapunov exponent (LE). We show that the CGR in QKR is related, but distinct from the LE in KR. We also show a singularity in the OTOC at the Ehrenfest time tᴱ due to a delay in the onset of quantum interference. Next, we study scaling of OTOC beyond tᴱ. We then explore how the OTOC-based approach to quantum chaos relates to the random-matrix-theoretical description by introducing an operator we dub the Lyapunovian. Its level statistics is calculated for quantum stadium billiard, a seminal model of quantum chaos, and aligns perfectly with the Wigner-Dyson surmise. In the semiclassical limit, the Lyapunovian reduces to the matrix of uncorrelated finite-time Lyapunov exponents, connecting the CGR at early times, when the quantum effects are weak, to universal level repulsion that hinges on strong quantum interference. Finally, we consider quantum polygonal billiards: their classical counterparts are non-chaotic. We show exponential growth of the OTOCs in these systems, sharply contrasted with the classical behavior even before quantum interference develops.en_US
dc.identifierhttps://doi.org/10.13016/jhya-zr5d
dc.identifier.urihttp://hdl.handle.net/1903/26199
dc.language.isoenen_US
dc.subject.pqcontrolledQuantum physicsen_US
dc.subject.pqcontrolledComputational physicsen_US
dc.subject.pqcontrolledPhysicsen_US
dc.subject.pquncontrolledLyapunov operatoren_US
dc.subject.pquncontrolledMany-body dynamical localizationen_US
dc.subject.pquncontrolledOut-of-time-ordered correlatoren_US
dc.subject.pquncontrolledQuantum chaosen_US
dc.subject.pquncontrolledQuantum Lyapunov exponenten_US
dc.subject.pquncontrolledSemi-classical physicsen_US
dc.titleNumerical Studies of Quantum Chaos in Various Dynamical Systemsen_US
dc.typeDissertationen_US

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