@article {ISI:000475499200001,
title = {Universal level statistics of the out-of-time-ordered operator},
journal = {Phys. Rev. B},
volume = {100},
number = {3},
year = {2019},
month = {JUL 15},
pages = {035112},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The out-of-time-ordered correlator has been proposed as an indicator of chaos in quantum systems due to its simple interpretation in the semiclassical limit. In particular, its rate of possible exponential growth at h -> 0 is closely related to the classical Lyapunov exponent. Here we explore how this approach to quantum chaos relates to the random-matrix theoretical description. To do so, we introduce and study the level statistics of the logarithm of the out-of-time-ordered operator, (Lambda) over cap (t) = In (-{[}(x) over cap (t),(p) over cap (x)(0)](2) )/(2t), that we dub the {\textquoteleft}{\textquoteleft}Lyapunovian{{\textquoteright}{\textquoteright}} or {\textquoteleft}{\textquoteleft}Lyapunov operator{{\textquoteright}{\textquoteright}} for brevity. The Lyapunovian{\textquoteright}s level statistics is calculated explicitly for the quantum stadium billiard. It is shown that in the bulk of the filtered spectrum, this statistics perfectly aligns with the Wigner-Dyson distribution. One of the advantages of looking at the spectral statistics of this operator is that it has a well-defined semiclassical limit where it reduces to the matrix of uncorrelated classical finite-time Lyapunov exponents in a partitioned phase space. We provide a heuristic picture interpolating these two limits using Moyal quantum mechanics. Our results show that the Lyapunov operator may serve as a useful tool to characterize quantum chaos and in particular quantum-to-classical correspondence in chaotic systems by connecting the semiclassical Lyapunov growth at early times, when the quantum effects are weak, to universal level repulsion that hinges on strong quantum interference effects.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.100.035112},
author = {Rozenbaum, Efim B. and Ganeshan, Sriram and Galitski, Victor}
}
@article {ISI:000393498700001,
title = {Dynamical localization of coupled relativistic kicked rotors},
journal = {PHYSICAL REVIEW B},
volume = {95},
number = {6},
year = {2017},
month = {FEB 6},
abstract = {A periodically driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent work {[}Phys. Rev. B 94, 085120 (2016)], A. C. Keser et al. considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization. In the present work, we study nonintegrable models of single and coupled quantum relativistic kicked rotors (QRKRs) that bridge the gap between the conventional quadratic rotors and the integrable linear models. For a single QRKR, we supplement the recent analysis of the angular-momentum-space dynamics with a study of the spin dynamics. Our analysis of two and three coupled QRKRs along with the proved localization in the many-body linear model indicate that dynamical localization exists in few-body systems. Moreover, the relation between QRKR and linear rotor models implies that dynamical many-body localization can exist in generic, nonintegrable many-body systems. And localization can generally result from a complicated interplay between Anderson mechanism and limiting integrability, since the many-body linear model is a high-angular-momentum limit of many-body QRKRs. We also analyze the dynamics of two coupled QRKRs in the highly unusual superballistic regime and find that the resonance conditions are relaxed due to interactions. Finally, we propose experimental realizations of the QRKR model in cold atoms in optical lattices.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.95.064303},
author = {Rozenbaum, Efim B. and Galitski, Victor}
}
@article {6621,
title = {Lyapunov Exponent and Out-of-Time-Ordered Correlator{\textquoteright}s Growth Rate in a Chaotic System},
journal = {Phys. Rev. Lett.},
volume = {118},
year = {2017},
month = {Feb},
pages = {086801},
doi = {10.1103/PhysRevLett.118.086801},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.118.086801},
author = {Rozenbaum, Efim B. and Ganeshan, Sriram and Galitski, Victor}
}