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Rangi C, Moreno J, Tam KM. Out of time order correlation of the Hubbard model with random local disorder. CHAOS (WOODBURY, N.Y.) 2024; 34:073143. [PMID: 39042506 DOI: 10.1063/5.0206420] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 07/02/2024] [Indexed: 07/25/2024]
Abstract
The out-of-time-order correlator (OTOC) serves as a powerful tool for investigating quantum information spreading and chaos in complex systems. We present a method employing non-equilibrium dynamical mean-field theory and coherent potential approximation combined with diagrammatic perturbation on the Schwinger-Keldysh contour to calculate the OTOC for correlated fermionic systems subjected to both random disorder and electron interaction. Our key finding is that random disorder enhances the OTOC decay in the Hubbard model for the metallic phase in the weakly interacting limit. However, the current limitation of our perturbative solver restricts the applicability to weak interaction regimes.
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Affiliation(s)
- Chakradhar Rangi
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Juana Moreno
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
- Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Ka-Ming Tam
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
- Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
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2
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Zhang C, Kundu S, Makri N, Gruebele M, Wolynes PG. Quantum information scrambling and chemical reactions. Proc Natl Acad Sci U S A 2024; 121:e2321668121. [PMID: 38557180 PMCID: PMC11009637 DOI: 10.1073/pnas.2321668121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 02/22/2024] [Indexed: 04/04/2024] Open
Abstract
The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.
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Affiliation(s)
- Chenghao Zhang
- Department of Physics, University of Illinois Urbana-Champaign, IL61801
| | - Sohang Kundu
- Department of Chemistry, University of Illinois Urbana-Champaign, IL61801
| | - Nancy Makri
- Department of Physics, University of Illinois Urbana-Champaign, IL61801
- Department of Chemistry, University of Illinois Urbana-Champaign, IL61801
| | - Martin Gruebele
- Department of Physics, University of Illinois Urbana-Champaign, IL61801
- Department of Chemistry, University of Illinois Urbana-Champaign, IL61801
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, IL61801
- Carle-Illinois College of Medicine, University of Illinois at Urbana-Champaign, IL61801
| | - Peter G. Wolynes
- Department of Chemistry, Rice University, Houston, TX77251
- Department Physics, Rice University, Houston, TX77251
- Center for Theoretical Biological Physics, Rice University, Houston, TX77251
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3
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Schuster T, Yao NY. Operator Growth in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2023; 131:160402. [PMID: 37925733 DOI: 10.1103/physrevlett.131.160402] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 09/06/2023] [Indexed: 11/07/2023]
Abstract
The spreading of quantum information in closed systems, often termed scrambling, is a hallmark of many-body quantum dynamics. In open systems, scrambling competes with noise, errors, and decoherence. Here, we provide a universal framework that describes the scrambling of quantum information in open systems: we predict that the effect of open-system dynamics is fundamentally controlled by operator size distributions and independent of the microscopic error mechanism. This framework allows us to demonstrate that open quantum systems exhibit universal classes of information dynamics that fundamentally differ from their unitary counterparts. Implications for the Loschmidt echo, nuclear magnetic resonance experiments, and the classical simulability of open quantum dynamics will be discussed.
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Affiliation(s)
- Thomas Schuster
- Department of Physics, University of California, Berkeley, California 94720, USA
- Walter Burke Institute for Theoretical Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Norman Y Yao
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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4
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Steinhuber M, Schlagheck P, Urbina JD, Richter K. Dynamical transition from localized to uniform scrambling in locally hyperbolic systems. Phys Rev E 2023; 108:024216. [PMID: 37723671 DOI: 10.1103/physreve.108.024216] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 07/23/2023] [Indexed: 09/20/2023]
Abstract
Fast scrambling of quantum correlations, reflected by the exponential growth of out-of-time-order correlators (OTOCs) on short pre-Ehrenfest time scales, is commonly considered as a major quantum signature of unstable dynamics in quantum systems with a classical limit. In two recent works [Phys. Rev. Lett. 123, 160401 (2019)0031-900710.1103/PhysRevLett.123.160401] and [Phys. Rev. Lett. 124, 140602 (2020)10.1103/PhysRevLett.124.140602], a significant difference in the scrambling rate of integrable (many-body) systems was observed, depending on the initial state being semiclassically localized around unstable fixed points or fully delocalized (infinite temperature). Specifically, the quantum Lyapunov exponent λ_{q} quantifying the OTOC growth is given, respectively, by λ_{q}=2λ_{s} or λ_{q}=λ_{s} in terms of the stability exponent λ_{s} of the hyperbolic fixed point. Here we show that a wave packet, initially localized around this fixed point, features a distinct dynamical transition between these two regions. We present an analytical semiclassical approach providing a physical picture of this phenomenon, and support our findings by extensive numerical simulations in the whole parameter range of locally unstable dynamics of a Bose-Hubbard dimer. Our results suggest that the existence of this crossover is a hallmark of unstable separatrix dynamics in integrable systems, thus opening the possibility to distinguish the latter, on the basis of this particular observable, from genuine chaotic dynamics generally featuring uniform exponential growth of the OTOC.
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Affiliation(s)
- Mathias Steinhuber
- Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
| | | | - Juan Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
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5
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Passetti G, Hofmann D, Neitemeier P, Grunwald L, Sentef MA, Kennes DM. Can Neural Quantum States Learn Volume-Law Ground States? PHYSICAL REVIEW LETTERS 2023; 131:036502. [PMID: 37540880 DOI: 10.1103/physrevlett.131.036502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Accepted: 06/27/2023] [Indexed: 08/06/2023]
Abstract
We study whether neural quantum states based on multilayer feed-forward networks can find ground states which exhibit volume-law entanglement entropy. As a testbed, we employ the paradigmatic Sachdev-Ye-Kitaev model. We find that both shallow and deep feed-forward networks require an exponential number of parameters in order to represent the ground state of this model. This demonstrates that sufficiently complicated quantum states, although being physical solutions to relevant models and not pathological cases, can still be difficult to learn to the point of intractability at larger system sizes. Hence, the variational neural network approach offers no benefits over exact diagonalization methods in this case. This highlights the importance of further investigations into the physical properties of quantum states amenable to an efficient neural representation.
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Affiliation(s)
- Giacomo Passetti
- Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany
| | - Damian Hofmann
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Pit Neitemeier
- Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany
| | - Lukas Grunwald
- Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael A Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
- H H Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Dante M Kennes
- Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
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6
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Wang Q, Robnik M. Statistics of phase space localization measures and quantum chaos in the kicked top model. Phys Rev E 2023; 107:054213. [PMID: 37328969 DOI: 10.1103/physreve.107.054213] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Accepted: 04/29/2023] [Indexed: 06/18/2023]
Abstract
Quantum chaos plays a significant role in understanding several important questions of recent theoretical and experimental studies. Here, by focusing on the localization properties of eigenstates in phase space (by means of Husimi functions), we explore the characterizations of quantum chaos using the statistics of the localization measures, that is the inverse participation ratio and the Wehrl entropy. We consider the paradigmatic kicked top model, which shows a transition to chaos with increasing the kicking strength. We demonstrate that the distributions of the localization measures exhibit a drastic change as the system undergoes the crossover from integrability to chaos. We also show how to identify the signatures of quantum chaos from the central moments of the distributions of localization measures. Moreover, we find that the localization measures in the fully chaotic regime apparently universally exhibit the beta distribution, in agreement with previous studies in the billiard systems and the Dicke model. Our results contribute to a further understanding of quantum chaos and shed light on the usefulness of the statistics of phase space localization measures in diagnosing the presence of quantum chaos, as well as the localization properties of eigenstates in quantum chaotic systems.
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Affiliation(s)
- Qian Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, People's Republic of China
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000, Maribor, Slovenia
| | - Marko Robnik
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000, Maribor, Slovenia
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7
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Wang Q. Quantum Chaos in the Extended Dicke Model. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1415. [PMID: 37420435 PMCID: PMC9602098 DOI: 10.3390/e24101415] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Revised: 09/29/2022] [Accepted: 09/30/2022] [Indexed: 07/09/2023]
Abstract
We systematically study the chaotic signatures in a quantum many-body system consisting of an ensemble of interacting two-level atoms coupled to a single-mode bosonic field, the so-called extended Dicke model. The presence of the atom-atom interaction also leads us to explore how the atomic interaction affects the chaotic characters of the model. By analyzing the energy spectral statistics and the structure of eigenstates, we reveal the quantum signatures of chaos in the model and discuss the effect of the atomic interaction. We also investigate the dependence of the boundary of chaos extracted from both eigenvalue-based and eigenstate-based indicators on the atomic interaction. We show that the impact of the atomic interaction on the spectral statistics is stronger than on the structure of eigenstates. Qualitatively, the integrablity-to-chaos transition found in the Dicke model is amplified when the interatomic interaction in the extended Dicke model is switched on.
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Affiliation(s)
- Qian Wang
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
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8
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Zonnios M, Levinsen J, Parish MM, Pollock FA, Modi K. Signatures of Quantum Chaos in an Out-of-Time-Order Tensor. PHYSICAL REVIEW LETTERS 2022; 128:150601. [PMID: 35499886 DOI: 10.1103/physrevlett.128.150601] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Revised: 02/26/2022] [Accepted: 03/02/2022] [Indexed: 06/14/2023]
Abstract
Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of interest interacts with a small quantum probe whose dynamical properties identify the chaoticity of the system. Specifically, we propose a fully quantum version of the out-of-time-order correlator-which we term the out-of-time-order tensor-whose correlations offer clear information theoretic meanings about the chaoticity of a process. We illustrate the utility of the out-of-time-order tensor as a signature of chaos using random unitary processes as well as in the quantum kicked rotor, where the chaoticity is tunable.
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Affiliation(s)
- Magdalini Zonnios
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Jesper Levinsen
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Meera M Parish
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Felix A Pollock
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Kavan Modi
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
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9
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Behrends J, Béri B. Sachdev-Ye-Kitaev Circuits for Braiding and Charging Majorana Zero Modes. PHYSICAL REVIEW LETTERS 2022; 128:106805. [PMID: 35333069 DOI: 10.1103/physrevlett.128.106805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 02/17/2022] [Indexed: 06/14/2023]
Abstract
The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely, charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.
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Affiliation(s)
- Jan Behrends
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Benjamin Béri
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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10
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Wang Q, Robnik M. Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1347. [PMID: 34682071 PMCID: PMC8534380 DOI: 10.3390/e23101347] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/11/2021] [Revised: 10/07/2021] [Accepted: 10/12/2021] [Indexed: 11/16/2022]
Abstract
We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.
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Affiliation(s)
- Qian Wang
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia;
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China
| | - Marko Robnik
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia;
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11
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Geiger B, Urbina JD, Richter K. Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems. PHYSICAL REVIEW LETTERS 2021; 126:110602. [PMID: 33798381 DOI: 10.1103/physrevlett.126.110602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Revised: 12/14/2020] [Accepted: 02/12/2021] [Indexed: 06/12/2023]
Abstract
We consider the fate of 1/N expansions in unstable many-body quantum systems, as realized by a quench across criticality, and show the emergence of e^{2λt}/N as a renormalized parameter ruling the quantum-classical transition and accounting nonperturbatively for the local divergence rate λ of mean-field solutions. In terms of e^{2λt}/N, quasiclassical expansions of paradigmatic examples of criticality, like the self-trapping transition in an integrable Bose-Hubbard dimer and the generic instability of attractive bosonic systems toward soliton formation, are pushed to arbitrarily high orders. The agreement with numerical simulations supports the general nature of our results in the appropriately combined long-time λt→∞ quasiclassical N→∞ regime, out of reach of expansions in the bare parameter 1/N. For scrambling in many-body hyperbolic systems, our results provide formal grounds to a conjectured multiexponential form of out-of-time-ordered correlators.
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Affiliation(s)
- Benjamin Geiger
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Juan Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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