Operator spreading in quantum maps

Moudgalya, Sanjay; Devakul, Trithep; von Keyserlingk, C. W.; Sondhi, S. L.

doi:10.1103/physrevb.99.094312

Title: Operator spreading in quantum maps

Journal Article · Wed Mar 27 00:00:00 EDT 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.99.094312· OSTI ID:1612444

Moudgalya, Sanjay ^[1]; Devakul, Trithep ^[1]; von Keyserlingk, C. W. ^[2]; Sondhi, S. L. ^[1]

Princeton Univ., NJ (United States)
Univ. of Birmingham (United Kingdom)

Operators in ergodic spin chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin chains. Here we initiate the study of “operator spreading” in quantum maps on a torus, systems which do not have a tensor-product Hilbert space or a notion of spatial locality. Using the perturbed Arnold cat map as an example, we analytically compare and contrast the evolutions of functions on classical phase space and quantum operator evolutions, and identify distinct timescales that characterize the dynamics of operators in quantum chaotic maps. Until an Ehrenfest time, the quantum system exhibits classical chaos, i.e., it mimics the behavior of the corresponding classical system. After an operator scrambling time, the operator looks “random” in the initial basis, a characteristic feature of quantum chaos. These timescales can be related to the quasienergy spectrum of the unitary via the spectral form factor. Furthermore, we show examples of “emergent classicality” in quantum problems far away from the classical limit. Lastly, we study operator evolution in nonchaotic and mixed quantum maps using the Chirikov standard map as an example.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0016244

OSTI ID:: 1612444

Journal Information:: Physical Review. B, Vol. 99, Issue 9; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 23 works

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Exact Excited States of Non-Integrable Models Moudgalya, Sanjay; Rachel, Stephan; Bernevig, B. Andrei arXiv https://doi.org/10.48550/arxiv.1708.05021	text	January 2017
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Out-of-time-ordered correlators and quantum walks Omanakuttan, Sivaprasad; Lakshminarayan, Arul Physical Review E, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevE.99.062128	journal	June 2019
Slow quantum thermalization and many-body revivals from mixed phase space Michailidis, A. A.; Turner, C. J.; Papić, Z. arXiv https://doi.org/10.48550/arxiv.1905.08564	text	January 2019

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75 CONDENSED MATTER PHYSICS
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Title: Operator spreading in quantum maps

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