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Space-time duality between quantum chaos and non-Hermitian boundary effect

Zhou, Tian-Gang and Zhou, Yi-Neng and Zhang, Pengfei and Zhai, Hui (2022) Space-time duality between quantum chaos and non-Hermitian boundary effect. Physical Review Research, 4 (2). Art. No. L022039. ISSN 2643-1564. doi:10.1103/physrevresearch.4.l022039.

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Quantum chaos in Hermitian systems concerns the sensitivity of long-time dynamical evolution to initial conditions. The skin effect discovered recently in non-Hermitian systems reveals the sensitivity to the spatial boundary condition even deep in the bulk. In this Letter, we show that these two seemingly different phenomena can be unified through the space-time duality. The intuition is that the space-time duality maps unitary dynamics to nonunitary dynamics and exchanges the temporal direction and spatial direction. Therefore, the space-time duality can establish the connection between the sensitivity to the initial condition in the temporal direction and the sensitivity to the boundary condition in the spatial direction. Here, we demonstrate this connection by studying the space-time duality of the out-of-time-ordered correlator in a concrete chaotic Hermitian model. We show that the out-of-time-ordered correlator is mapped to a special two-point correlator of a non-Hermitian system in the dual picture. For comparison, we show that the sensitivity disappears when the non-Hermiticity is removed in the dual picture.

Item Type:Article
Related URLs:
URLURL TypeDescription Material Paper
Zhou, Tian-Gang0000-0002-4815-2578
Zhou, Yi-Neng0000-0003-1690-4787
Zhang, Pengfei0000-0002-7408-0918
Zhai, Hui0000-0001-8118-6027
Additional Information:© 2022 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 6 August 2021; accepted 27 April 2022; published 20 May 2022. This work is supported by Beijing Outstanding Young Scientist Program, NSFC Grant No. 11734010, and the XPLORER Prize.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
National Natural Science Foundation of China11734010
Beijing Outstanding Young Scientist ProgramUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20220629-796883600
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115293
Deposited By: Tony Diaz
Deposited On:30 Jun 2022 16:27
Last Modified:30 Jun 2022 16:27

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