Out-of-time-order Correlators and Chaos in Quantum Billiards

• URL: http://arxiv.org/abs/2408.04052v1
• Date: Wed, 7 Aug 2024 19:23:14 GMT
• Title: Out-of-time-order Correlators and Chaos in Quantum Billiards
• Authors: Tasnim Anzum Ador, Nayeem Farid, Tibra Ali,
• Abstract summary: We compute the classical and quantum Lyapunov exponents of three billiard systems known to be classically chaotic. We identify the source of anomalous behaviour in the geometry of the ground state wave function of the Sinai billiard. We also remark on the late-time behaviour of the OTOCs and how the scrambling/Ehrenfest time is related to the temperature of quantum billiards.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We examine three billiard systems -- the cardioid, diamond (Superman), and Sinai billiards -- all of which are known to be classically chaotic. We compute their classical Lyapunov exponents, and using out-of-time-order correlators (OTOCs) in the semi-classical regime, we also derive their quantum Lyapunov exponents. We observe that the classical and quantum Lyapunov exponents are in agreement, strengthening the role of OTOCs as a diagnostic for quantum chaos in billiard systems. At very low temperatures, the OTOC of the Sinai billiard shows sharp growth, a phenomenon absent in the other two billiards. We identify the source of this anomalous behaviour in the geometry of the ground state wave function of the Sinai billiard, which is more sensitive to the curvature of the billiard compared to the other billiards. We also remark on the late-time behaviour of the OTOCs and how the scrambling/Ehrenfest time is related to the temperature of quantum billiards.

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