The Lyapunov exponent as a signature of dissipative many-body quantum chaos

• URL: http://arxiv.org/abs/2403.12359v2
• Date: Fri, 14 Jun 2024 15:20:30 GMT
• Title: The Lyapunov exponent as a signature of dissipative many-body quantum chaos
• Authors: Antonio M. García-García, Jacobus J. M. Verbaarschot, Jie-ping Zheng,
• Abstract summary: A positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. We show that a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order-correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs describe the growth of quantum uncertainty that crucially depends on the nature of the quantum motion. Here, we employ the OTOC in order to provide a precise definition of dissipative quantum chaos. For this purpose, we compute analytically the Lyapunov exponent for the vectorized formulation of the large $q$-limit of a $q$-body Sachdev-Ye-Kitaev model coupled to a Markovian bath. These analytic results are confirmed by an explicit numerical calculation of the Lyapunov exponent for several values of $q \geq 4$ based on the solutions of the Schwinger-Dyson and Bethe-Salpeter equations. We show that the Lyapunov exponent decreases monotonically as the coupling to the bath increases and eventually becomes negative at a critical value of the coupling signaling a transition to a dynamics which is no longer quantum chaotic. Therefore, a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. The observation of the breaking of the exponential growth for sufficiently strong coupling suggests that dissipative quantum chaos may require in certain cases a sufficiently weak coupling to the environment.

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