Quantum Chaos on Complexity Geometry

• URL: http://arxiv.org/abs/2004.03501v1
• Date: Tue, 7 Apr 2020 15:53:57 GMT
• Title: Quantum Chaos on Complexity Geometry
• Authors: Bin Yan and Wissam Chemissany
• Abstract summary: We show that complexity can exhibit exponential sensitivity in response to perturbations of initial conditions for chaotic systems. We show that the complexity linear response matrix gives rise to a spectrum that fully recovers the Lyapunov exponents in the classical limit.
• Score: 3.800391908440439
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase space. We develop a linear response theory for complexity, and demonstrate that the complexity can exhibit exponential sensitivity in response to perturbations of initial conditions for chaotic systems. Two immediate significant results follows: i) the complexity linear response matrix gives rise to a spectrum that fully recovers the Lyapunov exponents in the classical limit, and ii) the linear response of complexity is given by the out-of-time order correlators.

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