Quantum Chaos on Complexity Geometry

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.

5 pages, 1 figure

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• Nonlinear dynamics and quantum chaos of a family of kicked $p$-spin models
• Quantum Circuit Complexity of Primordial Perturbations
• Genuine Quantum Chaos and Physical Distance Between Quantum States
• Polynomial Equivalence of Complexity Geometries
• Quantum chaos measures for Floquet dynamics