Chaos and multifold complexity for an inverted harmonic oscillator

• URL: http://arxiv.org/abs/2211.04317v1
• Date: Sun, 6 Nov 2022 14:19:48 GMT
• Title: Chaos and multifold complexity for an inverted harmonic oscillator
• Authors: Le-Chen Qu, Hong-Yue Jiang, Yu-Xiao Liu
• Abstract summary: We prove that complexity is dominated by the longest permutation of the given time combination in an alternating zig-zag'' order. We conjecture that the general structure for multifold complexity should hold true universally for generic quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We examine the multifold complexity and Loschmidt echo for an inverted harmonic oscillator. We give analytic expressions for any number of precursors, implementing multiple backward and forward time evolutions of the quantum state, at the leading order in the perturbation. We prove that complexity is dominated by the longest permutation of the given time combination in an alternating ``zig-zag'' order, the exact same result obtained with holography. We conjecture that the general structure for multifold complexity should hold true universally for generic quantum systems, in the limit of a large number of precursors.

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