Super-exponential behaviors of out-of-time ordered correlators and Loschmidt echo in a non-Hermitian interacting system

• URL: http://arxiv.org/abs/2305.12150v2
• Date: Fri, 21 Mar 2025 07:13:12 GMT
• Title: Super-exponential behaviors of out-of-time ordered correlators and Loschmidt echo in a non-Hermitian interacting system
• Authors: Wen-Lei Zhao, Chao Han, Han Ke, Jie Liu,
• Abstract summary: We investigate the out-of-time ordered correlators and Loschmidt echo in a non-Hermitian interacting system.<n>We find that both of them can exhibit a super-exponential growth with time, indicating the emergence of super-exponential scrambling and instability.<n>The underlying mechanism is rooted in the super-exponentially fast diffusion of energy as well as the norm of quantum states.
• Score: 3.6977840915546856
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the out-of-time ordered correlators and Loschmidt echo in a non-Hermitian interacting system governed by a Gross-Pitaevskii map model, which incorporates a periodically modulated complex strength of the nonlinear interaction as delta kicks. We uncover that the time evolutions of the out-of-time ordered correlators follow that of the Loschmidt echo in certain situations. In particular, we find that both of them can exhibit a super-exponential growth with time, indicating the emergence of super-exponential scrambling and instability. Interestingly, after a proper scaling scheme, we find that all the super-exponential behaviors approximately collapse on a scaling-law curve that is independent on the non-Hermitian parameter as well as the effective Planck constant. The underlying mechanism is rooted in the super-exponentially fast diffusion of energy as well as the norm of quantum states. Our findings suggest a kind of fastest divergence of two nearby quantum states, which has implication in information scrambling.

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