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  • Open Access

Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems

Takato Yoshimura1,2,* and Lucas Sá3,†

  • 1All Souls College, Oxford OX1 4AL, United Kingdom
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
  • 3TCM Group, Cavendish Laboratory, Ray Dolby Centre, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0US, United Kingdom

  • *Contact author: takato.yoshimura@physics.ox.ac.uk
  • †Contact author: ld710@cam.ac.uk
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Phys. Rev. B 113, 144306 – Published 13 April, 2026

DOI: https://doi.org/10.1103/fmr4-14vd

Abstract

We study the dynamics of Loschmidt echoes in noisy quantum many-body systems without conservation laws. We first show that the operator Loschmidt echo in noisy unitary dynamics is equivalent to the operator norm of the corresponding dissipative dynamics upon noise averaging. We then analyze this quantity in two complementary ways, revealing universal dynamical behavior. First, we develop a heuristic picture for generic Floquet systems that connects Loschmidt echoes, out-of-time-order correlators, and operator growth, which is valid at any dissipation strength. We assert that the Loschmidt echo has two dynamical regimes depending on the time t and the strength of the noise p: Gaussian decay for pt≪1 and exponential decay (with a noise-independent decay rate) for pt≫1. Lastly, we rigorously prove all our results for a solvable chaotic many-body quantum circuit, the dissipative random phase model—thus providing exact insight into dissipative quantum chaos.

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Outline

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Phys. Rev. B 113, 144306– Published 13 April, 2026
  • Received 16 September 2025
  • Revised 21 February 2026
  • Accepted 25 February 2026
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