Out-of-time-order correlators in an open quantum system

Jochen Braumüller, Amir H. Karamlou, Yariv Yanay +13 more

Pablo D. Bergamasco, Gabriel G. Carlo, Alejandro M. F. Rivas

Out-of-time-ordered correlators (OTOCs) have emerged as powerful tools for diagnosing quantum chaos and information scrambling. While extensively studied in closed quantum systems, their behavior in dissipative environments remains less understood. In this work, we investigate the spectral decomposition of OTOCs in open quantum systems, using the dissipative modified kicked rotator as a paradigmatic model. By analyzing the eigenvalue spectrum of the quantum Liouvillian, we identify a crucial spectral truncation criterion that enables efficient modeling of OTOC dynamics. Our results reveal two distinct temporal regimes: a long-time decay phase governed by the spectral gap and an intermediate-time regime where a small subset of subdominant eigenvalues plays a crucial role. This spectral truncation criterion allows for efficient modeling of OTOC decay and reveals a direct connection between eigenvalue structure and information scrambling. Our results provide a quantitative framework for understanding OTOCs in dissipative quantum systems and suggest new avenues for experimental exploration in open quantum platforms.

Brian G. Swingle

Pablo D. Bergamasco, Gabriel G. Carlo, Alejandro M. F. Rivas

Out-of-time-ordered correlators (OTOCs) have emerged as powerful tools for diagnosing quantum chaos and information scrambling. While extensively studied in closed quantum systems, their behavior in dissipative environments remains less understood. In this work, we investigate the spectral decomposition of OTOCs in open quantum systems, using the dissipative modified kicked rotator (DMKR) as a paradigmatic model. By analyzing the eigenvalue spectrum of the quantum Liouvillian, we identify a crucial spectral truncation criterion that enables efficient modeling of OTOC dynamics. Our results reveal two distinct temporal regimes: a long-time decay phase governed by the spectral gap and an intermediate-time regime where a small subset of subdominant eigenvalues plays a crucial role. This spectral truncation criterion allows for efficient modeling of OTOC decay and reveals a direct connection between eigenvalue structure and information scrambling. Our results provide a quantitative framework for understanding OTOCs in dissipative quantum systems and suggest new avenues for experimental exploration in open quantum platforms.

Cheng-Ju Lin, Olexei I. Motrunich

Baibhab Bose, Devvrat Tiwari, Subhashish Banerjee

The information scrambling phenomena in an open quantum system modeled by Ising spin chains coupled to Lipkin-Meshkov-Glick (LMG) baths are observed via an interferometric method for obtaining out-of-time-ordered correlators ($\mathcal{F}\ensuremath{-}\mathrm{OTOC}$). We also use an anisotropic bath connecting to a system of tilted field Ising spin chains in order to confirm that such situations are suitable for the emergence of ballistic spreading of information manifested in the light cones in the $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ profiles. Bipartite OTOC is also calculated for a bipartite open system, and its behavior is compared with that of the $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ of a two-spin open system to get a picture of what these measures reveal about the nature of scrambling in different parameter regimes. Additionally, the presence of distinct phases in the LMG model motivated an independent analysis of its scrambling properties, where $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ diagnostics revealed that quantum chaos emerges exclusively in the symmetry-broken phase.