Analytical Determination of Multi-Time Correlation Functions Reveals Dynamical Contributions in Quantum Chaotic Systems

Understanding how quantum systems evolve in time requires detailed knowledge of multi-point correlation functions, quantities that describe the relationships between different measurable properties. Yoana R. Chorbadzhiyska, Peter A. Ivanov, and Charlie Nation, working at the Center for Quantum Technologies and the University of Exeter respectively, have achieved a significant breakthrough by analytically determining how these functions change over time in quantum chaotic systems. Their work utilises a random matrix approach to predict the dynamics of these correlations, including the out-of-time-ordered correlator, a key indicator of chaotic behaviour. By linking dynamical contributions to the behaviour of coarse-grained wave-functions and validating their predictions with numerical experiments, the team provides new insights into the emergence of predictable behaviour in otherwise complex systems and establishes connections to fundamental bounds on chaotic dynamics.

Higher-Order Correlations in Quantum Chaotic Systems

This research presents a systematic analytical determination of multi-time correlation functions in quantum chaotic systems, extending beyond traditional two-point calculations. Understanding how systems evolve requires examining the relationships between multiple observable properties at different moments in time, and this work provides a method for doing so. The approach combines random matrix theory with diagrammatic perturbation theory, allowing scientists to calculate these correlation functions to high accuracy, even in strongly chaotic conditions. The results reveal a clear connection between the spectral properties of a chaotic system and the rate at which multi-time correlations decay, offering new insights into the behaviour of open quantum systems.

Scientists investigate how an environment influences a quantum system, utilising the out-of-time-ordered correlator as a key tool for probing dynamical chaoticity. Researchers find that dynamical contributions relate to a simple function, connected to the Fourier transform of coarse-grained wave-functions, and comparing these predictions to experimental observations allows for a deeper understanding of quantum chaos and its environmental dependencies.

Spin Chain Dynamics and Environmental Coupling

This research investigates the dynamics of a quantum system, a spin chain, as it interacts with an external environment. Scientists explore how information propagates within the system and how the environment affects this propagation, focusing on understanding how the system reaches equilibrium. The study employs both analytical calculations and numerical simulations, utilising a random product state to model a thermalised environment, and examines one-point and two-point correlation functions, alongside the out-of-time-ordered correlator, to measure correlations and understand the system’s evolution.

The results demonstrate strong agreement between analytical predictions and numerical simulations, validating the theoretical model. The coupling strength between the system and the environment significantly influences the system’s dynamics, with distinct behaviours observed in weak and strong coupling regimes. In some cases, particularly with strong coupling, fluctuations appear in the early stages of evolution that do not average out, suggesting the spin chain’s geometry and edge effects play a role.

Correlator Dynamics and Closed System Markovianity

This research presents a detailed analysis of multi-point correlation functions in quantum systems, employing a random matrix approach to understand their time dependence. Researchers derived analytical results for these functions, including the out-of-time-ordered correlator, demonstrating that dynamical contributions relate to a function determined by the Fourier transform of coarse-grained wave-functions, and validated the theoretical framework with numerical experiments performed on a spin chain using various physical observables.

The findings offer insights into the emergence of Markovianity and regression in closed systems, and establish connections to existing bounds on chaotic dynamics. The study introduces a framework for defining chaotic eigenstates based on the distribution of their coefficients and a normalised function, which effectively represents a coarse-graining of individual eigenstates. While the analysis assumes a specific model, a random matrix Hamiltonian, the researchers acknowledge that the framework can be extended to other systems, and that the precise form of the coarse-grained function may vary.