Out-of-time-order correlators bridge classical transport and quantum dynamics

Abstract

The out-of-time-order correlator (OTOC) has emerged as a central tool for quantifying decoherence across wide-ranging physical platforms. Here we demonstrate its direct measurement in a classical ensemble using nuclear magnetic resonance (NMR) with a modulated gradient spin echo (MGSE) sequence and extend the method into a multidimensional correlation to track exchange phenomena. Position is encoded through magnetic field gradients and momentum through the velocity autocorrelation function, enabling experimental access to OTOCs for proton motion confined within the self-similar lattice of the metal-organic framework MOF-808. Here, water confined to specified geometries within the MOF pores gives rise to spatially distinct diffusive eigenmodes with characteristic relative entropies. We demonstrate that periodic radiofrequency (rf) driving combined with gradient modulation yields entropy evolution through the selection of distinct diffusion modes. Frequency-resolved diffusion spectra connect these entropy dynamics to classical heat-exchange laws, revealing how operational features of quantum systems are mirrored in confined, macroscopic spin ensembles.

References in corpus (21)

• A bound on chaos
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• Verified Quantum Information Scrambling
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Out-of-time-order correlators in quantum mechanics
• Scaling detection in time series: diffusion entropy analysis
• Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators
• Sub-ballistic growth of Rényi entropies due to diffusion
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Classical Prethermal Phases of Matter
• Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping
• Quantum scrambling with classical shadows
• Classical approaches to prethermal discrete time crystals in one, two, and three dimensions
• Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model
• Typical growth behavior of the out-of-time-ordered commutator in many-body localized systems
• Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method
• Molecular velocity auto-correlations in glycerol/water mixtures studied by NMR MGSE method
• Slow scrambling in sonic black holes
• Stochastic Fractal and Noether's Theorem
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling