Decoherence and Microscopic Diffusion at SYK

Abstract

Sachdev-Ye-Kitaev (SYK) or embedded random ensembles are models of $N$ fermions with random k-body interactions. They play an important role in understanding black hole dynamics, quantum chaos, and thermalization. We study out of equilibrium scenarios in these systems and show they display perfect decoherence at all times. This peculiar feature makes them very attractive in the context of the quantum-to-classical transition and the emergence of classical general relativity. Based on this feature and unitarity, we propose a rate/continuity equation for the dynamics of the $\mathcal{O}(e^N)$ microstates probabilities. The effective permutation symmetry of the models drastically reduces the number of variables, allowing for compact expressions of n-point correlation functions and entropy of the microscopic distribution. Further assuming a generalized Fermi golden rule allows finding analytic formulas for the kernel spectrum at finite $N$, providing a series of short and long time scales controlling the out of equilibrium dynamics of this model. This approach to chaos, long time scales, and $1/N$ corrections might be tested in future experiments.

9 pages. Expanded and reorganized results. Decoherence proven at all times. New references added

References in corpus (13)

• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Comments on Holographic Complexity
• Quantum chaos on a critical Fermi surface
• Higher Dimensional Generalizations of the SYK Model
• Quantum Chaos and Holographic Tensor Models
• Echoes of chaos from string theory black holes
• Quantitative approaches to information recovery from black holes
• Black Holes, Entanglement and Random Matrices
• De Finetti theorems and entanglement in large-N theories and gravity

Cited by in corpus (8)

• Quantum chaos and the complexity of spread of states
• The Bulk Dual of SYK: Cubic Couplings
• Supersymmetric SYK model and random matrix theory
• Black holes, complexity and quantum chaos
• Pure states in the SYK model and nearly-$Ad{S}_2$ gravity
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Holography from Decoherence and Entanglement