Operator growth in the SYK model

By Daniel A. Roberts, D. Stanford, Alexandre Streicher. Journal of High Energy Physics, 2018

245 citations recorded by the source corpus.

We discuss the probability distribution for the “size” of a time-evolving operator in the SYK model. Scrambling is related to the fact that as time passes, the distribution shifts towards larger operators. Initially, the rate is exponential and determined by the infinite-temperature chaos exponent. We evaluate the size distribution numerically for N = 30, and show how to compute it in the large-N theory using the dressed fermion propagator. We then evaluate the distribution explicitly at leading nontrivial order in the large-q expansion.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e7e99a45b6e9907e43aae0c50395a1f6f0cdd809

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Mathematical Physics

Citations in the corpus

Geometry of Krylov complexity (2021, methodology): “First, from a technical standpoint, the derivation of the operator wavefunctions in both [17] and [23] is quite involved.”
A Universal Operator Growth Hypothesis (2018, methodology): “Here α is obtained by exact numerical methods discussed in Appendix B, while λL is taken from the Appendix of [37].”