Physics

Exponential function

Operator (biology)

Mathematics

Mathematical physics

Exponential growth

Transcription factor

Gene

Algorithm

Propagator

Statistical physics

Statistics

Distribution (mathematics)

Mathematical analysis

Philosophy

Scrambling

Repressor

Chemistry

Exponent

Linguistics

Exponential distribution

Signal transduction

Tyrosine kinase

Biochemistry

Journal of High Energy Physics

A bstract 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.

Operator growth in the SYK model