Lindbladian dynamics of the Sachdev-Ye-Kitaev model

TL;DR

This paper analyzes the Lindbladian dynamics of the SYK model coupled to reservoirs, deriving analytical results for large system sizes and studying eigenvalue distributions for finite sizes, advancing understanding of open quantum chaotic systems.

Contribution

It provides an analytical study of the SYK model's Lindbladian dynamics with random and non-random jump operators, extending the understanding of open quantum systems in the large N limit.

Findings

Analytical expressions for stationary Green's functions in the large N limit.

Decay rates of the SYK Lindbladians derived from Green's functions.

Eigenvalue distributions characterized for finite N.

Abstract

We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Here, the linear jump operators are non-random while the quadratic jump operators are sampled from a Gaussian distribution. In the limit of large $N$, where $N$ is the number of Majorana fermion operators, and also in the limit of large $N$ and $M$, where $M$ is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite $N$, we also study the distribution of the eigenvalues of the SYK Lindbladians.