The SYK charging advantage as a random walk on graphs

TL;DR

This paper analyzes the charging dynamics of SYK models as quantum batteries, revealing how operator scaling and graph structures enable quantum charging advantages through a novel graph-theoretic framework.

Contribution

It introduces a new graph-based framework to analyze SYK charging dynamics and identifies key mechanisms for quantum advantage in energy storage.

Findings

Quantum charging advantage depends on operator scaling and graph structure.

A graph-theoretic model recasts charging as a random walk, enabling analysis.

Conditions for quantum advantage are rigorously established.

Abstract

We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size $N$ and the facilitation of operator delocalization by specific graph structures. A novel graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes.