Krylov Complexity of Open Quantum Systems: From Hard Spheres to Black Holes

TL;DR

This paper explores the complexity of open quantum systems, specifically analyzing Krylov complexity in a hard-sphere gas and connecting it to holographic complexity of black holes, revealing similar late-time growth behaviors.

Contribution

It analytically computes Krylov complexity for a leaking hard-sphere gas and links it to black hole holographic complexity using a novel spacetime stitching approach.

Findings

Late-time complexity growth rates are similar in both systems.

Krylov complexity can be analytically computed for chaotic open quantum systems.

Holographic complexity models can be connected to physical quantum systems.

Abstract

We examine the complexity of quasi-static chaotic open quantum systems. As a prototypical example, we analytically compute the Krylov complexity of a slowly leaking hard-sphere gas using Berry's conjecture. We then connect it to the holographic complexity of a $d+1$-dimensional evaporating black hole using the Complexity=Volume proposal. We model the black hole spacetime by stitching together a sequence of static Schwarzschild patches across incoming negative energy null shock waves. Under certain identification of parameters, we find the late time complexity growth rate during each quasi-static equilibrium to be the same in both systems.