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

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.

25 pages, 7 figures; v2: refs added, minor changes. Matches the published version

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• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
• Krylov complexity as an order parameter for quantum chaotic-integrable transitions
• Operator growth and spread complexity in open quantum systems
• Krylov Complexity in Mixed Phase Space
• Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity
• Speed limits to the growth of Krylov complexity in open quantum systems
• Krylov Complexity of Fermionic and Bosonic Gaussian States
• Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry
• Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory