Quantum dynamics in Krylov space: from tridiagonal matrices to quantum chaos

by Pratik Nandy

Thursday 26 Jun 2025, 15:15 → 17:15 Europe/Zurich

4/2-037 - TH meeting room (CERN)

The dynamics of quantum systems typically unfolds within a subspace of the state or operator space, known as the Krylov space. Krylov subspace methods provide a compact and computationally efficient description of quantum evolution and quantum chaos, which is particularly useful for describing nonequilibrium phenomena of many-body systems with a large Hilbert space. In this talk, I will explore the notion of Krylov complexity as a probe for operator growth and quantum chaos, scrambling, and quantum state evolution. Illustrative examples include quantum spin chains, Sachdev-Ye-Kitaev models, and random matrix theory. The talk is based on selected topics from the review article arXiv: 2405.09628 (Physics Reports).