Katja Klobas

Quantum and Classical Dynamics with Random Permutation Circuits

Understanding thermalisation in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e. whether thermalisation in quantum many-body systems is fundamentally different from that in classical many-body systems and, if so, which of its features are genuinely quantum. I will talk about a recent work [1], where we studied this question in minimally structured many-body systems which are only constrained to have local interactions, i.e. local random circuits. In particular we introduced a class of random permutation circuits, where the gates locally permute basis states modelling generic microscopic classical dynamics, and compared them to random unitary circuits, a standard toy model for generic quantum dynamics. Random permutation circuits permit the analytical computation of several key quantities such as out-of-time order correlators, or entanglement entropies. Remarkably, despite the fundamental differences between unitary and permutation dynamics, they exhibit qualitatively similar behaviours.

[1] B. Bertini, K. Klobas, P. Kos and D. Malz, Phys. Rev. X 15, 011015 (2025).