IQIM Postdoctoral and Graduate Student Seminar

Note: IQIM seminar will be held the Ginsburg seminar room.

Abstract: Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schrödinger's equation and the second law of thermodynamics. Despite its ubiquity and conceptual significance, the precise conditions that give rise to it are still not well understood. In the first part of this talk, I will present a rigorous proof of quantum thermalization for a broad class of translation-invariant local Hamiltonian dynamics, based on [arXiv:2409.07516, arXiv:2609.35973] and upcoming work. In the second part, I will ask what happens after thermalization: the global pure state keeps evolving, and its quantum circuit complexity is expected to keep growing even after the entanglement entropy has saturated. While many previous proofs of this expectation focused on models without energy conservation, such as random unitary circuits, we prove in [arXiv:2609.26885] that for generic local Hamiltonians at sufficiently high temperature, the complexity of typical initial product states must maintain a sustained growth up to an exponentially large value, although we do not establish that this growth is linear. As corollaries, we show that the late-time state displays robust volume-law entanglement, irremovable by efficient circuits, and we establish a no fast-forwarding result for generic local Hamiltonians. These results show how, in these settings, statistical physics can be proven to emerge directly from the first principles of quantum mechanics, without additional, unproven assumptions.

Lunch will be provided on the lawn north of Bridge, following the talk.