Week 10.11.2025 – 16.11.2025

I present results on the quantum dynamics of a minimal model with spatial structure and local interactions. The model features a time-independent Hamiltonian, in contrast to the widely studied quantum circuits, and is analytically tractable in the limit of large local Hilbert space dimension and weak intersite coupling. In this regime, I show that the energy dynamics are governed by a classical master equation exhibiting diffusive behavior. Furthermore, I demonstrate that the spectral form factor can be expressed exactly in terms of the solution to this master equation, demonstrating how the linear ramp emerges at long times, while locality gives rise to an additional enhancement at short times.

Swimming on the microscale has long been the subject of intense research efforts, from experimental studies of bacteria, sperm, and algae through to varied theoretical questions of low-Reynolds-number fluid mechanics. The biological and biophysical settings that drive this ongoing research are often confoundingly complex, a fact that has driven the development and use of simple models of microswimmers. In this talk, we will showcase how we can often exploit separated scales present in these problems and models to reveal surprisingly simple emergent dynamics, including predictions of globally attracting, long-term behaviours. In doing so, we'll also uncover a surprising cautionary tale that calls into question much of the intuition gained from commonplace models of microswimming. In particular, we'll see that a wave-of-the-hands, which I have been guilty of before, can drastically and qualitatively change the dynamics that simple models predict, and we'll see how such missteps can be addressed through systematic multiscale methods.