Speaker: Rob Klabbers (HU)

Title: Hybrid systems and deformation quantisation

Abstract:
Every good quantum system has a classical limit, but how to define the latter is not always obvious. In the standard formulation of deformation quantisation, the classical limit of a quantum system is a quotient of the quantum algebra of observables (and most often coincides with setting hbar=0). For quantum systems with spin, this procedure can yield a non-commutative algebra. This does not admit a natural interpretation as functions on some phase space, and hence does not seem like a good model of classical physics. If in the hamiltonian description of the system the spin degrees of freedom are somewhat separated, though, one can solve this problem by considering the classical limits of the hamiltonian separate from other observables.

I will review the general setting of deformation quantisation and show how for spin systems this adapted procedure gives rise to a consistent notion of time evolution. Moreover, it will be clear that the resulting system is not fully classical, and still has quantum spins; it is a hybrid. I will argue that at equilibria of the classical part one can consistently truncate to yield a model of interacting quantum spins.

Based on Sections 3 and 5 of https://arxiv.org/abs/2507.13104 written with Jules Lamers.