Faculty @ UCL

Wednesday June 29 – 8.45 BST

Zeno effects and entropy production for Brownian trajectories of a physical density matrix

If we regard the (reduced) density matrix of an open quantum system as a representation of real-world physical properties and not merely as a provider of probabilities for strong projective measurements, then it makes sense to imagine its time evolution to be stochastic, as it responds to physical interactions with an underspecified environment with many similar degrees of freedom. The uncertain evolution of the state of any physical system may be characterised by the production of stochastic entropy, and an ensemble of evolutions of a density matrix can be similarly treated. We use the quantum state diffusion framework to describe such continuous Brownian trajectories. We show that various stochastic couplings between the density matrix and its environment can lead to behaviour that corresponds to thermalisation or to eigenstate selection by measurement of an observable, with none of the interpretational issues that often distinguish these two effects. By regarding the density matrix as a stochastic physical property, we study simple two- and three-level systems undergoing deterministic Hamiltonian evolution and stochastic environmental disturbance, and demonstrate Zeno effects and entropy production that would not be apparent in a more traditional ensemble-averaged description of density matrix evolution.