A Derivation of Moment Evolution Equations for Linear Open Quantum Systems

Given a linear open quantum system which is described by a Lindblad master equation, we detail the calculation of the moment evolution equations from this master equation. We stress that the moment evolution equations are well-known, but their explicit derivation from the master equation cannot be found in the literature to the best of our knowledge, and so we provide this derivation for the interested reader

Lyapunov Stability Analysis for Invariant States of Quantum Systems

In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use weak convergence, in this article we analyze the convergence of density operators by considering the set of density operators as a subset of Banach space. We show that the set of invariant density operators is both closed and convex, which implies the impossibility of having multiple isolated invariant density operators. We then show how to analyze the stability of this set via a candidate Lyapunov operator.Comment: A version of this paper has been accepted at 56th IEEE Conference on Decision and Control 201

Unravelling photoprotection in microbial natural products

Mycosporine-like amino acids have long been known as a natural form of photoprotection for fungi and cyanobacteria. This review will highlight the key time-resolved experimental and theoretical techniques unravelling their photochemistry and photophysics, and directly link this to their use in commercial skin-care products, namely as sunscreen filters. Three case studies have been selected, each having aided advancement in this burgeoning field of research. We discuss these studies in the context of photoprotection and conclude by evaluating the necessary future steps towards translating the photochemistry and photophysics insight of these nature derived sunscreen filters to commercial application