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

Students with Late Emerging Reading Difficulties: Reading Engagement, Motivation, and Intervention Issues

This paper investigates the needs of students with late emerging reading difficulties focusing on the motivation requirements of these students. It is argued that educators need to enhance the readers' sense of self-worth and competence by providing materials and a learning environment that is challenging yet manageable. Because students with reading difficulties experience failure over a considerable period of time and have formed negative reading self-concepts, lower expectations, and a decreased incentive to try, this paper outlines suggestions on how teachers can better understand and address these problems, based on the authors' research using tutoring programs for students with reading and comprehension difficulties