Entanglement negativity in the harmonic chain out of equilibrium

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left-and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.

Experiences of Public-Private Collaboration for Stimulating

For over a decade now, work has been ongoing on the professional organization and management of town centre retail spaces in Spain under what is known as the Open Shopping Centre model. Introducing this model has involved a process of public-private collaboration in several different phases, conditioned to a large extent by the specific context of each initiative. With a view to furthering the process of benchmarking developed out of the experiences of recent years, we shall use case analysis to explain trends in initiatives for retail regeneration and stimulation undertaken in the Basque Country (an autonomous community in the north of Spain) since 2000. We analyze the factors that have prompted these initiatives, assessing and comparing the landmarks and conditions that have marked, or are determining, progress in the dynamic of collaboration between municipal authorities and retailers for a competitive improvement both in the retail sector and in the environment in which it operates: the city. Finally we list witch are these key factors.