Collective excitations of trapped Bose-Einstein condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-de Gennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, extremely efficient in our implementation with parallel fast Fourier transform methods, and produces highly accurate results. For high dimensionality or low symmetry the time-dependent approach is a more practical computational scheme and produces accurate and reliable data. The method is suitable for general trap geometries, condensate flows and condensates permeated with defects and vortex structures.

Collective decoherence of cold atoms coupled to a Bose-Einstein condensate

We examine the time evolution of cold atoms (impurities) interacting with an environment consisting of a degenerate bosonic quantum gas. The impurity atoms differ from the environment atoms, being of a different species. This allows one to superimpose two independent trapping potentials, each being effective only on one atomic kind, while transparent to the other. When the environment is homogeneous and the impurities are confined in a potential consisting of a set of double wells, the system can be described in terms of an effective spin-boson model, where the occupation of the left or right well of each site represents the two (pseudo)-spin states. The irreversible dynamics of such system is here studied exactly, i.e. not in terms of a Markovian master equation. The dynamics of one and two impurities is remarkably different in respect of the standard decoherence of the spin-boson system. In particular, we show: (i) the appearance of coherence oscillations, (ii) the presence of super and subdecoherent states that differ from the standard ones of the spin-boson model, and (iii) the persistence of coherence in the system at long times. We show that this behaviour is due to the fact that the pseudospins have an internal spatial structure. We argue that collective decoherence also prompts information about the correlation length of the environment. In a one-dimensional (1D) configuration, one can change even more strongly the qualitative behaviour of the dephasing just by tuning the interaction of the bath.

The Architecture of Home in Cairo: Socio-Spatial Practice of the Hawari's Everyday Life

The hawari of Cairo - narrow non-straight alleyways - are the basic urban units that have formed the medieval city since its foundation back in 969 AD. Until early in the C20th, they made up the primary urban divisions of the city and were residential in nature. Contemporary hawari, by contrast, are increasingly dominated by commercial and industrial activity. This medieval urban maze of extremely short, broken, zigzag streets and dead ends are defensible territories, powerful institutions, and important social systems. While the hawari have been studied as an exemplar for urban structure of medieval Islamic urbanism, and as individual building typologies, this book is the first to examine in detail the socio-spatial practice of the architecture of home in the city. It investigates how people live, communicate and relate to each other within their houses or shared spaces of the alleys, and in doing so, to uncover several new socio-spatial dimensions and meanings in this architectural form.

In an attempt to re-establish the link between architecture past and present, and to understand the changing social needs of communities, this book uncovers the notion of home as central to understand architecture in such a city with long history as Cairo. It firstly describes the historical development of the domestic spaces (indoor and outdoor), and provides an inclusive analysis of spaces of everyday activities in the hawari of old Cairo. It then broadens its analysis to other parts of the city, highlighting different customs and representations of home in the city at large. Cairo, in the context of this book, is represented as the most sophisticated urban centre in the Middle East with different and sometimes contrasting approaches to the architecture of home, as a practice and spatial system.

In order to analyse the complexity and interconnectedness of the components and elements of the hawari as a 'collective home', it layers its narratives of architectural and social developments as a domestic environment over the past two hundred years, and in doing so, explores the in-depth social meaning and performance of spaces, both private and public.