Interplay of Density and Phase Fluctuations in Ultracold One-dimensional Bose Gases

The relative importance of density and phase fluctuations in ultracold one dimensional atomic Bose gases is investigated. By defining appropriate characteristic temperatures for their respective onset, a broad experimental regime is found, where density fluctuations set in at a lower temperature than phase fluctuations. This is in stark contrast to the usual experimental regime explored up to now, in which phase fluctuations are largely decoupled from density fluctuations, a regime also recovered in this work as a limiting case. Observation of the novel regime of dominant density fluctuations is shown to be well within current experimental capabilities for both $^{23}Na$ and $^{87}Rb$, requiring relatively low temperatures, small atom numbers and moderate aspect ratios.Comment: Expanded experimental discussion, modified Fig.

Gapless Hartree-Fock-Bogoliubov Approximation for Bose Gases

A dilute Bose system with Bose-Einstein condensate is considered. It is shown that the Hartree-Fock-Bogolubov approximation can be made both conserving as well as gapless. This is achieved by taking into account all physical normalization conditions, that is, the normalization condition for the condensed particles and that for the total number of particles. Two Lagrange multipliers, introduced for preserving these normalization conditions, make the consideration completely self-consistent.Comment: Latex file, 22 pages, 2 figure

Ab initio methods for finite temperature two-dimensional Bose gases

The stochastic Gross-Pitaevskii equation and modified Popov theory are shown to provide an ab initio description of finite temperature, weakly-interacting two-dimensional Bose gas experiments. Using modified Popov theory, a systematic approach is developed in which the momentum cut-off inherent to classical field methods is removed as a free parameter. This is shown to yield excellent agreement with the recent experiment of Hung et al. [Nature, 470, 236 (2011)], verifying that the stochastic Gross-Pitaevskii equation captures the observed universality and scale-invariance.Comment: 5 pages, 4 figure

Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity

We consider polariton condensation in a generalized Dicke model, describing a single-mode cavity containing quantum dots, and extend our previous mean-field theory to allow for finite-size fluctuations. Within the fluctuation-dominated regime the correlation functions differ from their (trivial) mean-field values. We argue that the low-energy physics of the model, which determines the photon statistics in this fluctuation-dominated crossover regime, is that of the (quantum) anharmonic oscillator. The photon statistics at the crossover are different in the high- and low- temperature limits. When the temperature is high enough for quantum effects to be neglected we recover behavior similar to that of a conventional laser. At low enough temperatures, however, we find qualitatively different behavior due to quantum effects.Comment: 12 pages, 5 figures. v2: Revised version with minor corrections (typos, added reference, correction in argument following Eq. 25). v3: further typos correcte

Modeling the effects of combining diverse software fault detection techniques

The software engineering literature contains many studies of the efficacy of fault finding techniques. Few of these, however, consider what happens when several different techniques are used together. We show that the effectiveness of such multitechnique approaches depends upon quite subtle interplay between their individual efficacies and dependence between them. The modelling tool we use to study this problem is closely related to earlier work on software design diversity. The earliest of these results showed that, under quite plausible assumptions, it would be unreasonable even to expect software versions that were developed ‘truly independently’ to fail independently of one another. The key idea here was a ‘difficulty function’ over the input space. Later work extended these ideas to introduce a notion of ‘forced’ diversity, in which it became possible to obtain system failure behaviour better even than could be expected if the versions failed independently. In this paper we show that many of these results for design diversity have counterparts in diverse fault detection in a single software version. We define measures of fault finding effectiveness, and of diversity, and show how these might be used to give guidance for the optimal application of different fault finding procedures to a particular program. We show that the effects upon reliability of repeated applications of a particular fault finding procedure are not statistically independent - in fact such an incorrect assumption of independence will always give results that are too optimistic. For diverse fault finding procedures, on the other hand, things are different: here it is possible for effectiveness to be even greater than it would be under an assumption of statistical independence. We show that diversity of fault finding procedures is, in a precisely defined way, ‘a good thing’, and should be applied as widely as possible. The new model and its results are illustrated using some data from an experimental investigation into diverse fault finding on a railway signalling application