Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder

The effect of a weak three-dimensional (3d) isotropic laser speckle disorder on various thermodynamic properties of a dilute Bose gas is considered at zero temperature. First, we summarize the derivation of the autocorrelation function of laser speckles in 1d and 2d following the seminal work of Goodman. The goal of this discussion is to show that a Gaussian approximation of this function, proposed in some recent papers, is inconsistent with the general background of laser speckle theory. Then we propose a possible experimental realization for an isotropic 3d laser speckle potential and derive its corresponding autocorrelation function. Using a Fourier transform of that function, we calculate both condensate depletion and sound velocity of a Bose-Einstein condensate as disorder ensemble averages of such a weak laser speckle potential within a perturbative solution of the Gross-Pitaevskii equation. By doing so, we reproduce the expression of the normalfluid density obtained earlier within the treatment of Landau. This physically transparent derivation shows that condensate particles, which are scattered by disorder, form a gas of quasiparticles which is responsible for the normalfluid component

The Spatial Distribution of LGR5+ Cells Correlates With Gastric Cancer Progression

In this study we tested the prevalence, histoanatomical distribution and tumour biological significance of the Wnt target protein and cancer stem cell marker LGR5 in tumours of the human gastrointestinal tract. Differential expression of LGR5 was studied on transcriptional (real-time polymerase chain reaction) and translational level (immunohistochemistry) in malignant and corresponding non-malignant tissues of 127 patients comprising six different primary tumour sites, i.e. oesophagus, stomach, liver, pancreas, colon and rectum. The clinico-pathological significance of LGR5 expression was studied in 100 patients with gastric carcinoma (GC). Non-neoplastic tissue usually harboured only very few scattered LGR5+ cells. The corresponding carcinomas of the oesophagus, stomach, liver, pancreas, colon and rectum showed significantly more LGR5+ cells as well as significantly higher levels of LGR5-mRNA compared with the corresponding non-neoplastic tissue. Double staining experiments revealed a coexpression of LGR5 with the putative stem cell markers CD44, Musashi-1 and ADAM17. Next we tested the hypothesis that the sequential changes of gastric carcinogenesis, i.e. chronic atrophic gastritis, intestinal metaplasia and invasive carcinoma, are associated with a reallocation of the LGR5+ cells. Interestingly, the spatial distribution of LGR5 changed: in non-neoplastic stomach mucosa, LGR5+ cells were found predominantly in the mucous neck region; in intestinal metaplasia LGR5+ cells were localized at the crypt base, and in GC LGR5+ cells were present at the luminal surface, the tumour centre and the invasion front. The expression of LGR5 in the tumour centre and invasion front of GC correlated significantly with the local tumour growth (T-category) and the nodal spread (N-category). Furthermore, patients with LGR5+ GCs had a shorter median survival (28.0±8.6 months) than patients with LGR5− GCs (54.5±6.3 months). Our results show that LGR5 is differentially expressed in gastrointestinal cancers and that the spatial histoanatomical distribution of LGR5+ cells has to be considered when their tumour biological significance is sought