Localization by entanglement

We study the localization of bosonic atoms in an optical lattice, which interact in a spatially confined region. The classical theory predicts that there is no localization below a threshold value for the strength of interaction that is inversely proportional to the number of participating atoms. In a full quantum treatment, however, we find that localized states exist for arbitrarily weak attractive or repulsive interactions for any number ($>1$) of atoms. We further show, using an explicit solution of the two-particle bound state and an appropriate measure of entanglement, that the entanglement tends to a finite value in the limit of weak interactions. Coupled with the non-existence of localization in an optimized quantum product state, we conclude that the localization exists by virtue of entanglement.Comment: 6 pages, 4 figures; final published version with small changes in response to reviewer comment

Semi-classical analysis of real atomic spectra beyond Gutzwiller's approximation

Real atomic systems, like the hydrogen atom in a magnetic field or the helium atom, whose classical dynamics are chaotic, generally present both discrete and continuous symmetries. In this letter, we explain how these properties must be taken into account in order to obtain the proper (i.e. symmetry projected) $\hbar$ expansion of semiclassical expressions like the Gutzwiller trace formula. In the case of the hydrogen atom in a magnetic field, we shed light on the excellent agreement between present theory and exact quantum results.Comment: 4 pages, 1 figure, final versio

Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.Comment: 47 pages, 11 figures, final versio

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Profiling CpG island field methylation in both morphologically normal and neoplastic human colonic mucosa

Aberrant CpG island (CGI) methylation occurs early in colorectal neoplasia. Quantitative methylation-specific PCR profiling applied to biopsies was used to quantify low levels of CGI methylation of 18 genes in the morphologically normal colonic mucosa of neoplasia-free subjects, adenomatous polyp patients, cancer patients and their tumours. Multivariate statistical analyses distinguished tumour from mucosa with a sensitivity of 78.9% and a specificity of 100% (P=3 × 10−7). In morphologically normal mucosa, age-dependent CGI methylation was observed for APC, AXIN2, DKK1, HPP1, N33, p16, SFRP1, SFRP2 and SFRP4 genes, and significant differences in CGI methylation levels were detected between groups. Multinomial logistic regression models based on the CGI methylation profiles from normal mucosa correctly identified 78.9% of cancer patients and 87.9% of non-cancer (neoplasia-free+polyp) patients (P=4.93 × 10−7) using APC, HPP1, p16, SFRP4, WIF1 and ESR1 methylation as the most informative variables. Similarly, CGI methylation of SFRP4, SFRP5 and WIF1 correctly identified 61.5% of polyp patients and 78.9% of neoplasia-free subjects (P=0.0167). The apparently normal mucosal field of patients presenting with neoplasia has evidently undergone significant epigenetic modification. Methylation of the genes selected by the models may play a role in the earliest stages of the development of colorectal neoplasia

NSAIDs Modulate CDKN2A, TP53, and DNA Content Risk for Progression to Esophageal Adenocarcinoma

BACKGROUND: Somatic genetic CDKN2A, TP53, and DNA content abnormalities are common in many human cancers and their precursors, including esophageal adenocarcinoma (EA) and Barrett's esophagus (BE), conditions for which aspirin and other nonsteroidal anti-inflammatory drugs (NSAIDs) have been proposed as possible chemopreventive agents; however, little is known about the ability of a biomarker panel to predict progression to cancer nor how NSAID use may modulate progression. We aimed to evaluate somatic genetic abnormalities with NSAIDs as predictors of EA in a prospective cohort study of patients with BE. METHODS AND FINDINGS: Esophageal biopsies from 243 patients with BE were evaluated at baseline for TP53 and CDKN2A (p16) alterations, tetraploidy, and aneuploidy using sequencing; loss of heterozygosity (LOH); methylation-specific PCR; and flow cytometry. At 10 y, all abnormalities, except CDKN2A mutation and methylation, contributed to EA risk significantly by univariate analysis, ranging from 17p LOH (relative risk [RR] = 10.6; 95% confidence interval [CI] 5.2–21.3, p < 0.001) to 9p LOH (RR = 2.6; 95% CI 1.1–6.0, p = 0.03). A panel of abnormalities including 17p LOH, DNA content tetraploidy and aneuploidy, and 9p LOH was the best predictor of EA (RR = 38.7; 95% CI 10.8–138.5, p < 0.001). Patients with no baseline abnormality had a 12% 10-y cumulative EA incidence, whereas patients with 17p LOH, DNA content abnormalities, and 9p LOH had at least a 79.1% 10-y EA incidence. In patients with zero, one, two, or three baseline panel abnormalities, there was a significant trend toward EA risk reduction among NSAID users compared to nonusers (p = 0.01). The strongest protective effect was seen in participants with multiple genetic abnormalities, with NSAID nonusers having an observed 10-y EA risk of 79%, compared to 30% for NSAID users (p < 0.001). CONCLUSIONS: A combination of 17p LOH, 9p LOH, and DNA content abnormalities provided better EA risk prediction than any single TP53, CDKN2A, or DNA content lesion alone. NSAIDs are associated with reduced EA risk, especially in patients with multiple high-risk molecular abnormalities