Quantum physical relevance of the Einstein tensor

Taking quantum physics as well as large scale astronomical observations into account, a spacetime metric is introduced, such that the nonlinear part of the Einstein tensor contains effects of the order of Planck's constant.Comment: to appear in Brazilian Journal of Physic

On the Green's Function of the almost-Mathieu Operator

The square tight-binding model in a magnetic field leads to the almost-Mathieu operator which, for rational fields, reduces to a $q\times q$ matrix depending on the components $\mu$, $\nu$ of the wave vector in the magnetic Brillouinzone. We calculate the corresponding Green's function without explicit knowledge of eigenvalues and eigenfunctions and obtain analytical expressions for the diagonal and the first off-diagonal elements; the results which are consistent with the zero magnetic field case can be used to calculate several quantities of physical interest (e. g. the density of states over the entire spectrum, impurity levels in a magnetic field).Comment: 9 pages, 3 figures corrected some minor errors and typo

Supersymmetric Extension of the Quantum Spherical Model

In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short/long range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.Comment: 21 pages, fixed notation to match published versio

On the Finite-Temperature Generalization of the C-theorem and the Interplay between Classical and Quantum Fluctuations

The behavior of the finite-temperature C-function, defined by Neto and Fradkin [Nucl. Phys. B {\bf 400}, 525 (1993)], is analyzed within a d -dimensional exactly solvable lattice model, recently proposed by Vojta [Phys. Rev. B {\bf 53}, 710 (1996)], which is of the same universality class as the quantum nonlinear O(n) sigma model in the limit $n\to \infty$. The scaling functions of C for the cases d=1 (absence of long-range order), d=2 (existence of a quantum critical point), d=4 (existence of a line of finite temperature critical points that ends up with a quantum critical point) are derived and analyzed. The locations of regions where C is monotonically increasing (which depend significantly on d) are exactly determined. The results are interpreted within the finite-size scaling theory that has to be modified for d=4. PACS number(s): 05.20.-y, 05.50.+q, 75.10.Hk, 75.10.Jm, 63.70.+h, 05.30-d, 02.30Comment: 15 pages LATEX, ioplppt.sty file used, 6 EPS figures. Some changes made in section V (on finite-size scaling interpretation of the results obtained

Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields

We calculate the energy band structure for electrons in an external periodic potential combined with a perpendicular magnetic field. Electron-electron interactions are included within a Hartree approximation. The calculated energy spectra display a considerable degree of self-similarity, just as the ``Hofstadter butterfly.'' However, screening affects the butterfly, most importantly the bandwidths oscillate with magnetic field in a characteristic way. We also investigate the dynamic response of the electron system in the far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can be interpreted mainly in semiclassical terms, while others originate from inter(sub)band transitions.Comment: 4 pages with 2 embeded eps figures. Uses revtex, multicol and graphicx styles. Accepted for publication in PRB Brief Report

Dirac-Foldy term and the electromagnetic polarizability of the neutron

We reconsider the Dirac-Foldy contribution $\mu^2/m$ to the neutron electric polarizability. Using a Dirac equation approach to neutron-nucleus scattering, we review the definitions of Compton continuum ($\bar{\alpha}$), classical static ($\alpha^n_E$), and Schr\"{o}dinger ($\alpha_{Sch}$) polarizabilities and discuss in some detail their relationship. The latter $\alpha_{Sch}$ is the value of the neutron electric polarizability as obtained from an analysis using the Schr\"{o}dinger equation. We find in particular $\alpha_{Sch} = \bar{\alpha} - \mu^2/m$ , where $\mu$ is the magnitude of the magnetic moment of a neutron of mass $m$. However, we argue that the static polarizability $\alpha^n_E$ is correctly defined in the rest frame of the particle, leading to the conclusion that twice the Dirac-Foldy contribution should be added to $\alpha_{Sch}$ to obtain the static polarizability $\alpha^n_E$.Comment: 11 pages, RevTeX, to appear in Physical Review

One-dimensional fermions with incommensuration

We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from pi, and delta, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/ \delta --> 0, the number of states lying inside the q=0 gap is nonzero and equal to 2 \delta /\pi^2. Thus the limit q --> 0 differs from q=0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain close to dimerization, we use bosonization to argue that similar results hold; as q --> 0, we find a nontrivial density of states near zero energy. However, the limit q --> 0 and q=0 give the same results near commensurate wave numbers which are different from pi. We apply our results to the Azbel-Hofstadter problem of electrons hopping on a two-dimensional lattice in the presence of a magnetic field. Finally, we discuss the complete energy spectrum of noninteracting fermions with incommensurate hopping by going up to higher orders in delta.Comment: Revtex, 23 pages including 7 epsf figures; this is a greatly expanded version of cond-mat/981133

Vascular grading of angiogenesis: prognostic significance in breast cancer

The study aimed to evaluate the prognostic value of angiogenesis by vascular grading of primary breast tumours, and to evaluate the prognostic impact of adding the vascular grade to the Nottingham Prognostic Index (NPI). The investigation included 836 patients. The median follow-up time was 11 years and 4 months. The microvessels were immunohistochemically stained by antibodies against CD34. Angiogenesis was graded semiquantitatively by subjective scoring into three groups according to the expected number of microvessels in the most vascular tumour area. The vascular grading between observers was moderately reproduced (κ = 0.59). Vascular grade was significantly associated with axillary node involvement, tumour size, malignancy grade, oestrogen receptor status and histological type. In univariate analyses vascular grade significantly predicted recurrence free survival and overall survival for all patients (P< 0.0001), node-negative patients (P< 0.0001) and node-positive patients (P< 0.0001). Cox multivariate regression analysis showed that vascular grading contributed with independent prognostic value in all patients (P< 0.0001). A prognostic index including the vascular grade had clinical impact for 24% of the patients, who had a shift in prognostic group, as compared to NPI, and implied a better prognostic dissemination. We concluded that the angiogenesis determined by vascular grading has independent prognostic value of clinical relevance for patients with breast cancer. © 2000 Cancer Research Campaig

Does vascular endothelial growth factor (VEGF) predict local relapse and survival in radiotherapy-treated node-negative breast cancer?

The aim of this study was to determine the association of vascular endothelial growth factor (VEGF) content in 302 consecutive node-negative breast cancer (NNBC) patients treated with only locoregional radiotherapy to relapse free- (RFS) and overall survival (OS). VEGF content in tumour cytosols was measured by an enzymatic immunoassay for the major isoform VEGF165. The median age was 56 years, the median follow-up time 56 months. A wide range (0.01–144.79 pg μg−1 DNA) of VEGF content was found (median 1.92). Significant associations were found between VEGF and oestrogen receptor (ER) content, progesterone receptor (PR) and tumour size (P = 0.005). Univariate analysis displayed significant reduced RFS and OS for patients with higher VEGF content (P = 0.0113 and P = 0.0075 respectively). A total of 43 recurrences have been found (ten local relapses within the breast, five in the axillary or supraclavicular lymph nodes and 28 distant metastasis). There was no significant correlation between the localization of the relapse and the VEGF content. Multivariate analysis suggested VEGF as the only predictor of OS (relative risk (RR) = 3.6, 95% confidence interval (CI) = 0.97–13.37), and in patients with T1 tumours (n = 236) the multivariate analysis clearly displayed VEGF as the only independent predictor of both RFS and OS (RR = 5.1, CI = 1.07–24.59). In the sub-group with ER-positive tumours (n = 229), multivariate analysis showed VEGF as the only significant predictor of RFS and OS (RR = 10.44, CI = 1.26–86.38). The results suggest VEGF165 as a predictor of RFS and OS in NNBC patients treated with locoregional radiotherapy, comprising especially patients with favourable prognosis of T1 tumours, or ER-positive tumours. The high VEGF expression might define a radioresistant phenotype, or indicate an early distant spread which might require adjuvant systemic treatment. © 1999 Cancer Research Campaig

Genetic regulation of MUC1 alternative splicing in human tissues

The membrane mucin MUC1 is aberrantly expressed in a variety of cancers, and in stomach, it is a ligand for Helicobacter pylori where it plays a role in gastric carcinogenesis. Splicing variation, leading to a 9-amino acid insertion in the signal peptide region, was proposed to be because of a single-nucleotide polymorphism (rs4072037) at the 5′ end of exon 2, but is also reported to be cancer-associated. However, the effect of rs4072037 on this splicing event in healthy non-cancer tissues and on the additional spliceoforms of MUC1, including those lacking the polymorphic tandem repeat (TR) domain, has never been investigated. Here we show that in both foetal and adult tissues of known genotype, there is clear evidence for the role of rs4072037 in controlling alternative splicing of the 5′ exon 2 region of both full-length transcripts and those lacking the TR domain. Although there is some evidence for additional genetic and epigenetic influences, there is no indication of an effect of the TR domain on the proportions of the spliceoforms. In conclusion, over-representation of certain transcripts in tumour material cannot be evaluated without information on the SNP genotype as well