The low-energy phase-only action in a superconductor: a comparison with the XY model

The derivation of the effective theory for the phase degrees of freedom in a superconductor is still, to some extent, an open issue. It is commonly assumed that the classical XY model and its quantum generalizations can be exploited as effective phase-only models. In the quantum regime, however, this assumption leads to spurious results, such as the violation of the Galilean invariance in the continuum model. Starting from a general microscopic model, in this paper we explicitly derive the effective low-energy theory for the phase, up to fourth-order terms. This expansion allows us to properly take into account dynamic effects beyond the Gaussian level, both in the continuum and in the lattice model. After evaluating the one-loop correction to the superfluid density we critically discuss the qualitative and quantitative differences between the results obtained within the quantum XY model and within the correct low-energy theory, both in the case of s-wave and d-wave symmetry of the superconducting order parameter. Specifically, we find dynamic anharmonic vertices, which are absent in the quantum XY model, and are crucial to restore Galilean invariance in the continuum model. As far as the more realistic lattice model is concerned, in the weak-to-intermediate-coupling regime we find that the phase-fluctuation effects are quantitatively reduced with respect to the XY model. On the other hand, in the strong-coupling regime we show that the correspondence between the microscopically derived action and the quantum XY model is recovered, except for the low-density regime.Comment: 29 pages, 11 figures. Slightly revised presentation, accepted for publication in Phys. Rev.

On magnetic catalysis in even-flavor QED3

In this paper, we discuss the role of an external magnetic field on the dynamically generated fermion mass in even-flavor QED in three space-time dimensions. Based on some reasonable approximations, we present analytic arguments on the fact that, for weak fields, the magnetically-induced mass increases quadratically with increasing field, while at strong fields one crosses over to a mass scaling logarithmically with the external field. We also confirm this type of scaling behavior through quenched lattice calculations using the non-compact version for the gauge field. Both the zero and finite temperature cases are examined. A preliminary study of the fermion condensate in the presence of magnetic flux tubes on the lattice is also included.Comment: 38 pages latex, 18 figures and a style file (axodraw) incorporated (some clarifying remarks concerning the validity of the approximations made and some references were added correcting an earlier version; no effect on conclusions; version to appear in Phys. Rev. D.

Is the presence or absence of tumour necrosis a significant predictor of survival in renal cell cancer?

<b>OBJECTIVE:</b> Currently when renal cancer pathology is assessed the presence or absence of necrosis is simply reported. It has been suggested that a presence or absence response ignores heterogeneity and a classification based on the extent of necrosis involvement would aid prognostic value in cancer-specific survival. The aim of this study was to determine whether a quantitative assessment of tumour necrosis would provide additional prognostic information.<p></p> <b>METHODS:</b> We studied the pathological features and cancer-specific survival of 47 patients with renal cancer undergoing surgery with curative intent. A quantitative assessment of tumour necrosis was compared to the presence or absence of necrosis.<p></p> <b>RESULTS:</b> Tumour necrosis was present in 27 of 47 cases. A simple assessment of the presence or absence was not associated with cancer-specific survival (p = 0.052). When assessed quantitatively, tumour necrosis was associated with decreased cancer-specific survival (p < 0.001). A 2-tiered assessment, <25% and >25% involvement of necrosis, was further utilised and shown to predict cancer-specific survival (p < 0.001). On multivariate analysis, using this 2-tiered assessment of <25% and >25% involvement of necrosis was retained as a significant independent factor for cancer-specific survival (HR 11.84, 95% CI 3.81-36.75, p < 0.001).<p></p> <b>CONCLUSION:</b> A simple assessment of the presence/absence of tumour necrosis is reported to be a prognostic factor in renal cell cancer. In this study, the presence/absence was not shown to be a significant prognostic marker of cancer-specific survival. However, a more accurate quantitative assessment of tumour necrosis, whereby a 2-tiered response is still utilised, but basing this on <25% and >25% involvement of necrosis was statistically significant and independent in predicting cancer-specific survival