Relativistic BCS-BEC Crossover at Zero Temperature

We investigate the BCS-BEC crossover at zero temperature in the frame of a relativistic model. The universality of the BCS-BEC crossover for non-relativistic systems breaks down in relativistic case and the crossover can be induced by changing the density. When the effective scattering length is much less than the fermion Compton wavelength, we recover the non-relativistic result if the gas is initially in non-relativistic state. At ultra-strong coupling where the scattering length is of the order of the Compton wavelength, a new BEC state appears. In this state the condensed bosons become nearly massless and anti-fermions are excited. The behavior of the Goldstone mode and the mixing between the amplitude and phase modes are significantly different in different condensed regions.Comment: 8 pages, 3 figures. V2: typos corrected, a comment on mean field theory adde

Modified semiclassical approximation for trapped Bose gases

A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The results of the modified approach are shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. Effective thermodynamic limit is defined for any confining dimension. The behaviour of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed.Comment: Revtex file, 13 page

Syndecan-4 knockout leads to reduced extracellular transglutaminase-2 and protects against tubulointerstitial fibrosis

Transglutaminase type 2 (TG2) is an extracellular matrix crosslinking enzyme with a pivotal role in kidney fibrosis. The interaction of TG2 with the heparan sulfate proteoglycan syndecan-4 (Sdc4) regulates the cell surface trafficking, localization, and activity of TG2 in vitro but remains unstudied in vivo. We tested the hypothesis that Sdc4 is required for cell surface targeting of TG2 and the development of kidney fibrosis in CKD. Wild-type and Sdc4-null mice were subjected to unilateral ureteric obstruction and aristolochic acid nephropathy (AAN) as experimental models of kidney fibrosis. Analysis of renal scarring by Masson trichrome staining, kidney hydroxyproline levels, and collagen immunofluorescence demonstrated progressive fibrosis associated with increases in extracellular TG2 and TG activity in the tubulointerstitium in both models. Knockout of Sdc-4 reduced these effects and prevented AAN-induced increases in total and active TGF-b1. In wild-type mice subjected to AAN, extracellular TG2 colocalized with Sdc4 in the tubular interstitium and basement membrane, where TG2 also colocalized with heparan sulfate chains. Heparitinase I, which selectively cleaves heparan sulfate, completely abolished extracellular TG2 in normal and diseased kidney sections. In conclusion, the lack of Sdc4 heparan sulfate chains in the kidneys of Sdc4-null mice abrogates injury-induced externalization of TG2, thereby preventing profibrotic crosslinking of extracellular matrix and recruitment of large latent TGF-b1. This finding suggests that targeting the TG2- Sdc4 interaction may provide a specific interventional strategy for the treatment of CKD

An Optimal Algorithm for the Maximum-Density Segment Problem

We address a fundamental problem arising from analysis of biomolecular sequences. The input consists of two numbers $w_{\min}$ and $w_{\max}$ and a sequence $S$ of $n$ number pairs $(a_i,w_i)$ with $w_i>0$. Let {\em segment} $S(i,j)$ of $S$ be the consecutive subsequence of $S$ between indices $i$ and $j$. The {\em density} of $S(i,j)$ is $d(i,j)=(a_i+a_{i+1}+...+a_j)/(w_i+w_{i+1}+...+w_j)$. The {\em maximum-density segment problem} is to find a maximum-density segment over all segments $S(i,j)$ with $w_{\min}\leq w_i+w_{i+1}+...+w_j \leq w_{\max}$. The best previously known algorithm for the problem, due to Goldwasser, Kao, and Lu, runs in $O(n\log(w_{\max}-w_{\min}+1))$ time. In the present paper, we solve the problem in O(n) time. Our approach bypasses the complicated {\em right-skew decomposition}, introduced by Lin, Jiang, and Chao. As a result, our algorithm has the capability to process the input sequence in an online manner, which is an important feature for dealing with genome-scale sequences. Moreover, for a type of input sequences $S$ representable in $O(m)$ space, we show how to exploit the sparsity of $S$ and solve the maximum-density segment problem for $S$ in $O(m)$ time.Comment: 15 pages, 12 figures, an early version of this paper was presented at 11th Annual European Symposium on Algorithms (ESA 2003), Budapest, Hungary, September 15-20, 200

Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit

We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the thermodynamic limit. The BMPS is built on a dual series of reduced biorthonormal bases for the left and right Perron states of a non-Hermitian matrix. We propose two alternative infinite-size Biorthonormal TMRG (iBTMRG) algorithms and compare their numerical performance in both finite and infinite systems. We show that both iBTMRGs produce a dual infinite-BMPS (iBMPS) which are translationally invariant in the thermodynamic limit. We also develop an efficient wave function transformation of the iBTMRG, an analogy of McCulloch in the infinite-DMRG [arXiv:0804.2509 (2008)], to predict the wave function as the lattice size is increased. The resulting iBMPS allows for probing bulk properties of the system in the thermodynamic limit without boundary effects and allows for reducing the computational cost to be independent of the lattice size, which are illustrated by calculating the magnetization as a function of the temperature and the critical spin-spin correlation in the thermodynamic limit for a 2D classical Ising model.Comment: 14 pages, 9 figure

The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

Numerical Simulation of an Electroweak Oscillon

Numerical simulations of the bosonic sector of the $SU(2)\times U(1)$ electroweak Standard Model in 3+1 dimensions have demonstrated the existence of an oscillon -- an extremely long-lived, localized, oscillatory solution to the equations of motion -- when the Higgs mass is equal to twice the $W^\pm$ boson mass. It contains total energy roughly 30 TeV localized in a region of radius 0.05 fm. A detailed description of these numerical results is presented.Comment: 12 pages, 8 figures, uses RevTeX4; v2: expanded results section, fixed typo

Coupling of polarization and spatial degrees of freedom of highly divergent emission in broad-area square vertical-cavity surface-emitting lasers

The polarization of highly divergent modes of broad-area square vertical-cavity surface-emitting lasers is shown to be only marginally affected by material anisotropies but determined by an interplay of the polarization properties of the Bragg cavity mirrors and of the transverse boundary conditions. This leads to a locking of the polarization direction to the boundaries and its indeterminacy for wave vectors oriented along the diagonal. We point out a non-Poissonian character of nearest-neighbor frequency spacing distribution and the impossibility of single-wave number solutions