Incommensurate Charge Density Waves in the adiabatic Hubbard-Holstein model

The adiabatic, Holstein-Hubbard model describes electrons on a chain with step $a$ interacting with themselves (with coupling $U$) and with a classical phonon field \f_x (with coupling \l). There is Peierls instability if the electronic ground state energy F(\f) as a functional of \f_x has a minimum which corresponds to a periodic function with period ${\pi\over p_F}$, where $p_F$ is the Fermi momentum. We consider ${p_F\over\pi a}$ irrational so that the CDW is {\it incommensurate} with the chain. We prove in a rigorous way in the spinless case, when \l,U are small and {U\over\l} large, that a)when the electronic interaction is attractive $U<0$ there is no Peierls instability b)when the interaction is repulsive $U>0$ there is Peierls instability in the sense that our convergent expansion for F(\f), truncated at the second order, has a minimum which corresponds to an analytical and ${\pi\over p_F}$ periodic \f_x. Such a minimum is found solving an infinite set of coupled self-consistent equations, one for each of the infinite Fourier modes of \f_x.Comment: 16 pages, 1 picture. To appear Phys. Rev.

Gap generation in the BCS model with finite range temporal interaction

In the [BCS] paper the theory of superconductivity was developed for the BCS model, in which the (instantaneous) interaction is only between fermions of opposite momentum and spin. Such model was analyzed by variational methods, finding that a superconducting behavior is energetically favorable. Subsequently it was claimed that in the thermodynamic limit the BCS model is equivalent to the (exactly solvable) quadratic mean field BCS model; a rigorous proof of this claim is however still lacking. In this paper we consider the BCS model with a finite range temporal interaction, and we prove rigorously its equivalence with the mean field BCS model in the thermodinamic limit if the range is long enough, by a (uniformly convergent) perturbation expansion about mean field theory.Comment: 14 page

Coherent x-ray wavefront reconstruction of a partially illuminated Fresnel zone plate

International audienceA detailed characterization of the coherent x-ray wavefront produced by a partially illuminated Fresnel zone plate is presented. We show, by numerical and experimental approaches, how the beam size and the focal depth are strongly influenced by the illumination conditions, while the phase of the focal spot remains constant. These results confirm that the partial illumination can be used for coherent diffraction experiments. Finally, we demonstrate the possibility of reconstructing the complex-valued illumination function by simple measurement of the far field intensity in the specific case of partial illumination

Constructive Field Theory and Applications: Perspectives and Open Problems

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the constructive methods well within the 21st century

Management of Complications Caused By a Massive Left Ventricle Tumor in a Neonate

We report a case of a neonate born with a giant fibroma occupying the entirety of her left ventricle. Due to the extensive resection, her postoperative course was complicated by severely diminished left ventricular function and complete heart block necessitating extracorporeal support. Ultimately, cardiac resynchronization therapy was employed, after which the infant’s ventricular function gradually improved and she was successfully discharged to home

Rigorous proof of Luttinger liquid behavior in the 1d Hubbard model

We give the first rigorous (non perturbative) proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from half filling. The analysis is based on the combination of multiscale analysis with Ward identities bases on a hidden and approximate local chiral gauge invariance. No use is done of exact solutions or special integrability properties of the Hubbard model, and the results can be in fact easily generalized to include non local interactions, magnetic fields or interaction with external potential

Exact solution of a 2D interacting fermion model

We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior.Comment: 59 pages, 3 figures, v2: further references added; additional subsections elaborating mathematical details; additional appendix with details on the relation to lattice fermion

From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index α∈(1/8,1/4)\alpha\in(1/8,1/4)

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\'evy area

Virgo cluster early-type dwarf galaxies with the Sloan Digital Sky Survey. II. Early-type dwarfs with central star formation

Despite the common picture of an early-type dwarf (dE) as a quiescent galaxy with no star formation and little gas, we identify 23 dEs that have blue central colors caused by recent or ongoing star formation in our sample of 476 Virgo cluster dEs. In addition, 14 objects that were mostly classified as (candidate) BCDs have similar properties. Among the certain cluster members, the dEs with blue centers reach a fraction of more than 15% of the dE population at brighter (B<=16) magnitudes. A spectral analysis of the centers of 16 galaxies reveals in all cases an underlying old population that dominates the mass, with M(old)>=90% for all but one object. Therefore the majority of these galaxies will appear like ordinary dEs within ~one Gigayear or less after the last episode of star formation. Their overall gas content is less than that of dwarf irregular galaxies, but higher than that of ordinary dEs. Their flattening distribution suggests the shape of a thick disk, similar to what has been found for dEs with disk features in Paper I of this series. Their projected spatial distribution shows no central clustering, and their distribution with projected local density follows that of irregular galaxies, indicative of an unrelaxed population. This is corroborated by their velocity distribution, which displays two side peaks characteristic of recent infall. We discuss possible formation mechanisms (ram-pressure stripping, tidally induced star formation, harassment) that might be able to explain both the disk shape and the central star formation of the dEs with blue centers.Comment: 16 pages + 15 figures. Accepted for publication in AJ. We recommend downloading the full resolution version from http://www.virgo-cluster.com/lisker2006b.ps.g

Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging

Coherent diffraction imaging (CDI) on Bragg reflections is a promising technique for the study of three-dimensional (3D) composition and strain fields in nanostructures, which can be recovered directly from the coherent diffraction data recorded on single objects. In this article we report results obtained for single homogeneous and heterogeneous nanowires with a diameter smaller than 100 nm, for which we used CDI to retrieve information about deformation and faults existing in these wires. The article also discusses the influence of stacking faults, which can create artefacts during the reconstruction of the nanowire shape and deformation.Comment: 18 pages, 6 figures Submitted to New Journal of Physic