Flow equation approach to the linear response theory of superconductors

We apply the flow equation method for studying the current-current response function of electron systems with the pairing instability. To illustrate the specific scheme in which the flow equation procedure determines the two-particle Green's functions we reproduce the standard response kernel of the BCS superconductor. We next generalize this non-perturbative treatment considering the pairing field fluctuations. Our study indicates that the residual diamagnetic behavior detected above the transition temperature in the cuprate superconductors can originate from the noncondensed preformed pairs.Comment: 12 pages, 4 figure

Pairing of bosons in the condensed state of the boson-fermion model

A two component model of negative U centers coupled with the Fermi sea of itinerant fermions is discussed in connection with high-temperature superconductivity of cuprates, and superfluidity of atomic fermions. We examine the phase transition and the condensed state of this boson-fermion model (BFM) beyond the ordinary mean-field approximation in two and three dimensions. No pairing of fermions and no condensation are found in two-dimensions for any symmetry of the order parameter. The expansion in the strength of the order parameter near the transition yields no linear homogeneous term in the Ginzburg-Landau-Gor'kov equation and a zero upper critical field in any-dimensional BFM, which indicates that previous mean-field discussions of the model are flawed. Normal and anomalous Green's functions are obtained diagrammatically and analytically in the condensed state of a simplest version of 3D BFM. A pairing of bosons analogous to the Cooper pairing of fermions is found. There are three coupled condensates in the model, described by the off-diagonal single-particle boson, pair-fermion and pair-boson fields. These results negate the common wisdom that the boson-fermion model is adequately described by the BCS theory at weak coupling.Comment: 7 pages, 4 figure

Real space inhomogeneities in high temperature superconductors: the perspective of two-component model

The two-component model of high temperature superconductors in its real space version has been solved using Bogoliubov-de Gennes equations. The disorder in the electron and boson subsystem has been taken into account. It strongly modifies the superconducting properties and leads to local variations of the gap parameter and density of states. The assumption that the impurities mainly modify boson energies offers natural explanation of the puzzling positive correlation between the positions of impurities and the values of the order parameter found in the scanning tunnelling microscopy experiments.Comment: 19 pages, IOPP style include

Atomistic mechanism of transmembrane helix association

Transmembrane helix association is a fundamental step in the folding of helical membrane proteins. The prototypical example of this association is formation of the glycophorin dimer. While its structure and stability have been well-characterized experimentally, the detailed assembly mechanism is harder to obtain. Here, we use all-atom simulations within phospholipid membrane to study glycophorin association. We find that initial association results in the formation of a non-native intermediate, separated by a significant free energy barrier from the dimer with a native binding interface. We have used transition-path sampling to determine the association mechanism. We find that the mechanism of the initial bimolecular association to form the intermediate state can be mediated by many possible contacts, but seems to be particularly favoured by formation of non-native contacts between the C-termini of the two helices. On the other hand, the contacts which are key to determining progression from the intermediate to the native state are those which define the native binding interface, reminiscent of the role played by native contacts in determining folding of globular proteins. As a check on the simulations, we have computed association and dissociation rates from the transition-path sampling. We obtain results in reasonable accord with available experimental data, after correcting for differences in native state stability. Our results yield an atomistic description of the mechanism for a simple prototype of helical membrane protein folding

Effect of disorder on superconductivity in the boson-fermion model

We study how a randomness of either boson or fermion site energies affects the superconducting phase of the boson fermion model. We find that, contrary to what is expected for s-wave superconductors, the non-magnetic disorder is detrimental to the s-wave superconductivity. However, depending in which subsystem the disorder is located, we can observe different channels being affected. Weak disorder of the fermion subsystem is responsible mainly for renormalization of the single particle density of states while disorder in the boson subsystem directly leads to fluctuation of the strength of the effective pairing between fermions.Comment: 7 pages, 6 figures. Physical Review B (accepted for publication

Dynamical elastic bodies in Newtonian gravity

Well-posedness for the initial value problem for a self-gravitating elastic body with free boundary in Newtonian gravity is proved. In the material frame, the Euler-Lagrange equation becomes, assuming suitable constitutive properties for the elastic material, a fully non-linear elliptic-hyperbolic system with boundary conditions of Neumann type. For systems of this type, the initial data must satisfy compatibility conditions in order to achieve regular solutions. Given a relaxed reference configuration and a sufficiently small Newton's constant, a neigborhood of initial data satisfying the compatibility conditions is constructed

The impact of health on professionally active people's incomes in Poland. Microeconometric analysis

The outcome of the research confirms the occurrence of positive interaction between professionally active people's incomes and the self-assessed state of health. People declaring a bad state of health have incomes by 20% on average lower than people who enjoy good health (assuming that the remaining characteristics of the surveyed person are the same). In case of men, the impact of health state on incomes is slightly greater than in case of women.Wyniki badań potwierdzają istnienie pozytywnej zależności dochodów osób aktywnych zawodowo od stanu zdrowia mierzonego jego samooceną. Osoby deklarujące zły stan zdrowia osiągają dochody przeciętnie o 20% niższe niż osoby, które cieszą się dobrym stanem zdrowia (przy założeniu, że pozostałe charakterystyki badanej osoby są takie same). W przypadku mężczyzn zależność dochodów od stanu zdrowia jest nieznacznie silniejsza niż w przypadku kobiet

Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions

We obtain full description of eigenvalues and eigenvectors of composition operators Cϕ : A (R) → A (R) for a real analytic self map ϕ : R → R as well as an isomorphic description of corresponding eigenspaces. We completely characterize those ϕ for which Abel’s equation f ◦ ϕ = f + 1 has a real analytic solution on the real line. We find cases when the operator Cϕ has roots using a constructed embedding of ϕ into the so-called real analytic iteration semigroups.(1) The research of the authors was partially supported by MEC and FEDER Project MTM2010-15200 and MTM2013-43540-P and the work of Bonet also by GV Project Prometeo II/2013/013. The research of Domanski was supported by National Center of Science, Poland, Grant No. NN201 605340. (2) The authors are very indebted to K. Pawalowski (Poznan) for providing us with references [26,27,47] and also explaining some topological arguments of [10]. The authors are also thankful to M. Langenbruch (Oldenburg) for providing a copy of [29].Bonet Solves, JA.; Domanski, P. (2015). Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions. Integral Equations and Operator Theory. 81(4):455-482. https://doi.org/10.1007/s00020-014-2175-4S455482814Abel, N.H.: Determination d’une function au moyen d’une equation qui ne contient qu’une seule variable. In: Oeuvres Complètes, vol. II, pp. 246-248. Christiania (1881)Baker I.N.: Zusammensetzung ganzer Funktionen. Math. Z. 69, 121–163 (1958)Baker I.N.: Permutable power series and regular iteration. J. Aust. Math. Soc. 2, 265–294 (1961)Baker I.N.: Permutable entire functions. Math. Z. 79, 243–249 (1962)Baker I.N.: Fractional iteration near a fixpoint of multiplier 1. J. Aust. Math. Soc. 4, 143–148 (1964)Baker I.N.: Non-embeddable functions with a fixpoint of multiplier 1. Math. Z. 99, 337–384 (1967)Baker I.N.: On a class of nonembeddable entire functions. J. Ramanujan Math. 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Evidence for the Gompertz Curve in the Income Distribution of Brazil 1978-2005

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in "The European Physical Journal B

Magnetic and quadrupolar order in a one-dimensional ferromagnet with cubic crystal-field anisotropy

The zero temperature phase diagram of a one-dimensional S=2 Heisenberg ferromagnet with single-ion cubic anisotropy is studied numerically using the density-matrix renormalization group method. Evidence is found that although the model does not involve quadrupolar couplings, there is a purely quadrupolar phase for large values of the anisotropy. The phase transition between the magnetic and quadrupolar phases is continuous and it seems to be characterized by Ising critical exponents.Comment: 11 pages, 7 figures, REVTeX, accepted in Phys. Rev. B (scheduled on June 99