Proximity effect in ferromagnet/triplet p-wave superconductor structures

The superconducting proximity effect in normal metal/insulator/ferromagnet/triplet p  -wave superconductor (N/I/FP) structures is studied based on an extended Blonder–Tinkham–Klapwijk (BTK) theory. Three kinds of pairings for the P side are chosen: px$p_x$, py$p_y$, px+ipy$p_x+i{p}_y$ waves. The transition from the “0” to “π” state is found in the conductance spectra with increasing the thickness of F or the ferromagnetic exchange energy. The large amplitude of the normalized conductance suggests the possible coexistence of the ferromagnetism and p-wave superconductivity in a small region near the F/P interface induced by the proximity effect.     

Coulomb impurity problem of graphene in magnetic fields

Analytical solutions to the Coulomb impurity problem of graphene in the absence of a magnetic field show that when the dimensionless strength of the Coulomb potential g$g$ reaches a critical value the solutions become supercritical with imaginary eigenenergies. Application of a magnetic field is a singular perturbation, and no analytical solutions are known except at a denumerably infinite set of magnetic fields. We find solutions to this problem by numerical diagonalization of the large Hamiltonian matrices. Solutions are qualitatively different from those of zero magnetic field. All energies are discrete and no complex energies are allowed. We have computed the finite-size scaling function of the probability density containing an s$s$-wave component of the Dirac wavefunctions. This function depends on the coupling constant, regularization parameter, and the gap. In the limit of vanishing regularization parameter our findings are consistent with the expected values of the exponent ν$\nu$ which determines the asymptotic behavior of the wavefunction near r=0$r=0$.     

Gromov–Witten invariants and rational curves on Grassmannians

We study the enumerative significance of the s$s$-pointed genus zero Gromov–Witten invariant on a homogeneous space X$X$. For that, we give an interpretation in terms of rational curves on X$X$.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

An efficient community detection method based on rank centrality

Community detection is a very important problem in social network analysis. Classical clustering approach, K$K$-means, has been shown to be very efficient to detect communities in networks. However, K$K$-means is quite sensitive to the initial centroids or seeds, especially when it is used to detect communities. To solve this problem, in this study, we propose an efficient algorithm K$K$-rank, which selects the top-K$K$ nodes with the highest rank centrality as the initial seeds, and updates these seeds by using an iterative technique like K$K$-means. Then we extend K$K$-rank to partition directed, weighted networks, and to detect overlapping communities. The empirical study on synthetic and real networks show that K$K$-rank is robust and better than the state-of-the-art algorithms including K$K$-means, BGLL, LPA, infomap and OSLOM.     

Skeleton of weighted social network

In the literature of social networks, understanding topological structure is an important scientific issue. In this paper, we construct a network from mobile phone call records and use the cumulative number of calls as a measure of the weight of a social tie. We extract skeletons from the weighted social network on the basis of the weights of ties, and we study their properties. We find that strong ties can support the skeleton in the network by studying the percolation characters. We explore the centrality of w$w$-skeletons based on the correlation between some centrality measures and the skeleton index w$w$ of a vertex, and we find that the average centrality of a w$w$-skeleton increases as w$w$ increases. We also study the cumulative degree distribution of the successive w$w$-skeletons and find that as w$w$ increases, the w$w$-skeleton tends to become more self-similar. Furthermore, fractal characteristics appear in higher w$w$-skeletons. We also explore the global information diffusion efficiency of w$w$-skeletons using simulations, from which we can see that the ties in the high w$w$-skeletons play important roles in information diffusion. Identifying such a simple structure of a w$w$-skeleton is a step forward toward understanding and representing the topological structure of weighted social networks.     

Influence of interface states on the temperature dependence and current–voltage characteristics of Ni/p-InP Schottky diodes

The ideality factor n$n$ and the barrier height _Φap${\Phi }_{ap}$ of the sputtered Ni/p-InP Schottky diodes have been calculated from their experimental Current–voltage (I–V)$\left(I\text{–}V\right)$ characteristics in the temperature range of 60–400 K with steps of 10 K. The n$n$ and _Φap${\Phi }_{ap}$ values for the device have been obtained as 1.27 and 0.87 eV at 300 K and 1.13 and 0.91 eV at 400 K, respectively. The n$n$ values larger than unity at high temperatures indicate the presence of a thin native oxide layer at the semiconductor/metal interface. The barrier height (BH) has been assumed to be bias dependent due to the presence of an interfacial layer and interface states located at the interfacial layer-semiconductor interface. Interfacial layer-thermionic emission current mechanism has been fitted to experimental I–V$I\text{–}V$ data by considering the bias-dependence of the BH at each temperature. The best fitting values of the series resistance _Rs$R_s$ and interface state density _Ns$N_s$ together with the bias-dependence of the BH have been used at each temperature, and the _Rs$R_s$ and _Ns$N_s$ versus temperature plots have been drawn. It has been seen that the experimental and theoretical forward bias I–V$I\text{–}V$ data are in excellent agreement with each other in the temperature range of 60–400 K. It has been seen that the _Rs$R_s$ and _Ns$N_s$ values increase with a decrease in temperature, confirming the results in the literature.     

Inflationary predictions at small γ

This Letter explores single field inflation models with a constant, but arbitrary speed of sound cs$c_s$, obtained by deforming the kinetic energy terms to a Dirac–Born–Infeld form. Allowing cs<1$c_s<1$ provides a simple parametrization of non-Gaussianity. The dependence of inflationary observables on the parameter cs$c_s$ is considered in the leading order slow roll approximation. The results show that in most cases the dependence is actually rather weak for the range of cs$c_s$ allowed by existing bounds on non-Gaussianity.     

Hermitian–Einstein connections on polystable orthogonal and symplectic parabolic Higgs bundles

Let X$X$ be a smooth complex projective curve and S⊂X$S\subset X$ a finite subset. We show that an orthogonal or symplectic parabolic Higgs bundle on X$X$ with parabolic structure over S$S$ admits a Hermitian–Einstein connection if and only if it is polystable.     

Analytical expressions for partial wave two-body Coulomb transition matrices at ground-state energy

Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann–Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p$p$-, d$d$- and f$f$-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states.     

The Tsallis–Laplace transform

We introduce here the q$q$-Laplace transform as a new weapon in Tsallis’ arsenal, discussing its main properties and analyzing some examples. The q$q$-Gaussian instance receives special consideration. Also, we derive the q$q$-partition function from the q$q$-Laplace transform.     

Probing many-body interactions in an optical lattice clock

We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p$p$-wave and s$s$-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA ⁸⁷${}^{87}$Sr and NIST ¹⁷¹${}^{171}$Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems.     

Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

We have studied the stochastic resonance (SR) of bistable systems coupled to a bath with a nonlinear system–bath interaction, by using the microscopic, generalized Caldeira–Leggett (CL) model. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and state-dependent (multiplicative) diffusion which preserve the fluctuation–dissipation relation (FDR). Results of our simulations are given as follows: (1) the spectral power amplification (SPA) exhibits SR not only for a$a$ and b$b$ but also for τ$\tau$ while the stationary probability distribution function is independent of them where a$a$ and b$b$ denote magnitudes of multiplicative and additive noises, respectively, and τ$\tau$ expresses the relaxation time of Ornstein–Uhlenbeck (OU) colored noise; (2) the SPA for coexisting additive and multiplicative noises has a single-peak but two-peak structure as functions of a$a$, b$b$ and/or τ$\tau$. Results (1) and (2) are qualitatively different from previous ones obtained by phenomenological Langevin models where the FDR is not held or indefinite. These show an importance of the FDR in a study on SR of open bistable systems.     

On the geometry of prequantization spaces

Given a Poisson (or more generally Dirac) manifold P$P$, there are two approaches to its geometric quantization: one involves a circle bundle Q$Q$ over P$P$ endowed with a Jacobi (or Jacobi–Dirac) structure; the other one involves a circle bundle with a (pre)contact groupoid structure over the (pre)symplectic groupoid of P$P$. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre)symplectic groupoid of P$P$ is obtained from the Lie groupoid of Q$Q$ via an S¹$S^1$ reduction that preserves both the Lie groupoid and the geometric structures.     

Intertwining operators for Sklyanin algebra and elliptic hypergeometric series

Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ?$?$ and −?−1$-?-1$ are constructed using the technique of intertwining vectors for elliptic L$L$-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W$W$-operators) serve as building blocks for the elliptic R$R$-matrix which intertwines tensor product of two L$L$-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang–Baxter equation for this R$R$-matrix follows from simpler equations of the star–triangle type for the W$W$-operators. A natural graphic representation of the objects and equations involved in the construction is used.