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.     

Graphite C-axis thermal conductivity

This paper models the c$c$-axis thermal conductivity of thin graphite layers taking into account phonon confinement. A Debye model is used to calculate graphite c$c$-axis thermal conductivity, which is found to be 4 orders of magnitude smaller than in the graphite basal plane. This reduced thermal conductivity is promising for devices with improved thermoelectric figure of merit, ZT$ZT$, and thermal conduction along graphite c$c$-axis. Results of graphite thermal conductivity in the basal plane are also presented and discussed. These calculations have been done for ideal graphite structures that are a few monolayers thick, free of defects, and free of boundary scattering processes. To achieve the low calculated values of thermal conductivity, it will be necessary to fabricate high-quality graphite structures; this will pose significant fabrication challenges.     

Some properties of generalized Fisher information in the context of nonextensive thermostatistics

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q$q$-Gaussian distributions and the q$q$-entropies. The minimum of the generalized Fisher information among distributions with a fixed moment, or with a fixed q$q$-entropy is attained, in both cases, by a generalized q$q$-Gaussian distribution. This complements the fact that the q$q$-Gaussians maximize the q$q$-entropies subject to a moment constraint, and yields new variational characterizations of the generalizedq$q$-Gaussians. We show that the generalized Fisher information naturally pop up in the expression of the time derivative of the q$q$-entropies, for distributions satisfying a certain nonlinear heat equation. This result includes as a particular case the classical de Bruijn identity. Then we study further properties of the generalized Fisher information and of their minimization. We show that, though non additive, the generalized Fisher information of a combined system is upper bounded. In the case of mixing, we show that the generalized Fisher information is convex for q≥1$q\ge 1$. Finally, we show that the minimization of the generalized Fisher information subject to moment constraints satisfies a Legendre structure analog to the Legendre structure of thermodynamics.     

Detection of community structure in networks based on community coefficients

Determining community structure in networks is fundamental to the analysis of the structural and functional properties of those networks, including social networks, computer networks, and biological networks. Modularity function Q$Q$, which was proposed by Newman and Girvan, was once the most widely used criterion for evaluating the partition of a network into communities. However, modularity Q$Q$ is subject to a serious resolution limit. In this paper, we propose a new function for evaluating the partition of a network into communities. This is called community coefficient C$C$. Using community coefficient C$C$, we can automatically identify the ideal number of communities in the network, without any prior knowledge. We demonstrate that community coefficient C$C$ is superior to the modularity Q$Q$ and does not have a resolution limit. We also compared the two widely used community structure partitioning methods, the hierarchical partitioning algorithm and the normalized cuts (Ncut) spectral partitioning algorithm. We tested these methods on computer-generated networks and real-world networks whose community structures were already known. The Ncut algorithm and community coefficient C$C$ were found to produce better results than hierarchical algorithms. Unlike several other community detection methods, the proposed method effectively partitioned the networks into different community structures and indicated the correct number of communities.     

Kac’s ring: Entropy and Poincaré recurrence

We study the entropy of an N$N$-site Kac ring in a non-equilibrium state. As the system dynamically evolves towards equilibrium and eventually to the initial state exhibiting Poincaré recurrence, we see that the entropy saturates over a period of time which is large for large N$N$. At about the time of order N$N$, the system starts to return to its initial state. We show that there is indeed a perfect “recurrence of statistical fluctuations”, which we are able to explore, as Kac’s ring possesses a finite recurrence time. Entropy is shown here to be a periodic function of the Poincaré recurrence time.     

Calculating statistical distributions from operator relations: The statistical distributions of various intermediate statistics

In this paper, we give a general discussion on the calculation of the statistical distribution from a given operator relation of creation, annihilation, and number operators. Our result shows that as long as the relation between the number operator and the creation and annihilation operators can be expressed as a^†b=Λ(N)$a^{†}b=\Lambda \left(N\right)$ or N=Λ⁻¹(a^†b)$N={\Lambda }^{-1}\left(a^{†}b\right)$, where N$N$, a^†$a^{†}$, and b$b$ denote the number, creation, and annihilation operators, i.e., N$N$ is a function of quadratic product of the creation and annihilation operators, the corresponding statistical distribution is the Gentile distribution, a statistical distribution in which the maximum occupation number is an arbitrary integer. As examples, we discuss the statistical distributions corresponding to various operator relations. In particular, besides the Bose–Einstein and Fermi–Dirac cases, we discuss the statistical distributions for various schemes of intermediate statistics, especially various q$q$-deformation schemes. Our result shows that the statistical distributions corresponding to various q$q$-deformation schemes are various Gentile distributions with different maximum occupation numbers which are determined by the deformation parameter q$q$. This result shows that the results given in much literature on the q$q$-deformation distribution are inaccurate or incomplete.     

On generalisations of the log-Normal distribution by means of a new product definition in the Kapteyn process

We discuss the modification of the Kapteyn multiplicative process using the q$q$-product of Borges [E.P. Borges, A possible deformed algebra and calculus inspired in nonextensive thermostatistics, Physica A 340 (2004) 95]. Depending on the value of the index q$q$ a generalisation of the log-Normal distribution is yielded. Namely, the distribution increases the tail for small (when q<1$q<1$) or large (when q>1$q>1$) values of the variable upon analysis. The usual log-Normal distribution is retrieved when q=1$q=1$, which corresponds to the traditional Kapteyn multiplicative process. The main statistical features of this distribution as well as related random number generators and tables of quantiles of the Kolmogorov–Smirnov distance are presented. Finally, we illustrate the validity of this scenario by describing a set of variables of biological and financial origin.     

Exact solution of the alternating XXZ spin chain with generic non-diagonal boundaries

The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K$K$-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused R$R$-matrices and K$K$-matrices, we obtain certain closed operator identities and conditions, which allow us to construct an inhomogeneous T−Q$T-Q$ relation and the associated Bethe Ansatz equations accounting for the eigenvalues of the transfer matrix.     

A centrality measure for communication ability in weighted network

This paper proposes a new node centrality measurement in a weighted network, the communication centrality, which is inspired by Hirsch’s h$h$-index. We investigated the properties of the communication centrality, and proved that the distribution of the communication centrality has the power-law upper tail in weighted scale-free networks. Relevant measures for node and network are discussed as extensions. A case study of a scientific collaboration network indicates that the communication centrality is different from other common centrality measures and other h$h$-type indexes. Communication centrality displays moderate correlation with other indexes, and contains a well-balanced mix of other centrality measures and cannot be replaced by any of them.     

Cross sections for (d–t) neutron interaction with germanium isotopes

The cross sections for (n,x)$(n,x)$ reactions with Ge isotopes were measured at (d–t) neutron energies around 14 MeV with the activation technique using metal discs of natural composition. Calculations of detector efficiency, incident neutron spectrum and correction factors were performed with the Monte Carlo technique (MCNP4C code). Cross sections data are presented for ⁷⁰Ge(n,2n$n,2n$)⁶⁹Ge, ⁷⁴Ge(n,α$n,\alpha$)^71mZn, ⁷⁶Ge(n,2n$n,2n$)^75(m + g)Ge, ⁷⁰Ge(n,p$n,p$)⁷⁰Ga and ⁷²Ge(n,2n$n,2n$)^71gGe reactions. The cross section results for ⁷²Ge(n,2n$n,2n$)^71gGe reaction were reported for the first time. Some other cross sections were obtained with higher precision, including the ⁷⁰Ge(n,p$n,p$)⁷⁰Ga reaction. Theoretical calculations of excitation functions were performed with the TALYS-1.0 code and compared with the experimental cross section values. Data were included in the EXFOR database.     

String modular phases in Calabi–Yau families

We investigate the structure of singular Calabi–Yau varieties in moduli spaces that contain a Brieskorn–Pham point. Our main tool is a construction of families of deformed motives over the parameter space. We analyze these motives for general fibers and explicitly compute the L$L$-series for singular fibers for several families. We find that the resulting motivic L$L$-functions agree with the L$L$-series of modular forms whose weight depends both on the rank of the motive and the degree of the degeneration of the variety. Surprisingly, these motivic L$L$-functions are identical in several cases to L$L$-series derived from weighted Fermat hypersurfaces. This shows that singular Calabi–Yau spaces of non-conifold type can admit a string worldsheet interpretation, much like rational theories, and that the corresponding irrational conformal field theories inherit information from the Gepner conformal field theory of the weighted Fermat fiber of the family. These results suggest that phase transitions via non-conifold configurations are physically plausible. In the case of severe degenerations we find a dimensional transmutation of the motives. This suggests further that singular configurations with non-conifold singularities may facilitate transitions between Calabi–Yau varieties of different dimensions.     

Ranking the spreading influence in complex networks

Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a target node and the node set with the highest k$k$-core value, we present an improved method to generate the ranking list to evaluate the node spreading influence. Comparing with the epidemic process results for four real networks and the Barabási–Albert network, the parameterless method could identify the node spreading influence more accurately than the ones generated by the degree k$k$, closeness centrality, k$k$-shell and mixed degree decomposition methods. This work would be helpful for deeply understanding the node importance of a network.     

Nonextensivity measure for earthquake networks

Studying earthquakes and the associated geodynamic processes based on the complex network theory enables us to learn about the universal features of the earthquake phenomenon. In addition, we can determine new indices for identification of regions geophysically. It was found that earthquake networks are scale free and its degree distribution obeys the power law. Here we claim that the q$q$-exponential function is better than power law model for fitting the degree distribution. We also study the behavior of q$q$ parameter (nonextensivity measure) with respect to resolution. It was previously asserted in Eur. Phys. J. B (2012) 85: 23; that the topological characteristics of earthquake networks are dependent on each other for large values of the resolution. A peak in the plot of q$q$ against resolution determines the beginning of the assertion range.     

Entanglement thresholds for displaying the quantum nature of teleportation

A protocol for transferring an unknown single qubit state evidences quantum features when the average fidelity of the outcomes is, in principle, greater than 2/3$2/3$. We propose to use the probabilistic and unambiguous state extraction scheme   as a mechanism to redistribute the fidelity in the outcome of the standard teleportation when the process is performed with an X$X$-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the average fidelity f_X$f_X$ to display quantum features, i.e., we find a threshold C_X$C_X$ for the concurrence of the channel. On the other hand, if the mechanism for redistributing fidelity is successful then we find a filterable outcome with average fidelity f_X,0$f_{X,0}$ that can be greater than f_X$f_X$. In addition, we find the threshold concurrence of the channel C_X,0$C_{X,0}$ in order for the average fidelity f_X,0$f_{X,0}$ to display quantum features and surprisingly, the threshold concurrence C_X,0$C_{X,0}$ can be less than C_X$C_X$. Even more, we find some special cases for which the threshold values become zero.     

Electrodynamics of a generalized charged particle in doubly special relativity framework

In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative κ$\kappa$-Minkowski space–time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard–Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of κ$\kappa$-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.     

Probing Planckian physics in de Sitter space with quantum correlations

We study the quantum correlation and quantum communication channel of both free scalar and fermionic fields in de Sitter space, while the Planckian modification presented by the choice of a particular α$\alpha$-vacuum has been considered. We show the occurrence of degradation of quantum entanglement between field modes for an inertial observer in curved space, due to the radiation associated with its cosmological horizon. Comparing with standard Bunch–Davies choice, the possible Planckian physics causes some extra decrement on the quantum correlation, which may provide the means to detect quantum gravitational effects via quantum information methodology in future. Beyond single-mode approximation, we construct proper Unruh modes admitting general α$\alpha$-vacua, and find a convergent feature of both bosonic and fermionic entanglements. In particular, we show that the convergent points of fermionic entanglement negativity are dependent on the choice of α$\alpha$. Moreover, an one-to-one correspondence between convergent points H_c$H_c$ of negativity and zeros of quantum capacity of quantum channels in de Sitter space has been proved.     

Theory of extreme correlations using canonical Fermions and path integrals

The  t$t$–J$J$  model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson–Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained.