On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty principle to Rényi entropies. We recall that in both Shannon and Rényi cases, and for a given dimension n$n$, the only case of equality occurs for Gaussian random vectors. We show that as n$n$ grows, however, the bound is also asymptotically attained in the cases of n$n$-dimensional Student-t$t$ and Student-r$r$ distributions. A complete analytical study is performed in a special case of a Student-t$t$ distribution. We also show numerically that this effect exists for the particular case of a n$n$-dimensional Cauchy variable, whatever the Rényi entropy considered, extending the results of Abe and illustrating the analytical asymptotic study of the Student-t$t$ case. In the Student-r$r$ case, we show numerically that the same behavior occurs for uniformly distributed vectors. These particular cases and other ones investigated in this paper are interesting since they show that this asymptotic behavior cannot be considered as a “Gaussianization” of the vector when the dimension increases.     

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.     

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.     

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.     

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.     

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

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.     

Mixed density wave state in quasi-2D organic conductor

The density wave phase of α-$\alpha \mathrm{-}$(BEDT-TTF)₂KHg(SCN)₄ was investigated by transport properties and magnetic susceptibility. The density wave transition was observed as a broad increase at T_DW$T_{\mathrm{DW}}$=9 K by resistance measurement. Temperature dependence of the static magnetic susceptibility χ$\chi$ shows a large Curie tail below 100 K. By subtracting the Curie component, we found that the magnetic susceptibility increases like weak ferromagnetism with decreasing temperature below 7.4 K. The gradual increase of χ$\chi$ below T_DW$T_{\mathrm{DW}}$ is not expected in simple CDW or SDW, where the magnetic susceptibility decreases with decreasing temperature due to the reduction of Pauli paramagnetic component. To explain the weak ferromagnetic behavior, we consider the coexistence of CDW and SDW. We propose a model of the mixed density wave, where CDW exists with antiferromagnetically coupled canting spins.     

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.     

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.     

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.     

The H2+ molecular ion: Low-lying states

Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H₂⁺ of the quantum numbers (n,m,Λ,±)$(n,m,\Lambda ,\pm )$  with n=m=0$n=m=0$ at Λ=0,1,2$\Lambda =0,1,2$, with n=1$n=1$, m=0$m=0$ and n=0$n=0$, m=1$m=1$ at Λ=0$\Lambda =0$ of both parities are explored for all interproton distances R$R$. For all these states this approximation provides the relative accuracy ?10⁻⁵$?10^{-5}$ (not less than 5 s.d.) locally, for any real coordinate x$x$ in eigenfunctions, when for total energy E(R)$E\left(R\right)$ it gives 10-11 s.d. for R∈[0,50]$R\in [0,50]$  a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1$E1$ is calculated with not less than 6 s.d. A dramatic dip in the E1$E1$ oscillator strength f_{1sσg−3pσu}$f_{1s{\sigma }_g-3p{\sigma }_u}$ at R∼R_eq$R\sim R_{eq}$ is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±)$(0,0,0,\pm )$ (or, equivalently, 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ potential curves is approximated with modified Pade Re^−R[Pade(8/7)](R)$R{e}^{-R}\left[Pade(8/7)\right]\left(R\right)$ with not less than 4-5 figures at R∈[0,40]$R\in [0,40]$ a.u. Sum of potential curves E_1sσg+E_2pσu$E_{1s{\sigma }_g}+E_{2p{\sigma }_u}$ is approximated by Pade 1/R[Pade(5/8)](R)$1/R\left[Pade(5/8)\right]\left(R\right)$ in R∈[0,40]$R\in [0,40]$ a.u. with not less than 3-4 figures.     

Critical dynamics in systems controlled by fractional kinetic equations

The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0<α<1$0<\alpha <1$, fractional Laplacian of the order σ$\sigma$, and Gaussian noise correlator. The case of non-linearity φ^m${\phi }^m$ with odd m≥3$m\ge 3$ is considered. It is proved that the model is multiplicatively renormalizable. Propagators were found in the momentum and coordinate representation, expressed in terms of Fox’s H functions.     

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.     

Charmonium suppression at RHIC and SPS: A hadronic baseline

A kinetic equation approach is applied to model anomalous J/ψ$J/\psi$ suppression at RHIC and SPS by absorption in a hadron resonance gas which successfully describes statistical hadron production in both experiments. The puzzling rapidity dependence of the PHENIX data is reproduced as a geometric effect due to a longer absorption path for J/ψ$J/\psi$ production at forward rapidity.