abstract

General properties of an Abelian connection in Fedosov deformation quantization are investigated. The definition and the criterion of being a finite formal series for an Abelian connection are presented. A proof that in \(2\)-dimensional (2D) case the Abelian connection is an infinite formal series is done.

abstract

Considerations concerning the possibility to associate some “phenome- nological” quantities that describe the field of point charges and the “particle” characteristics of point sources are presented. Relationships between the potential of the charges and the flux density of particles of the sources and relations among cross sections and some fundamental constants are also presented in this paper.

abstract

We investigate self-similar solutions of evolution equation of a (1+1) dimensional real, scalar field \(\varphi \) with V-shaped field potential \(U\,(\varphi ) = | \varphi |.\) The equation contains a nonlinear term of the form \({\rm sign}\,(\varphi )\), and it has a scaling symmetry. It turns out that there are several families of the self-similar solutions with qualitatively different behaviour. We also discuss a rather interesting example of evolution with non self-similar initial data — the corresponding solution contains a self-similar component.

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We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker–Planck equation with boundary conditions and calculate the mean first passage time (MFPT) which appears always finite, also for the subdiffusive case. Then, for the case of the jumping-size distribution in form of the Lévy distribution, we determine the probability density distributions and MFPT by means of numerical simulations. Dependence of the results on process parameters, as well as on the Lévy distribution width, is discussed.

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First, in order to support the empirical mass formula discussed in this paper for fundamental fermions, our previous work on an “intrinsic interpretation” of lepton and quark generations is summarized. In this framework, some intrinsic dynamical factors are proposed as responsible for the structure of fundamental-fermion empirical mass formula. Then, a satisfactory mass sum rule for charged leptons is derived, predicting perfectly the (actual) experimental central value 1776.99 MeV of \(m_\tau \), when the input of experimental values of \(m_e\) and \(m_\mu \) is applied. The derivation goes through identifying in the structure of three-parameter empirical mass formula for charged leptons a tiny combination of parameters which, if postulated to be exactly zero, gives a parameter constraint leading to the satisfactory mass sum rule.

abstract

We are going to construct the interpolating action for the free superstring. We start from Nambu–Goto action and construct interpolating Lagrangian. We generate a first class algebra with primary constraint. Then this leads us to obtain the Lagrangian density in Polyakov form. Also we calculate interpolating boundary condition.

abstract

A systematic extension of the Monte Carlo (MC) algorithm, that solves the DGLAP equation, into the so-called the one-loop CCFM evolution is presented. Modifications are related to a \(z\)-dependent coupling constant; transverse momentum dependence is added to the \(x\)-dependence of the parton distributions. The presented Markovian algorithm for one-loop CCFM evolution is the first step in extending it to other more sophisticated schemes beyond DGLAP. In particular, implementing the complete CCFM will be the next step. The presently implemented one-loop CCFM option will be a useful tool in testing the forthcoming MC solutions. Numerical results of the new MC are confronted with other non-MC numerical solutions. The agreement within the MC statistical error of \(\sim 0.1\%\) is found. Also, numerical results for \(k^{\rm T}\)-dependent structure functions are presented.

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Following a model recently investigated by Veneziano and Wosiek we briefly introduce Planar Quantum Mechanics (PQM). Then, we present high precision numerical results in the sectors with two and three fermions. We confirm, that the transition point in the ’t Hooft’s coupling constant \(\lambda \) occurs in these sectors at \(\lambda _{\rm c} = 1\), as was expected in this model.

abstract

After a pedestrian review of the noncommutative standard model we compute the 1-loop corrections to its seesaw mechanism.

abstract

Electron captures are amongst the most important weak interaction rates related to the dynamics of stellar core collapse. They play a key role in the gravitational collapse of the core of a massive star triggering the supernova explosion. Titanium isotopes are believed to have significant impact on controlling the lepton-to-baryon fraction in the late phases of evolution of core of massive stars. This work consists of the calculation of electron capture rates on titanium isotopes. The \(pn\)-QRPA theory is used to calculate electron capture rates in stellar matter. The electron capture rates are calculated over a wide range of densities \((10 \leq \rho Y_{e}\) (g / cm\(^{3}) \leq 10^{11})\) and temperatures \((10^{7} \leq T\,(K) \leq 30 \times 10^{9})\). Here we also report the differences in electron capture rates with the earlier calculations including those using large scale shell model.

abstract

The volume and surface symmetry parts of the nuclear symmetry energy and other coefficients of the liquid droplet model are determined from the measured atomic masses by the maximum likelihood estimator. The volume symmetry energy coefficient extracted from finite nuclei provides a constraint on the nuclear symmetry energy. This approach also yields the neutron skin of a finite nucleus through its relationship with the volume and surface symmetry terms and the Coulomb energy coefficient. The description of nuclear matter from the isoscalar and isovector components of the density dependent M3Y effective interaction provides a value of the symmetry energy that is consistent with the empirical value of the symmetry energy extracted from measured atomic masses and with other modern theoretical descriptions of nuclear matter.

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Shell model features are investigated for the Deuterium and \({}^4\)He with a semirealistic potential, using the Hybrid Multideterminant method applied to the bare Hamiltonian. For a sufficiently large single-particle space we found that few Slater determinants account for most of the binding energy of \({}^4\)He. Using only one Slater determinant with all symmetries restored with the appropriate projectors to good quantum numbers, we can account for about 84% of the binding energy of \({}^4\)He.

abstract

The effects of different forms of the sound-velocity function \(c_{\rm s}(T)\) on the hydrodynamic evolution of matter created in the central region of ultra-relativistic heavy-ion collisions are studied. At high temperatures (above the critical temperature \(T_{\rm c}\)) we use the sound velocity function obtained from the recent lattice simulations of QCD, whereas at low temperatures we use the ideal hadron gas model. At moderate temperatures different interpolations between those two results are employed. They are characterized by different values of the local maximum (at \(T = 0.4 \,T_{\rm c}\)) and local minimum (at \(T=T_{\rm c}\)). The extreme values are chosen in such a way that at high temperature all considered sound-velocity functions yield the entropy density consistent with the lattice simulations of QCD. We find that the presence of a distinct minimum of the sound velocity leads to a very long (\(\sim \) 20 fm/c) evolution time of the system. Since such long evolution times are not compatible with the recent estimates based on the HBT interferometry, we conclude that the hydrodynamic description becomes adequate if the QCD cross-over phase transition renders the smooth temperature variations of the sound velocity, with a possible shallow minimum at \(T_{\rm c}\) where the values of \(c_{\rm s}^2(T)\) remain well above 0.1.

abstract

The numerical algorithm solving Kohn–Sham (KS) equation for the free or confined atom on uniform mesh is presented. Using the spherical symmetry of system, the three-dimensional KS equation is reduced to the one-dimensional functional eigenproblem. The functional eigenproblem is transformed to the algebraic eigenproblem with symmetric, tridiagonal matrix where the smallest eigenvalues are searched by the bisection. The Poisson equation is solved using Numerov algorithm. The atom electron density is calculated by the self-consistent-field procedure. The final solution is obtained by the Richardson extrapolation. The RAtom program is presented, where all described algorithms are implemented. The RAtom is used to analyze N, Al, Ga and In atom applying Slater and VWN approximation for the correlation and exchange energy. For these atoms the eigenvalues, the components of total energy and the electron distribution are calculated. The obtained eigenvalues agree with the results reported for the shooting method on the logarithmic mesh within \(10^{-5}\) Ha.

abstract

Motivated on the very recent experiments to determine the acceleration of the alpha decay of meta-stable radionuclides in metallic environment some work has been done to strengthten the importance in the process of electrons screening in metals. Thus, by combining the Gamow decay theory with electrostatic screening in Debye–Hückel approximation (jellium model) a formula for “the shift” in screening energy which enters in the decay enhancement factor expression that copes well with these experiments has been derived. It was established that to simulate the poly-atoms system containing decaying isotopes in QM&MD codes calculations, and to include “the screening energy shift” of protons, decay alpha, beta\(^{+}\) particles due to all surrounding interacting effects, it is sufficiently only to substitute the code ruly pseudo-potential input for hydrogen-like atoms (including alpha) by a screened Coulomb potential as from the well-known Gamow alpha decay theory. For demonstration is used the QM&MD code package which usually performs density-functional theory (DFT) total-energy calculations for materials ranging from insulators to transition metals. This package employs first-principles pseudo-potentials and a plane-wave basis-set, and it was used to do a special calculus for some metal environments (Pd) where protons–deuterons are implanted or when it is alloyed with a radionuclide-like isotopes (\(^{174}\)Hf\(_{72}\)), the results compare well with the existing experiments on the decay enhancement. These works give further arguments for a cheap solution to remove the transuranic waste (involving all alpha-decay) of used-up rods of fission reactors in a time period of a few years.

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At the linking length \(R=0.2\,{\bar n}^{-1\,/\,3}\approx 6.3\) Mpc (\(\bar n\) is the mean galaxy density), we have extracted 540 groups from a approximately volume-limited LRG sample of the SDSS Data Release 5. In order to investigate the correlations between galaxy properties and environment, we compare basic properties of member galaxies of groups with those of field galaxies in different redshift bins, and find that these properties of LRGs are nearly independent of environment.