abstract

PT-symmetry gives rise to a new class of complex Hamiltonians with real spectrum. The pseudo-Hermicity of Hamiltonians are discussed and PT-symmetric Hamiltonians are shown to belong to class of pseudo-Hermitian Hamiltonians. We have studied this for a general potential with an emphasis on a particular type.

abstract

Solutions of the generalized Langevin equation are simulated by using a jumping process as a model of the stochastic force. This force is strongly correlated; we consider two forms of correlations’ tail: \(\sim 1\)/\(t^2\) and \(\sim 1\)/\(\sqrt t\). We demonstrate that remnants of the initial condition can be recognized in the velocity probability distributions after a long time if the correlation function falls slowly. Moreover, the system can exhibit both normal and anomalously slow diffusion which is reflected by the structure of the spectra.

abstract

The Arrhenius activation energy for the reaction \(A + A \leftrightarrows B + B\) in a dilute gas is calculated from a temperature dependence of the rate constant obtained from the perturbation solution of the Boltzmann equation. The first and the second approximation to the velocity distribution function are used in an analysis of nonequilibrium effects. Results obtained for the line-of-centers model and the Prigogine–Xhrouet model of reactive differential cross sections are presented. The Arrhenius activation energy is represented as a function of appropriate threshold energies.

abstract

This paper contains a detailed analysis of the properties of the scalar product of short and long living superpositions of neutral \(|K_{0}\rangle , |{\overline {K}}_{0}\rangle \) mesons. It is shown for the exact effective Hamiltonian for neutral meson subsystem that the scalar product of its eigenvectors, which correspond with these short and long living superpositions, cannot be real under the assumption of CPT conserved and CP violated. The standard conclusion obtained within the Lee–Oehme–Yang theory of neutral kaons is that in this case such a product should be real. Also, the general and model independent proof that probabilities of transitions \(|K_{0}\rangle \, \rightarrow \,|{\overline {K}}_{0}\rangle \) and \(|{\overline {K}}_{0}\rangle \, \rightarrow \,|K_{0}\rangle \) are not equal in the CP non–invariant system is given.

abstract

Algorithm is constructed which models single-file motion of particles interacting with each other and with the surroundings. As an example, we present the results of Brownian Dynamics simulations of the motion of cations moving through a short very narrow channel containing a device called “gate”, which may open and close the channel.

abstract

In this paper we examine the Casimir effect for charged fields in presence of external magnetic field. We consider scalar field (connected with spinless particles) and the Dirac field (connected with 1/2-spin particles). In both cases we describe quantum field using the canonical formalism. We obtain vacuum energy by direct solving field equations and using the mode summation method. In order to compute the renormalized vacuum energy we use the Abel–Plana formula.

abstract

The coupling constant of \(f_0\to \omega \gamma \) decay is calculated using 3-point sum rule and light cone QCD sum rules. We investigate the results within the two-models which depend on \(\theta \) angle.

abstract

We continue the discussion of a very simple empirical neutrino mass formula, implying the mass proportion \(m_1 : m_2 : m_3 = 1 : 4 : 24(1-\beta ^2)\). For the value \(\beta = (5-1)(5-3)\)/\(5^2 = 8\)/\(25\) the formula predicts precisely \(\Delta m^2_{21} \sim 8.0\times 10^{-5}\,{\rm eV}^2\) in consistency with the experiment, when the input of experimental estimate \(\Delta m^2_{32} \sim 2.4\times 10^{-3}\,{\rm eV}^2\) is applied.

abstract

We present precision Monte Carlo calculations solving the QCD evolution equations up to the next-to-leading-order (NLO) level. They employ forward Markovian Monte Carlo (FMC) algorithms, which provide the rigorous solutions of the QCD evolution equations. Appropriate Monte Carlo algorithms are described in detail. They are implemented in the form of the Monte Carlo program EvolFMC, which features the NLO kernels for the QCD evolution. The presented numerical results agree with those from independent, non-MC, programs (QCDNum16, APCheb33) at the level of \(0.1\%\). In this way we have demonstrated the feasibility of the precision MC calculations for the QCD evolution and provided very useful numerical tests (benchmarks) for other, non-Markovian, MC algorithms developed recently.

abstract

The coefficients of the volume, surface, Coulomb, asymmetry and pairing energy terms of the semiempirical liquid drop model mass formula have been determined by furnishing best fit to the observed mass excesses. Slightly different sets of the weighting parameters for liquid drop model mass formula have been obtained from minimizations of \(\chi ^2\) and mean square deviation. The most recent experimental and estimated mass excesses from Audi–Wapstra–Thibault atomic mass table have been used for the least square fitting procedure. Equation of state, nuclear incompressibility, nuclear mean free path and the most stable nuclei for corresponding atomic numbers, all are in good agreement with the experimental results.

abstract

We have calculated the range of protons and alpha particles in NaI scintillator which is a commonly used substance in scintillation detector manufacturing. The electronic stopping power of protons and alpha particles in NaI is calculated first by using the theoretical formulation of Montenegro et al. The range calculation has been performed by applying a technique that we developed in the earlier works. The results are compared with Monte Carlo simulation program SRIM2003 and PRAL. It is found that the obtained results are in satisfactory agreement with the literature.

abstract

The fusion dynamics is studied in heavy-ion collisions over wide range of neutron content \((0.5 \le N\)/\(Z \le 2.0)\) by employing several different theoretical models such as Skyrme energy density model and proximity potential, as well as parameterized potentials due to Bass, Christensen and Winther, Ngô and Ngô and Denisov. We find that all these potentials give similar isotopic dependence for the fusion barrier heights, positions as well as cross-sections. Fusion barrier heights and positions follow a second order non-linear isotopic dependence whereas fusion cross-sections follow a linear dependence. The collision of neutron-deficient nuclei results into a reduced fusion cross-section whereas collision of neutron-rich nuclei leads to an enhanced fusion probability. The maximal isotopic dependence is obtained for the near barrier energies that reduces to insignificant level for higher incident energies. Our normalised observations are almost model independent indicating the universality in these predictions.

abstract

Quantum Molecular Dynamics model was applied to reproduce the experimentally obtained charge, isotopic and velocity distributions of forward emitted fragments for the \(^{18}\)O+\(^{9}\)Be and \(^{18}\)O+\(^{181}\)Ta systems at \(E_{\rm proj}=35\,A\)MeV. The charge numbers of the analyzed outgoing fragments were in the range of \(Z=2-11\) and \(Z=2-9\), respectively. The model taking into account the mutual two- and three-body effective nucleon–nucleon interactions and the short range of two body scattering appeared to be not completely suitable for the description of collisions leading to the forward emission of fragments.