A series of analytical nonautonomous soliton solutions for the (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients in the presence of gain (loss) and a harmonic potential are obtained. The explicit functions which describe the evolution of the amplitude, phase and velocity are also given. Soliton’s phase and velocity are independent of the gain parameter, and only the amplitude is affected by the gain parameter. The dynamical behaviors for nonautonomous chirp-free and chirped solitons in a periodic distributed and dispersion decreasing systems are discussed. By modulating appropriate diffraction/dispersion parameters, we can trap the velocity of each soliton to control the interaction between soliton pairs. The real and imaginary parts of the spectral parameters control the separating or interacting behavior of chirp-free soliton pairs. However, the appearance of the chirp restrains the interaction between the chirped soliton pairs.

The quantum theory of the Coulomb field has been developed by Andrzej Staruszkiewicz in the long series of papers. This theory explains the universality and quantization of the electric charge observed in Nature. Moreover, the efforts have been made to determine the value of the elementary charge from its mathematical structure. Nonetheless, no other immediate applications of this theory have been proposed. We make such an attempt by (i) considering the classical energy operator and defining its counterpart in the quantum theory of the Coulomb field; (ii) determining the eigenstates of the energy operator and assigning energy to the excitations of the theory; and (iii) proposing a simple theoretical scheme to estimate the effect of the quantum fluctuations of the Coulomb field on the energy levels of hydrogen-like atoms. We argue that the recent experimental advances in hydrogen and muonic-hydrogen spectroscopy may provide the unique window of opportunity for the verification of the Staruszkiewicz theory.

In this paper, we integrate the (3+1)-dimensional Dirac equation for massless fermions, minimally coupled at static electric and magnetic external fields. For intense fields, the differential equation admits a closed-form analytical solution, expressed by biconfluent Heun functions (BHE). The obtained bi-spinors allow us to calculate the components of the four-current, and to obtain a special relation for the quantized energy as well. By cancelling out the electric field, the general relation of energy quantization finally leads to a discrete spectrum, similar to that obtained by Novoselov in graphene layers.

It is important to obtain effective operators by integrating out high energy degrees of freedom in physics. We suggest a general method of calculating accurate irrelevant operators in a scattering process without use of equation of motions. By using this method, for example, we will represent a complete set of dimension six operators in QCD, which are induced from physics beyond the standard model, supersymmetry and universal extra dimension. We will also show an example of effective anomalous 4-Fermi interactions induced from a little Higgs model.

Using the classical argument about tree level unitarity breakdown in combination with the precision electroweak data, it is shown, that if part of the Higgs sector is heavy and strongly interacting, this part is small and is out of range of the LHC. The limits take into account the recent Higgs search results at the LHC.

The rotational bands of \(^{161,163}\)Er are studied by deformed Hartree–Fock and angular momentum projection techniques. Energy spectra and the matrix elements of electromagnetic operators are calculated up to high spin values \(J={59/2}\) and compared with experimental measurement wherever available. The \(B(E2)\) and \(B(M1)\) values for some of the bands are evaluated.

The density fluctuation of the final state charged mesons are investigated in terms of two-dimensional scaled factorial moments in \(^{28}\)Si–Ag/Br interaction at an incident energy of \(14.5\) GeV per nucleon. The experimental results are compared with a microscopic transport model based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD). To accommodate the Bose–Einstein type correlation, that dominates the origin of intermittency, an algorithm based on reassigning charges of produced particles has been employed to the UrQMD data. However, our investigation shows that a strong self-affine intermittent behavior in the experiment still cannot be replicated by the simulation. The Hurst exponent is used to account for the experimentally observed anisotropy in the pseudorapidity — azimuthal angle plane. The usual power law type of scaling behavior of the factorial moments, typical of intermittency in one dimension, is retrieved only when independent phase-space directions are partitioned unequally. Several issues related to the underlying (multi)fractal structure of the density function are also examined.