Related papers: Analytical Characterization of Oscillon Energy and…
We study the energy properties of a particle in one dimensional semi-harmonic rectangular wells and barriers. The integration of energies is obtained by solving a simple transcendental equation. Scattering states are shown to include cases…
We present the O(alpha) and O(alpha^3 ln(alpha)) corrections to the total decay width of orthopositronium in closed analytic form, in terms of basic transcendental numbers, which can be evaluated numerically to arbitrary precision.
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged soft matter problems, we work out the Coulombic grand potential of a long cylindrical charged polyion in a binary electrolyte solution of arbitrary valency and for…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
Scalars carrying a conserved global charge $Q$ can form stable localized field configurations composed of a large number of particles. These non-topological solitons are spherically symmetric and are called Q-balls. While usually analyzed…
Two interacting electrons in a harmonic oscillator potential under the influence of a perpendicular homogeneous magnetic field are considered. Analytic expressions are obtained for the energy spectrum of the two- and three-dimensional…
We consider two situations that can be modeled by oscillators. First we show that the universe itself is a normal mode of Planck scale oscillators. Next we show that a background Zero Point Field or dark energy can be modeled by…
A stable oscillon was found in the (classical) analysis of the SU(2) gauged Higgs model under a 2:1 ratio between the Higgs and W masses, both analytically and numerically. We extend these results by constructing oscillons for all values of…
The harmonic quarks are applied to the analysis of quark structures of long-lived $D$-mesons and $\psi/J$. In the harmonic quark model the quarks of long-lived mesons ($\pi^0$, $\pi^\pm$, $K^\pm$, $K^0$, $B^0$, $B^\pm$) are weakly…
We analyze the results of a paper on ``Relativistic quantum dynamics of a charged particle in cosmic string spacetime in the presence of magnetic field and scalar potential''. We show that the authors did not obtain the spectrum of the…
We discuss similarity between oscillons and oscillational mode in perturbed $\phi^4$. For small depths of the perturbing potential it is difficult to distinguish between oscillons and the mode in moderately long time evolution, moreover one…
We compute the vacuum polarization energies for a couple of soliton models in one space and one time dimensions. These solitons are mappings that connect different degenerate vacua. From the considered sample solitons we conjecture that the…
We consider decay of the inflaton with a quartic potential coupled to other fields, including gravity, but restricted to spherical symmetry. We describe analytically an early, quasilinear regime, during which inflaton fluctuations and the…
The classical two-dimensional one-component plasma is an exactly solvable model, at some special temperature, even when the one-body potential acting on the particles has a quadrupolar term. As a supplement to a recent work of Di Francesco,…
Analytic expressions for the energy eigenvalues and eigenfunctions of a one-dimensional harmonic crystal are obtained. The average energy and density profiles are obtained numerically as a function of temperature. A surprisingly large…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented.…
We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…
Matrix elements of potential energy are examined in detail. We consider a model problem - a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and…