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A detailed comparative qualitative analysis and numerical simulation of evolution of the cosmological models based on the doublet of classical and phantom scalar fields with self-action. The 2-dimensional and 3-dimensional projections of…
We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform.…
We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy,…
We study cosmological effects of homogeneous tachyon field as dark energy. We concentrate on two different scalar field potentials, the inverse square potential and the exponential potential. These models have a unique feature that the…
The structure of cylindrical double layers is studied using a modified Poisson Boltzmann theory and the density functional approach. In the model double layer, the electrode is a cylindrical polyion that is infinitely long, impenetrable,…
Using a probabilistic interpretation of resonant states, we propose a formula useful to calculate the lifetime of a resonance using square-integrable real basis-set expansion techniques. Our approach does not require an estimation of the…
We construct a scalar field based cosmological model, possessing a cosmological singularity characterized by a finite value of the cosmological radius and an infinite scalar curvature. Using the methods of the qualitative theory of…
In this work, we obtained energy levels of one dimensional quartic anharmonic oscillator by using neural network system. Quartic anharmonic oscillator is a very important tool in quantum mechanics and also in quantum field theory. Our…
We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a…
New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a…
Using the technique of tridiagonal representation approach; for the first time, we extend this method to study quantum systems with literally perturbed Hamiltonians. Specifically, we consider a quantum system in a 3D spherical oscillator…
The multifractal properties of the electronic spectrum of a general quasiperiodic chain are studied in first order in the quasiperiodic potential strength. Analytical expressions for the generalized dimensions are found and are in good…
In this work, we report on the possibility of occurrence of oscillon configurations in the fourth state of matter. Oscillons are extremely long-lived, time-periodic, spatially-localised scalar field structures. Starting from a scalar field…
We study the dynamics of a scalar field in the brane cosmology. We assume that a scalar field is confined in our 4-dimensional world. As for the potential of the scalar field, we discuss three typical models: (1) a power-law potential, (2)…
We develop a versatile and analytically solvable potential which fairly reproduces the combined potential of an $\alpha+$nucleus system resulting from both the attractive nuclear and repulsive electrostatic potentials. The potential is…
We present an asymptotic analysis of a mesoscale energy for bilayer membranes that has been introduced and analyzed in two space dimensions by the second and third author (Arch. Ration. Mech. Anal. 193, 2009). The energy is both non-local…
Shapes and energies of icosahedral fullerenes are studied on an atomically detailed level. The numerical results based on the effective binary carbon-carbon potential are related to the theory of elasticity of crystalline membranes with…
We study two uncoupled oscillators, horizontal and vertical, residing in rectilinear polygons (with only vertical and horizontal sides) and impacting elastically from their boundary. The main purpose of the article is to analyze the…
The three-dimensional nonlinear dynamics of an electron gas in a semiconductor quantum well is analyzed in terms of a self-consistent fluid formulation and a variational approach. Assuming a time-dependent localized profile for the fluid…
We study the analytic structure for the eigenvalues of the one-dimensional Dirac oscillator, by analytically continuing its frequency on the complex plane. A twofold Riemann surface is found, connecting the two states of a pair of particle…