Related papers: Structure, Time Propagation and Dissipative Terms …
We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches,…
A novel method for the calculation of eigenfrequencies of non-uniformly filled spherical cavity resonators is developed. The impact of the system symmetry on the electromagnetic field distribution as well as on its degrees of freedom (the…
In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical…
This work investigates the multiplicity and differentiability of eigenfrequencies in structures with various symmetries. In particular, the study explores how the geometric and design variable symmetries affect the distribution of…
We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration…
A first comprehensive treatment on complex eigenmodes is presented for general lossy traveling-wave electromagnetic structures where the per unit length propagation phase shift ($\beta$) dependent complex eigenfrequencies $\Omega(\beta)$…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
The Schr\"odinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different…
We consider Schr\"odinger equations with variable coefficients and the harmonic potential. We suppose the perturbation is short-range type in the sense of [Nakamura 2004]. We characterize the wave front set of the solutions to the equation…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
We introduce an analytical framework to calculate the values of key observables in a strongly disordered discrete time crystal (DTC) without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement…
Energy dissipation is highly intermittent in turbulent plasmas, being localized in coherent structures such as current sheets. The statistical analysis of spatial dissipative structures is an effective approach to studying turbulence. In…
The concept of a generalized nonanalytic expansion which involves nonanalytic combinations of exponentials, logarithms and powers of a coupling is introduced and its use illustrated in various areas of physics. Dispersion relations for the…
A time-domain numerical code based on the constitutive relations of nonlinear acoustics for simulating ultrasound propagation is presented. To model frequency power law attenuation, such as observed in biological media, multiple relaxation…
We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional…