Related papers: Derivative Expansion of Wave Function Equivalent P…

This article is a continuation of our previous work (Phys. Rev. A 88, 032511 (2013)). The prefactors for the partial-wave expansion of the helium atom are derived. Due to series of cancellations, the partial-wave increments of the energy…

Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…

This paper presents a new technique to calculate the evolution of a quantum wavefunction in a chosen spatial basis by minimizing the accumulated action. Introduction of a finite temporal basis reduces the problem to a set of linear…

By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…

The electromagnetic scattering amplitude of a dielectric wedge is not known in closed form. This makes the computation of the Casimir-Polder (CP) interaction between a polarizable particle and a dielectric wedge challenging. This geometry…

Solutions for a class of wave equations with effective potentials are obtained by a method of a Laplace-transform. Quasinormal modes appear naturally in the solutions only in a spatially truncated form; their coefficients are uniquely…

We continue our explorations of the transport characteristics in junction-configurations comprising semimetals with quadratic band-crossings, observed in the bandstructures of both two- and three-dimensional materials. Here, we consider…

We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the…

We show that the pre-factors of all terms of the one-dimensional Hubbard model correlation-function asymptotic expansions have an universal form, as the corresponding critical exponents. In addition to calculating such pre-factors, our…

We propose a method to determine the effective potential of QCD from the gap equation, by introducing the homotopy method between the solutions of the equation of motion. Via this method, the effective potential beyond the bare vertex…

We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also…

We construct generally applicable short-time perturbative expansions for some fidelities, such as the input-output fidelity, the entanglement fidelity, and the average fidelity. Successive terms of these expansions yield characteristic…

The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…

Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…

Extending density functional theory (DFT) to an {\it ab initio} orbital functional theory (OFT) requires new methodology for nonlocal exchange and correlation potentials. This paper describes such modifications to a standard Dirac-Slater…

The positron-hydrogen atom scattering system is considered within the S-wave model. Convergence in the elastic scattering, excitation, ionization, and positronium formation channels is studied as a function of the number and type of states…

General depth weighted scatter estimators are introduced and investigated. For general depth functions, we find out that these affine equivariant scatter estimators are Fisher consistent and unbiased for a wide range of multivariate…

The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…

A two-parameter extension of the density-scaled double hybrid approach of Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)] is presented. It is based on the explicit treatment of a fraction of multideterminantal exact exchange. The…

We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…