Related papers: Variation and Series Approach to the Thomas-Fermi …
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
The Schwinger quantum correction to the classic Thomas-Fermi atom is directly derived by solving for the latter without recourse to a modeling after the harmonic oscillator potential and without solving for the particle density.
The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and…
This paper presents the Thomas-Fermi approach generalized to consider the particle correlations in many-body systems with non-Coulomb interaction potentials. The key points of the generalization consist in using integral formulation and…
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
We consider the probability measure minimizing a free energy functional equal to the sum of a Coulomb interaction, a confinement potential and an entropy term, which arises in the statistical mechanics of Coulomb gases. In the limit where…
We discuss a new simple field theory approach of Coulomb systems. Using a description in terms of fields, we introduce in a new way the statistical degrees of freedom in relation with the quantum mechanics. We show on a series of examples…
The correction to Maxwell-Boltzmann's velocity distribution law is obtained in the framework of the modified special relativity theory. The detection of velocity and velocity rate distributions for thermal molecules or atoms or other…
A recently introduced analytical model for the nuclear density profile[1] is implemented in the Extended Thomas-Fermi (ETF) energy density functional. This allows to (i) shed a new light on the issue of the sign of surface symmetry energy…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
A modification of Coulomb's law of friction uses a variable coefficient of friction that depends on a power law in the energy of mechanical oscillation. Through the use of three different exponents: 0, 1/2 and 1; all commonly encountered…
An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like $\gamma$-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in…
We use variational methods to calculate quasilocal energy quantum corrections. A comparison with the effective potential calculated at quadratic order is made by means of gaussian wave functionals. The method is a particular case of the…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
The application of van der Waals equation of state to the asymmetric nuclear matter is considered in a critical state region. The corrections to the van der Waals pressure and free energy due to the Fermi statistics are obtained starting…
We present a self-contained formalism for analyzing scale invariant differential equations. We first cast the scale invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background…
Considering the problem of scattering of charged particles, we introduce a new approach of taking the Coulomb interaction into account within the HORSE formalism. Compared to the conventional HORSE approach for uncharged particles, we add a…
Controllable nonlinear quantum interactions are a much sought after target for modern quantum technologies. They are typically difficult and costly to engineer for bespoke purposes. However controllable nonlinearities may have always been…