Related papers: Energy approximation for some double phase functio…
Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…
We establish some new results about the $\Gamma$-limit, with respect to the $L^1$-topology, of two different (but related) phase-field approximations of the so-called Euler's Elastica Bending Energy for curves in the plane.
An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+\epsilon =…
This simple text considers an application of Bohr-Sommerfeld quantization rule. It might be of interest for the students of physics.
A Density Matrix Functional theory is constructed semi-empirically for the two-level Lipkin model. This theory, based on natural orbitals and occupation numbers, is shown to provide a good description for the ground state energy of the…
In this thesis we study energy forms. These are quadratic forms on the space of real-valued measurable $m$-a.e. determined functions $$E:L^0(m) \to [0,\infty],$$ which assign to a measurable function $f$ its energy $E(f)$. Their two…
The electron and photon structure functions are compared. Advantages of the electron structure function are demonstrated. At very high momenta probabilistic (partonic) interpretation can be preserved despite strong $\gamma$-$Z$…
An exchange energy functional is proposed and tested for obtaining a class of excited-state energies using density-functional formalism. The functional is the excited-state counterpart of the local-density approximation functional for the…
A general approach for constructing multidimensional quasi-exactly solvable (QES) potentials with explicitly known eigenfunctions for two energy levels is proposed. Examples of new QES potentials are presented.
We derive a generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems. This class of approximations has a long and successful history, but it has not yet been…
The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently…
We construct a generalized-gradient approximation for the exchange-energy density of finite two-dimensional systems. Guided by non-empirical principles, we include the proper small-gradient limit and the proper tail for the exchange-hole…
Free electron approximation for electron states in poly($p$-phenylene vinylene) and other conjugated systems is developed. It provides simple and clear analytical expressions for energies of electron states and for wave functions. The…
We predict the existence of an energy barrier for collapse in a system of two tunnel-coupled repulsive and attractive quasi two-dimensional condensates trapped in a double-well potential. The ground state in such a system can have a lower…
New, approximate, two-electron wavefunctions are introduced for the two-electron atoms (cations), which account remarkably well for the ground-state energies and the lowest-excxited states (where available). A new scheme of electronic…
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled…
In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the…
Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger…
An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that…
In this note we formulate a sufficient condition for the quasiconvexity at $x \mapsto \lambda x$ of certain functionals $I(u)$ which model the stored-energy of elastic materials subject to a deformation $u$. The materials we consider may…