Related papers: The kinetic energy operator in the subspaces of wa…
We propose a simple and efficient real-space approach for the calculation of the ground-state energies of Wigner crystals in 1, 2, and 3 dimensions. To be precise, we calculate the first two terms in the asymptotic expansion of the total…
Recent advances in {matrix-mimetic} tensor frameworks have made it possible to preserve linear algebraic properties for multilinear data analysis and, as a result, to obtain optimal representations of multiway data. Matrix mimeticity arises…
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful…
We consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated, the composite gradient and the implicit noise. Results are…
One-dimensional ideal diatomic gas is simulated through possible types of motion of a molecule. Energy of each type of its motion is calculated from theory and numerical method. Calculation of kinetic energy of an atom in…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
Simple thermodynamics considers kinetic energy to be an extensive variable which is proportional to the number, N, of particles. We present a quantum state of N non-interacting particles for which the kinetic energy increases quadratically…
Dynamic synthesis of human movements raises the question of the selection of a suitable performance criterion able to generate proper dynamic behaviors. Two quite different criteria are likely to be appropriate candidates: the minimum…
Generally speaking, there is a negative kinetic energy term in the Lagrangian of the Einstein-Hilbert action of general relativity; On the other hand, the negative kinetic energy term can be vanished by designating a special coordinate…
A refinement of an argument due to Maxwell for the equipartition of kinetic energy in a mixture of ideal gases with different masses is proposed. The argument is elementary, yet it may work as an illustration of the role of symmetry and…
Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…
The model-QED-operator approach [Phys. Rev. A 88, 012513 (2013)] to calculations of the radiative corrections to binding and transition energies in atomic systems is extended to the range of nuclear charges $110 \leqslant Z \leqslant 170$.…
A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied with taking into account the minimization of the corresponding integral functional. Such integral, as being not sequentially weakly…
We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an…
We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space…
We consider the one-loop renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative \phi^4 scalar field theory. Proper operator bases are constructed and it is proved that the bare composite…
We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in…
The matrix elements connected non physic angles space representation with the space of physic observables of alternative O(2,4) world found on explicit form. All such matrix elements are represented in terms of solutions of Gauss…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including…