Related papers: Operator method in solving non-linear equations of…
We perform Hartree-Fock calculations to show that quantum dots (i.e. two dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with…
In $L_2(\mathbb{R}^d;\mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\mathcal{A}_\varepsilon$, $\varepsilon >0$. The coefficients of the operator $\mathcal{A}_\varepsilon$ are periodic…
We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering or electron-electron scattering. These…
For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This…
The optical theorem is applied to the process of electron-positron pair creation in the superposition of a nuclear Coulomb and a strong laser field. We derive new representations for the total production rate as two-fold integrals, both for…
This paper addresses the optimal control problem for a class of nonlinear fractional systems involving Caputo derivatives and nonlocal initial conditions. The system is reformulated as an abstract Hammerstein-type operator equation,…
A nonlinear operator equation $F(x)=0$, $F:H\to H,$ in a Hilbert space is considered. Continuous Newton's-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point $x_0$ and becoming…
We calculate the ground state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation and show that broken symmetry states are energetically favored at any density against the homogeneous…
We consider the ground state of the homogeneous electron gas and we prove that a Hartree-Fock solution, motivated by previous simulations, has lower energy than the Fermi gas in the large density limit. This solution is a metallic phase :…
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
The existing formalism used to compute the operator overlaps necessary to carry out generator coordinate method calculations using a set of Hartree- Fock- Bogoliubov wave functions, is generalized to the case where each of the HFB states…
Here the recently proposed time-dependent quantum Monte Carlo method is applied to three dimensional para- and ortho-helium atoms subjected to an external electromagnetic field with amplitude sufficient to cause significant ionization. By…
Extensive variational computations are reported for the ground state energy of the non-relativistic two-electron atom. Several different sets of basis functions were systematically explored, starting with the original scheme of Hylleraas.…
Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and…
The method of effective interaction, traditionally used in the framework of an harmonic oscillator basis, is applied to the hyperspherical formalism of few-body nuclei (A=3-6). The separation of the hyperradial part leads to a state…
Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…
We calculate the photoionization with excitation-to photoionization ratios for atomic helium and heliumlike ions at intermediate values of the photon energies. The final state interactions between the electrons are included in the lowest…
We investigate the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable. In particular, such a coupling is discussed for the multilevel families of…
Ground state energies are obtained using the unrestricted Hartree Fock method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund…
The structure of approximate two electron wavefunction is deeply investigated, both theoretically and numerically, in the strong-field driven ionization dynamics. Theoretical analyses clarify that for two electron singlet systems, the…