Related papers: Helium and Hamiltonian delay equations
We present variational characterizations of frozen planet orbits for the helium atom in the Lagrangian and the Hamiltonian picture. They are based on a Levi-Civita regularization with different time reparametrizations for the two electrons…
On the assumption that two electrons with the same group velocity effectively attract each other a simple model Hamiltonian is proposed to question the existence of unconventional electron pairs formed by electrons in a strong periodic…
We review our recent progress in the determination of the high-density correlation energy $\Ec$ in two-electron systems. Several two-electron systems are considered, such as the well known helium-like ions (helium), and the Hooke's law atom…
About twenty years ago, Rabinowitz showed firstly that there exist heteroclinic orbits of autonomous Hamiltonian system joining two equilibria. A special case of autonomous Hamiltonian system is the classical pendulum equation. The phase…
Isolated electrons resting above a helium surface are predicted to have a bound spectrum corresponding to a one-dimensional hydrogen atom. But in fact, the observed spectrum is closer to that of a quantum-defect atom. Such a model is…
The hydrogen molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The hydrogen molecule is…
We present an efficient approach to the electron correlation problem that is well-suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. %which is based on orbital optimization of electron…
We use a nonlinear Schroedinger-Poisson equation to describe two interacting electrons with opposite spins confined in a parabolic potential, a quantum dot. We propose an effective form of the Poisson equation taking into account the…
In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence…
We prove that either there exists at least one hamilton periodic orbit in a given energy close smooth hypersurface or there exist at least two hamilton periodic orbits in a near-by energy close smooth hypersurface. More general results also…
We present a unified treatment of the prevalence of different double ionization (DI) pathways as a function of the sum of the final electron energies in strongly driven Helium. We do so as a function of laser frequency and intensity. At…
The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis…
Fully relativistic approach to evaluate the correlation effects in highly charged ions is presented. The interelectronic-interaction contributions of first and second orders in $1/Z$ are treated rigorously within the framework of…
We propose an approach to entangle spins of electrons floating on liquid helium by coherently manipulating their spin-orbit interactions. The configuration consists of single electrons, confined individually on liquid helium by the…
We study mutual ionization in collisions between atomic hydrogen and helium at impact velocities near the electronic threshold for this process (determined by the condition that kinetic energy of an equivelocity free electron is…
The quantum mechanics of two-electron systems is reviewed, starting with the ground state of the helium atom and helium-like ions, with central charge $Z\ge 2$. For Z=1, demonstrating the stability of the negative hydrogen ion, H$^-$,…
Scattering or tunneling of an electron at a potential barrier is a fundamental quantum effect. Electron-electron interactions often affect the scattering, and understanding of the interaction effect is crucial in detection of various…
We seek frozen planet orbits for the helium atom through an application of the Mountain Pass Lemma to the Lagrangian action functional. Our method applies to a wide class of gravitational-like interaction potentials thus generalising the…
The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius $r$, and angle $\theta$ characterizes their positions on sphere, are investigated. Unlike the previous…
The different types of orbits in the classical problem of two particles with equal masses and opposite charges on a plane under the influence of a constant orthogonal magnetic field are classified. The equations of the system are reduced to…