Related papers: Classical and semiclassical studies of the hydroge…
We have developed a semiclassical theory of short periodic orbits to obtain all quantum information of a bounded chaotic Hamiltonian system. If T_1 is the period of the shortest periodic orbit, T_2 the period of the next one and so on, the…
Probing dynamic and static correlation in glass-forming supercooled liquids has been a challenge for decades in spite of extensive research. Dynamic correlation which manifests itself as Dynamic Heterogeneity is ubiquitous in a vast variety…
A method is presented for determining the initial conditions of classical orbits from the quantum spectra of the diamagnetic hydrogen atom. Each classical trajectory which is closed at the nucleus produces a sinusoidal fluctuation in the…
The article presents results of preliminary study of solutions to recently offered basic thermodynamic equation for equilibrium in chemical systems with focus on chaotic behavior. Classical part of that equation was investigated earlier in…
High order terms in the electromagnetic multipole development expose a stabilizing mechanism for the atomic orbitals in the presence of the ZPF-background. Boyer and Puthoff set forward the idea that for the Bohr orbits in the hydrogen…
Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and require solving the…
In molecules like hydrogen, most chemical bonds are formed by sharing two electrons from each atom in the bonding molecular orbital (two-center-two-electron (2c2e) bonding). There are, however, different kinds of chemical bonding. The I3-…
Expressions for energy and angular momentum changes of the hydrogen atom due to interaction with the electromagnetic field during the period of the electron motion in the Coulomb field are derived. It is shown that only the energy change…
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…
We use a simple system, the electron configuration in a Hydrogen-like atom, to demonstrate the importance of using a complete basis set to provide a proper quantum mechanical description. We first start with what might be considered a…
We study the linear stability of a circular orbit in a two-electron atom, with the inclusion of retardation and self-interaction effects. We calculate all the eigenvalues of the linear stability of the circular orbit, expanded up to third…
The behavior of a classical charged point particle under the influence of only a Coulombic binding potential and classical electromagnetic zero-point radiation, is shown to yield agreement with the probability density distribution of…
We present a new methodology to analyze complicated multi-physics simulations by introducing a fictitious parameter. Using the method, we study quantum mechanical aspects of an organic molecule in water. The simulation is variationally…
We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…
Although hydrogen in external fields is a paradigm for the application of periodic orbits and the Gutzwiller trace formula to a real system, the trace formula has never been applied successfully to other Rydberg atoms. We show that spectral…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…
We consider the noncommutative algebra which is rotationally invariant. The hydrogen atom is studied in a rotationally invariant noncommutative space. We find the corrections to the energy levels of the hydrogen atom up to the second order…
Niels Bohr successfully predicted in 1913 the energy levels for the hydrogen atom by applying certain quantization rules to classically obtained periodic orbits. Many physicists tried to apply similar methods to other atoms. In his…
The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…
Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the…