Related papers: Note on the 8$_{18}$-Knot
The effect of "anomalous" scattering of neutrons and electrons from protons in the electron-volt energy-transfer range is considered, and related experimental results are mentioned. A recent independent confirmation of this effect with a…
Knots have been put forward to explain various physical phenomena because of their topological stability. Nevertheless, few works have reported on the exotic symmetry properties that certain knots possess. Here we reveal an exceptional form…
We present exact, explicit, convergent periodic-orbit expansions for individual energy levels of regular quantum graphs. One simple application is the energy levels of a particle in a piecewise constant potential. Since the classical ray…
The problem of interacting electrons moving under the influence of a strong magnetic field in two dimensions on a finite disk is reconsidered. First, the results of exact diagonalizations for up to $N=9$ electrons for Coulomb as well as for…
In this study, equilibrium points and periodic orbits in the potential field of asteroids are investigated. We present the linearized equations of motion relative to the equilibrium points and characteristic equations. We find that the…
A molecular description for magic-number configurations of interacting electrons in a quantum dot in high magnetic fields developed by one of the authors has been elaborated for four, five and six electron dots. For four electrons, the…
We have considered a system consisting of two coupled quantum dots containing two electrons, i.e., two quantum dots next to each other with one excess electron each, subjected to an uniform magnetic field perpendicular to the quantum dots…
We argue that the tunneling between two 2D electron gases in a weak magnetic field is of resonance character, and involves a long lifetime excitonic state of an electron and hole {\it uniformly spread} over cyclotron orbits. We find that…
The altenating knots, links and twists projected on the S_2 sphere are identified with the phase Space of a Hamiltonian dynamic system of one degree of freedom. The saddles of the system correspond to the crossing points, the edges, to the…
We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The…
We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known…
Under certain symmetries, degenerate points in three-dimensional metals form one-dimensional nodal lines. These nodal lines sometimes exhibit intricate knotted structures and have been studied in various contexts. As one of the most common…
The recent literature shows a renewed interest, with various independent approaches, in the classical models for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…
Knots (emission features in jets of active galactic nuclei) often show non-ballistic dynamics and variable emission/polarization properties. We model these features as emission pattern propagating in a jet that carries helical magnetic…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
Minimizing the bending energy within knot classes leads to the concept of elastic knots which has been initiated in [von der Mosel, Asymptot. Anal. 1998]. Motivated by numerical experiments in arxiv:1804.02206 (doi:10.1090/mcom/3633) we…
We review recent theoretical developments about the role of spins, electron-electron interactions, and spin-orbit coupling in metal nanoparticles and semiconductor quantum dots. For a closed system, in the absence of spin-orbit coupling or…
Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations…
Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at…
The symmetry constraints imposing on the quantum states of a dot with 13 electrons has been investigated. Based on this study, the favorable structures (FSs) of each state has been identified. Numerical calculations have been performed to…