Related papers: Note on the 8$_{18}$-Knot
Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which…
We investigate the stability of few-electron quantum phases in vertically coupled quantum dots under a magnetic field of arbitrary strength and direction. The orbital and spin stability diagrams of realistic devices containing up to five…
Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined.…
We study the transport properties of two electrons in a quasi one-dimensional disordered wire. The electrons are subject to both, a disorder potential and a short range two-body interaction. Using the approach developed by Iida et al. […
We construct a generalization of the quantum Hall effect where particles move in an eight dimensional space under an SO(8) gauge field. The underlying mathematics of this particle liquid is that of the last normed division algebra, the…
The paper introduces Slope Conjecture which relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement. More precisely, we introduce two knot invariants, the…
We define two laterally gated small quantum dots (~ 15 electrons) in an Aharonov-Bohm geometry in which the coupling between the two dots can be broadly changed. For weakly coupled quantum dots we find Aharonov-Bohm oscillations. In an…
Cosmic vortons are closed loops of superconducting cosmic strings carrying current and charge. Despite a large number of studies the existence and stability of cosmic vorton solutions is still an open problem. Numerical simulations of the…
The exact numerical diagonalization of the Hamiltonian of a 2D circular quantum dot is performed for 2, 3, and 4 electrons.The results are compared with those of the perturbation theory.Our numerical results agree reasonably well for small…
The atom's orbital electron structure in terms of quantum numbers (principal, azimuthal, magnetic and spin) results in space for a maximum of: 2 electrons in the n=1 orbit, 8 electrons in the n=2 orbit, 18 electrons in the n=3 orbit, and so…
A knot K is called n-adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any m (no larger than n) of them yields a projection of the unknot. We show that a non-trivial satellite knot K is…
I review recent progress and developments in parity-violating electron scattering as it bears on three topics: strange quarks and hadron structure, electroweak radiative corrections, and physics beyond the Standard Model. I also discuss…
The differential cross section for elastic scattering of protons on electrons at rest is calculated taking into account the QED radiative corrections to the leptonic part of interaction. These model-independent radiative corrections arise…
We study quantum corrections to conductivity in a 2D system with a smooth random potential and strong spin-orbit splitting of the spectrum. We show that the interference correction is positive and down to the very low temperature can exceed…
We determine the nucleon electromagnetic form factors and their uncertainties from world electron scattering data. The analysis incorporates two-photon exchange corrections, constraints on the low-Q2 and high-Q2 behavior, and additional…
We describe in this short review the influence of discrete symmetries in complex quantum dots on the Kondo co-tunneling through these nano-objects. These discrete symmetries stem from the geometrical structure of the tunneling devices (e.g…
In this note we complete the calculation of the number of $GL(\mathbb R^n)$-orbits on $\Lambda^k(\mathbb R^n)^*$, by treating the cases $(n,k)= (7,4)$ and $(8,5)$ not covered in the literature. We also calculate the number of of…
Energy spectra, spin configurations, and entanglement characteristics of a system of four electrons in lateral double quantum dots are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic…
A virtual knot, which is one of generalizations of knots in $\mathbb{R}^{3}$ (or $S^{3}$), is, roughly speaking, an embedded circle in thickened surface $S_{g} \times I$. In this paper we will discuss about knots in 3 dimensional $S_{g}…
A short resume is given about the nature of exceptional points (EPs) followed by discussions about their ubiquitous occurrence in a great variety of physical problems. EPs feature in classical as well as in quantum mechanical problems. They…