Related papers: Noncommutative Coulombic Monopole
A Fock space representation of the monopole part of the Coulomb potential is presented. Quantum effects show through a small orbital term in $l(l+1)$. Once it is averaged out, the classical electrostatic energy emerges as an essentially…
This article aims to study the Coulomb gas model over the $d$-dimensional $p$-adic space. We establish the existence of equilibria measures and the $\Gamma$-limit for the Coulomb energy functional when the number of configurations tends to…
We propose three effective Hamiltonians which approximate atoms in very strong homogeneous magnetic fields $B$ modelled by the Pauli Hamiltonian, with fixed total angular momentum with respect to magnetic field axis. All three Hamiltonians…
By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…
In the present article we analyze the bound states of an electron in a Coulomb field when an Aharonov-Bohm field as well as a magnetic Dirac monopole are present. We solve, via separation of variables, the Schr\"odinger equation in…
The dynamics of a spin--1/2 neutral particle possessing electric and magnetic dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms…
In this paper we extend the analysis of magnetic monopoles in quantum mechanics in three dimensional rotationally invariant noncommutative space $\textbf{R}^3_\lambda$. We construct the model step-by-step and observe that physical objects…
We discuss the issue of the cosmological constant in non-commutative non-supersymmetric gauge theories. In particular, in orbifold field theories non-commutativity acts as a UV cut-off. We suggest that in these theories quantum corrections…
Controllable nonlinear quantum interactions are a much sought after target for modern quantum technologies. They are typically difficult and costly to engineer for bespoke purposes. However controllable nonlinearities may have always been…
We derive the relativistic Hamiltonian of hydrogen atom in dynamical noncommutative spaces (DNCS or {\tau}-space). Using this Hamiltonian we calculate the energy shift of the ground state and as well the [2P]_(1/2), [2S]_(1/2) levels. In…
The non-relativistic static and dynamic dipole polarizabilities of hydrogen atom experiencing a cylindrical confinement are investigated. Two methods based on B-Splines are used for the computations of the energies and wavefunctions. The…
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear…
A general three-dimensional noncommutative quantum mechanical system mixing spatial and spin degrees of freedom is proposed. The analogous of the harmonic oscillator in this description contains a magnetic dipole interaction and the ground…
By viewing non-commutative polynomials, that is, elements in free associative algebras, in terms of linear representations, we generalize Horner's rule to the non-commutative (multivariate) setting. We introduce the concept of Horner…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
A survey of the stability of matter problem is given, starting with the stability of the hydrogen atom. The stablity of bulk matter with Coulomb potentials, with or without relativistic mechanics, and with or without magnetic fields is…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…
After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with non-trivial topology and the operator representation of the $\star$-product on them, we consider the Aharonov-Bohm and Casimir effects for such spaces.…
We study conductance through a quantum dot under Coulomb blockade conditions in the presence of an external periodic perturbation. The stationary state is determined by the balance between the heating of the dot electrons by the…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…