Related papers: Two anyons on the sphere: nonlinear states and spe…
The energy density is computed for a U(2) Chern-Simons theory coupled to a non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the assumptions of uniform charge and matter density. When the matter field is a spinless…
The energy levels of two interacting electrons in a 2D quantum dot confined by a finite Gaussian potential and subjected to a uniform magnetic field perpendicular to the plane of the dot are studied. Analytic results are obtained for the…
A simple method of variational calculations of the electronic structure of a two-electron atom/ion, primarily near the nucleus, is proposed. The method as a whole consists of a standard solution of a generalized matrix eigenvalue equation,…
Synthetic anyons can be implemented in a noninteracting many-body system, by using specially tailored localized (physical) probes, which supply the demanded nontrivial topology in the system. We consider the Hamiltonian for noninteracting…
We investigate the energy spectrum and the corresponding eigenfunctions of a 2D Dirac oscillator confined by an antidot potential in the presence of a magnetic field and Aharonov-Bohm flux field. Analytical solutions are obtained and…
By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary $m$-state in two-dimensional Schr\"{o}dinger wave equation with various power interaction potentials in constant magnetic and…
In the framework of Einstein-Maxwell-axion theory we consider static spherically symmetric solutions, which describe a magnetic monopole in the axionic environment. These solutions are interpreted as the solutions for an axionic dyon, the…
We obtain the exact spectrum and the unique ground state of two composite fermions (in a Rajaraman - Sondhi like formulation) in an external magnetic field $B$. We show that the energy eigenvalues decrease with increasing angular momentum,…
The effect of homogeneous electric field on the energy spectrum, wave functions of electron and oscillator strengths of intra-band quantum transitions in a double cylindrical quantum ring (GaAs/Al$_{x}$Ga$_{1-x}$As) is studied within the…
We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the…
We show that the exact solution of the Schr\"odinger equation for two electrons confined to two distinct concentric rings or spheres can be found in closed form for particular sets of the ring or sphere radii. In the case of two concentric…
The effect of a magnetic field on the energy spectrum and on the wave functions of an electron in spherical nano-structures such as single quantum dot and spherical layer is investigated. It is shown that the magnetic field removes the…
The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic…
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…
The problem of a spin-$\frac{1}{2}$ particle moving in a linear potential field in two-dimensions is searched to obtain for nonzero energy eigenvalues and the corresponding normalized eigenfunctions. The zero-mode ($E=0$) eigenfunctions are…
We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schroedinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those…
The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…
We consider the electron gas moving on the surface of a sphere in a uniform magnetic field. An exact solution of the problem is found in terms of oblate spheroidal functions, depending on the parameter $p= \Phi/\Phi_0$, the number of flux…
In this paper, motivated by the experimental evidence of rapidly rotating $C_{60}$ molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is…
Using the appropriate representation of the Poincare group and a definition of minimal coupling, we discuss some aspects of the electromagnetic interactions of charged anyons. In a nonrelativistic expansion, we derive a Schrodinger-type…