Related papers: Separability and Dynamical Symmetry of Quantum Dot…
We consider a particle moving on a cone and bound to its tip by $1/r$ or harmonic oscillator potentials. When the deficit angle of the cone divided by $2 \pi$ is a rational number, all bound classical orbits are closed. Correspondingly, the…
We theoretically investigate the properties of two interacting ultracold highly magnetic atoms trapped in a one-dimensional harmonic potential. The atoms interact via an anisotropic long-range dipole-dipole interaction, which in one…
The symmetry properties of transport beyond the linear regime in chaotic quantum dots are investigated experimentally. A component of differential conductance that is antisymmetric in both applied source-drain bias V and magnetic field B,…
An exactly soluble non-linear interaction Hamiltonian is proposed to study fundamental properties of the entanglement dynamics for a coupled non-linear oscillators. The time-evolved state is obtained analytically for initial products of two…
A new strategy for trapping quantum particles is presented, which behaves like an effective harmonic oscillator potential trap wherever is desired. The approach is based on harmonic contraction and expansion of the system around a fixed…
Compact lattice Quantum Electrodynamics is a complex quantum field theory with dynamical gauge and matter fields and it has similarities with Quantum Chromodynamics, in particular asymptotic freedom and confinement. We consider a…
We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigar-shaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with the cubic self-repulsive…
The assemblies of either quantum dots or magnetic nanoclusters are studied. It is shown that such assemblies can produce coherent radiation. A method is developed for solving the systems of nonlinear equations describing the dynamics of…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
We propose a system of sine-Gordon equations, with the $\mathcal{PT}$ symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from…
This paper begins with some background information and a summary of results in atomic supersymmetry. The connection between the supersymmetric Coulomb and oscillator problems in arbitrary dimensions is outlined. Next, I treat the issue of…
We consider the one-dimensional Schroedinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the…
The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
The correlation energies for two interacting electrons in a parabolic quantum dot are studied via a pseudo-perturbation recipe. It is shown that the central spike term, ($m^2-1/4)/r^2$, plays a distinctive role in determining the spectral…
We study the influence of perturbations in the three dimensional isotropic harmonic oscillator problem considering different perturbing force laws and apply our results in the context of celestial mechanics, particularly in the movement of…
We establish exactly solvable models for the motion of neutral particles, electrically charged point and spin particles (U(1) symmetry), isospin particles (SU(2) symmetry), and particles with color charges (SU(3) symmetry) in a…
We show that two spatially separated semiconductor quantum dots under resonant and continuous-wave excitation can be strongly entangled in the steady-state, thanks to their radiative coupling by mutual interaction through the normal modes…
We study a two-dimensional cylindrically-symmetric electron droplet separated from a surrounding electron ring by a tunable barrier using the exact diagonalization method. The magnetic field is assumed strong so that the electrons become…
Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry…