Search results for "Abstract algebra"

Preparation of macroscopically distinguishable superpositions of circular or linear oscillatory states of a bidimensionally trapped ion

2000

A simple scheme for the generation of two different classes of bidimensional vibrational Schrodinger cat-like states of an isotropically trapped ion is presented. We show that by appropriately adjusting an easily controllable parameter having a clear physical meaning, the states prepared by our procedure are quantum superpositions of either vibrational axial angular momentum eigenstates or Fock states along two orthogonal directions.

Some remarks on few recent results on the damped quantum harmonic oscillator

2020

Abstract In a recent paper, Deguchi et al. (2019), the authors proposed an analysis of the damped quantum harmonic oscillator in terms of ladder operators. This approach was shown to be partly incorrect in Bagarello et al. (2019), via a simple no-go theorem. More recently, (Deguchi and Fujiwara, 2019), Deguchi and Fujiwara claimed that our results in Bagarello et al. (2019) are wrong, and compute what they claim is the square integrable vacuum of their annihilation operators. In this brief note, we show that their vacuum is indeed not a vacuum, and we try to explain what is behind their mistakes in Deguchi et al. (2019) and Deguchi and Fujiwara (2019). We also propose a very simple example …

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

2015

Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the self-modulation of the continuous “envelope waves” with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superre…

Influence of atomic data on non-LTE chromospheric modelling

1997

Abstract The influence of various kinds of atomic parameters on computed Mg II h and k line profiles is studied. For this purpose, we have run a non-LTE code on several versions of a Mg II model atom differing from one another in the quality and source of the atomic data employed, while keeping fixed the underlying atmospheric structure. With this simple setup we show that employing good quality atomic data is a necessary condition to obtain reliable atmosphere diagnostics. This is of interest in many fields of stellar astrophysics, e. g. semi-empirical chromospheric modelling in our case, but also when modelling external velocity fields, circumstellar/interstellar absorption, etc. and so t…

Models of Metal Clusters and Quantum Dots

2007

The electronic structure of simple metal clusters and quantum dots is studied on the basis of the density functional theory and simple models. It is demonstrated that single-particle models explain well the gross features of deformation and magnetism in small clusters, nuclei and quantum dots and that the local density approximation can give valuable information of the internal structure of the manybody state.

Deformations of quasi-two-dimensional electron gas clusters

1998

Shell effects and Jahn-Teller deformations of quasi-two-dimensional jellium droplets are studied. Utilizing the ultimate jellium assumption, previously successfully used for three-dimensional systems, we calculate unrestricted shape relaxations and binding energies of the ground-state and the lowest isomers, using the methods of density-functional theory in the local spin-density approximation. Strong variations with particle number are found in the shape of the droplets. In particular, for certain magic electron numbers the shapes show triangular or circular symmetry, while for other electron numbers, more complicated symmetries are found. We finally show that from a more simple ``billiard…

Diffusive Motion in Simple Liquids

2014

The diffusive motion of single particles in a simple liquids is shown to be related to the incoherent part of the neutron-scattering cross-section. Miscallaneous topics concerning the diffusive motion are discussed.

Simple sampling Monte Carlo methods

2005

Gaussian approximations for the exchange-energy functional of current-carrying states: Applications to two-dimensional systems

2009

Electronic structure calculations are routinely carried out within the framework of density-functional theory, often with great success. For electrons in reduced dimensions, however, there is still a need for better approximations to the exchange-correlation energy functional. Furthermore, the need for properly describing current-carrying states represents an additional challenge for the development of approximate functionals. In order to make progress along these directions, we show that simple and efficient expressions for the exchange energy can be obtained by considering the short-range behavior of the one-body spin-density matrix. Applications to several two-dimensional systems confirm…

Revised periodic boundary conditions: Fundamentals, electrostatics, and the tight-binding approximation

2011

Many nanostructures today are low-dimensional and flimsy, and therefore get easily distorted. Distortion-induced symmetry-breaking makes conventional, translation-periodic simulations invalid, which has triggered developments for new methods. Revised periodic boundary conditions (RPBC) is a simple method that enables simulations of complex material distortions, either classically or quantum-mechanically. The mathematical details of this easy-to-implement approach, however, have not been discussed before. Therefore, in this paper we summarize the underlying theory, present the practical details of RPBC, especially related to a non-orthogonal tight-binding formulation, discuss selected featur…