6,777 research outputs found
Noncommutative theories and general coordinate transformations
We study the class of noncommutative theories in dimensions whose spatial
coordinates can be obtained by performing a smooth change of
variables on , the coordinates of a standard noncommutative
theory, which satisfy the relation , with a
constant tensor. The variables verify a commutation
relation which is, in general, space-dependent. We study the main properties of
this special kind of noncommutative theory and show explicitly that, in two
dimensions, any theory with a space-dependent commutation relation can be
mapped to another where that is constant.Comment: 21 pages, no figures, LaTeX. v2: section 5 added, typos corrected.
Version to appear in Physical Review
The Electrostatic Ion Beam Trap : a mass spectrometer of infinite mass range
We study the ions dynamics inside an Electrostatic Ion Beam Trap (EIBT) and
show that the stability of the trapping is ruled by a Hill's equation. This
unexpectedly demonstrates that an EIBT, in the reference frame of the ions
works very similar to a quadrupole trap. The parallelism between these two
kinds of traps is illustrated by comparing experimental and theoretical
stability diagrams of the EIBT. The main difference with quadrupole traps is
that the stability depends only on the ratio of the acceleration and trapping
electrostatic potentials, not on the mass nor the charge of the ions. All kinds
of ions can be trapped simultaneously and since parametric resonances are
proportional to the square root of the charge/mass ratio the EIBT can be used
as a mass spectrometer of infinite mass range
Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement
Exact-diagonalization calculations for N=3 electrons in anisotropic quantum
dots, covering a broad range of confinement anisotropies and strength of
inter-electron repulsion, are presented for zero and low magnetic fields. The
excitation spectra are analyzed as a function of the strength of the magnetic
field and for increasing quantum-dot anisotropy. Analysis of the intrinsic
structure of the many-body wave functions through spin-resolved two-point
correlations reveals that the electrons tend to localize forming Wigner
molecules. For certain ranges of dot parameters (mainly at strong anisotropy),
the Wigner molecules acquire a linear geometry, and the associated wave
functions with a spin projection S_z=1/2 are similar to the representative
class of strongly entangled states referred to as W-states. For other ranges of
parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a
more complex structure consisting of two mirror isosceles triangles. This
latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal
in quantum wires. The degree of entanglement in three-electron quantum dots can
be quantified through the use of the von Neumann entropy.Comment: To appear in Physical Review B. REVTEX4. 13 pages with 16 color
figures. To download a copy with higher-quality figures, go to publication
#78 in http://www.prism.gatech.edu/~ph274cy
Exchange effects on electron scattering through a quantum dot embedded in a two-dimensional semiconductor structure
We have developed a theoretical method to study scattering processes of an
incident electron through an N-electron quantum dot (QD) embedded in a
two-dimensional (2D) semiconductor. The generalized Lippmann-Schwinger
equations including the electron-electron exchange interaction in this system
are solved for the continuum electron by using the method of continued
fractions (MCF) combined with 2D partial-wave expansion technique. The method
is applied to a one-electron QD case. Cross-sections are obtained for both the
singlet and triplet couplings between the incident electron and the QD electron
during the scattering. The total elastic cross-sections as well as the
spin-flip scattering cross-sections resulting from the exchange potential are
presented. Furthermore, inelastic scattering processes are also studied using a
multichannel formalism of the MCF.Comment: 11 pages, 4 figure
Electron-vibration interaction in transport through atomic gold wires
We calculate the effect of electron-vibration coupling on conduction through
atomic gold wires, which was measured in the experiments of Agra\"it et al.
[Phys. Rev. Lett. 88, 216803 (2002)]. The vibrational modes, the coupling
constants, and the inelastic transport are all calculated using a tight-binding
parametrization and the non-equilibrium Green function formalism. The
electron-vibration coupling gives rise to small drops in the conductance at
voltages corresponding to energies of some of the vibrational modes. We study
systematically how the position and height of these steps vary as a linear wire
is stretched and more atoms are added to it, and find a good agreement with the
experiments. We also consider two different types of geometries, which are
found to yield qualitatively similar results. In contrast to previous
calculations, we find that typically there are several close-lying drops due to
different longitudinal modes. In the experiments, only a single drop is usually
visible, but its width is too large to be accounted for by temperature.
Therefore, to explain the experimental results, we find it necessary to
introduce a finite broadening to the vibrational modes, which makes the
separate drops merge into a single, wide one. In addition, we predict how the
signatures of vibrational modes in the conductance curves differ between linear
and zigzag-type wires.Comment: 19 pages, 12 figure
Network formation of tissue cells via preferential attraction to elongated structures
Vascular and non-vascular cells often form an interconnected network in
vitro, similar to the early vascular bed of warm blooded embryos. Our
time-lapse recordings show that the network forms by extending sprouts, i.e.,
multicellular linear segments. To explain the emergence of such structures, we
propose a simple model of preferential attraction to stretched cells. Numerical
simulations reveal that the model evolves into a quasi-stationary pattern
containing linear segments, which interconnect above the critical volume
fraction of 0.2. In the quasi-stationary state the generation of new branches
offset the coarsening driven by surface tension. In agreement with empirical
data, the characteristic size of the resulting polygonal pattern is
density-independent within a wide range of volume fractions
Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems
This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition.
The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods
On three-rowed Chomp
Chomp is a 50 year-old game played on a partially ordered set P. It has been in the center of interest of several mathematicians since then. Even when P is simply a 3 × n lattice, we have almost no information about the winning strategy. In this paper we present a new approach and a cubic algorithm for computing the winning positions for this case. We also prove that from the initial positions there are infinitely many winning moves in the third row
Theoretical study of molecular electronic excitations and optical transitions of C60
We report results on ab initio calculations of excited states of the
fullerene molecule by using configuration interaction (CI) approach with singly
excited determinants (SCI). We have used both the experimental geometry and the
one optimized by the density functional method and worked with basis sets at
the cc-pVTZ and aug-cc-pVTZ level. Contrary to the early SCI semiempirical
calculations, we find that two lowest electron
optical lines are situated at relatively high energies of ~5.8 eV (214 nm) and
~6.3 eV (197 nm). These two lines originate from two transitions: from HOMO to (LUMO+1) () and from (HOMO--1)
to LUMO (). The lowest molecular excitation, which is the level, is found at ~2.5 eV. Inclusion of doubly excited determinants
(SDCI) leads only to minor corrections to this picture. We discuss possible
assignment of absorption bands at energies smaller than 5.8 eV (or
larger than 214 nm).Comment: 6 pages, 1 figure, 9 Table
On three-rowed Chomp
Chomp is a 50 year-old game played on a partially ordered set P. It has been in the center of interest of several mathematicians since then. Even when P is simply a 3 × n lattice, we have almost no information about the winning strategy. In this paper we present a new approach and a cubic algorithm for computing the winning positions for this case. We also prove that from the initial positions there are infinitely many winning moves in the third row
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