1,177 research outputs found
Optical absorption in semiconductor quantum dots: Nonlocal effects
The optical absorption of a single spherical semiconductor quantum dot in an
electrical field is studied taking into account the nonlocal coupling between
the field of the light and the polarizability of the semiconductor. These
nonlocal effects lead to a small size anf field dependent shift and broadening
of the excitonic resonance which may be of interest in future high precision
experiments.Comment: 6 pages, 4 figure
Dynamics of two colliding Bose-Einstein condensates in an elongated magneto-static trap
We study the dynamics of two interacting Bose-Einstein condensates, by
numerically solving two coupled Gross-Pitaevskii equations at zero temperature.
We consider the case of a sudden transfer of atoms between two trapped states
with different magnetic moments: the two condensates are initially created with
the same density profile, but are trapped into different magnetic potentials,
whose minima are vertically displaced by a distance much larger than the
initial size of both condensates. Then the two condensates begin to perform
collective oscillations, undergoing a complex evolution, characterized by
collisions between the two condensates. We investigate the effects of their
mutual interaction on the center-of-mass oscillations and on the time evolution
of the aspect ratios. Our theoretical analysis provides a useful insight into
the recent experimental observations by Maddaloni et al., cond-mat/0003402.Comment: 8 pages, 7 figures, RevTe
Matter wave solitons at finite temperatures
We consider the dynamics of a dark soliton in an elongated harmonically
trapped Bose-Einstein condensate. A central question concerns the behavior at
finite temperatures, where dissipation arises due to the presence of a thermal
cloud. We study this problem using coupled Gross-Pitaevskii and -body
simulations, which include the mean field coupling between the condensate and
thermal cloud. We find that the soliton decays relatively quickly even at very
low temperatures, with the decay rate increasing with rising temperature.Comment: 6 pages, 2 figures, submitted to the Proceedings of QFS '0
Causal explanation for observed superluminal behavior of microwave propagation in free space
In this paper we present a theoretical analysis of an experiment by Mugnai
and collaborators where superluminal behavior was observed in the propagation
of microwaves. We suggest that what was observed can be well approximated by
the motion of a superluminal X wave. Furthermore the experimental results are
also explained by the so called scissor effect which occurs with the
convergence of pairs of signals coming from opposite points of an annular
region of the mirror and forming an interference peak on the intersection axis
traveling at superluminal speed. We clarify some misunderstandings concerning
this kind of electromagnetic wave propagation in vacuum.Comment: 9 pages, 3 figures, accepted for publication in Physics Letters
The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions
We show that the Lieb-Liniger model for one-dimensional bosons with repulsive
-function interaction can be rigorously derived via a scaling limit
from a dilute three-dimensional Bose gas with arbitrary repulsive interaction
potential of finite scattering length. For this purpose, we prove bounds on
both the eigenvalues and corresponding eigenfunctions of three-dimensional
bosons in strongly elongated traps and relate them to the corresponding
quantities in the Lieb-Liniger model. In particular, if both the scattering
length and the radius of the cylindrical trap go to zero, the
Lieb-Liniger model with coupling constant is derived. Our bounds
are uniform in in the whole parameter range , and apply
to the Hamiltonian for three-dimensional bosons in a spectral window of size
above the ground state energy.Comment: LaTeX2e, 19 page
On spherical averages of radial basis functions
A radial basis function (RBF) has the general form
where the coefficients a 1,…,a n are real numbers, the points, or centres, b 1,…,b n lie in ℝ d , and φ:ℝ d →ℝ is a radially symmetric function. Such approximants are highly useful and enjoy rich theoretical properties; see, for instance (Buhmann, Radial Basis Functions: Theory and Implementations, [2003]; Fasshauer, Meshfree Approximation Methods with Matlab, [2007]; Light and Cheney, A Course in Approximation Theory, [2000]; or Wendland, Scattered Data Approximation, [2004]). The important special case of polyharmonic splines results when φ is the fundamental solution of the iterated Laplacian operator, and this class includes the Euclidean norm φ(x)=‖x‖ when d is an odd positive integer, the thin plate spline φ(x)=‖x‖2log ‖x‖ when d is an even positive integer, and univariate splines. Now B-splines generate a compactly supported basis for univariate spline spaces, but an analyticity argument implies that a nontrivial polyharmonic spline generated by (1.1) cannot be compactly supported when d>1. However, a pioneering paper of Jackson (Constr. Approx. 4:243–264, [1988]) established that the spherical average of a radial basis function generated by the Euclidean norm can be compactly supported when the centres and coefficients satisfy certain moment conditions; Jackson then used this compactly supported spherical average to construct approximate identities, with which he was then able to derive some of the earliest uniform convergence results for a class of radial basis functions. Our work extends this earlier analysis, but our technique is entirely novel, and applies to all polyharmonic splines. Furthermore, we observe that the technique provides yet another way to generate compactly supported, radially symmetric, positive definite functions. Specifically, we find that the spherical averaging operator commutes with the Fourier transform operator, and we are then able to identify Fourier transforms of compactly supported functions using the Paley–Wiener theorem. Furthermore, the use of Haar measure on compact Lie groups would not have occurred without frequent exposure to Iserles’s study of geometric integration
Transverse NMR relaxation in magnetically heterogeneous media
We consider the NMR signal from a permeable medium with a heterogeneous
Larmor frequency component that varies on a scale comparable to the
spin-carrier diffusion length. We focus on the mesoscopic part of the
transverse relaxation, that occurs due to dispersion of precession phases of
spins accumulated during diffusive motion. By relating the spectral lineshape
to correlation functions of the spatially varying Larmor frequency, we
demonstrate how the correlation length and the variance of the Larmor frequency
distribution can be determined from the NMR spectrum. We corroborate our
results by numerical simulations, and apply them to quantify human blood
spectra.Comment: 9 pages, 4 figure
U.S. Election Analysis 2020: Media, Voters and the Campaign
Featuring 91 contributions from over 115 leading US and international academics, this publication captures the immediate thoughts, reflections and early research insights on the 2020 U.S. presidential election from the cutting edge of media and politics research. Published within eleven days of the election, these contributions are short and accessible. Authors provide authoritative analysis – including research findings and new theoretical insights – to bring readers original ways of understanding the campaign. Contributions also bring a rich range of disciplinary influences, from political science to cultural studies, journalism studies to geography
Vortex Lattice Structures of a Bose-Einstein Condensate in a Rotating Lattice Potential
We study vortex lattice structures of a trapped Bose-Einstein condensate in a
rotating lattice potential by numerically solving the time-dependent
Gross-Pitaevskii equation. By rotating the lattice potential, we observe the
transition from the Abrikosov vortex lattice to the pinned lattice. We
investigate the transition of the vortex lattice structure by changing
conditions such as angular velocity, intensity, and lattice constant of the
rotating lattice potential.Comment: 6 pages, 8 figures, submitted to Quantum Fluids and Solids Conference
(QFS 2006
Hypersurface-Invariant Approach to Cosmological Perturbations
Using Hamilton-Jacobi theory, we develop a formalism for solving
semi-classical cosmological perturbations which does not require an explicit
choice of time-hypersurface. The Hamilton-Jacobi equation for gravity
interacting with matter (either a scalar or dust field) is solved by making an
Ansatz which includes all terms quadratic in the spatial curvature.
Gravitational radiation and scalar perturbations are treated on an equal
footing. Our technique encompasses linear perturbation theory and it also
describes some mild nonlinear effects. As a concrete example of the method, we
compute the galaxy-galaxy correlation function as well as large-angle microwave
background fluctuations for power-law inflation, and we compare with recent
observations.Comment: 51 pages, Latex 2.09 ALBERTA THY/20-94, DAMTP R94/25 To appear in
Phys. Rev.
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