Exact dynamical response of an N-electron quantum dot subject to a time-dependent potential

We calculate analytically the exact dynamical response of a droplet of N interacting electrons in a quantum dot with an arbitrarily time-dependent parabolic confinement potential \omega(t) and a perpendicular magnetic field. We find that, for certain frequency ranges, a sinusoidal perturbation acts like an attractive effective interaction between electrons. In the absence of a time-averaged confinement potential, the N electrons can bind together to form a stable, free-standing droplet.Comment: 10 pages, RevTex, 3 Postscript figures. This version to appear as a Rapid Communication in PR

Vacuum Polarization on the Schwarzschild Metric with a Cosmic String

We consider the problem of the renormalization of the vacuum polarization in a symmetry space-time with axial but not spherical symmetry, Schwarzschild space-time threaded by an infinite straight cosmic string. Unlike previous calculations, our framework to compute the renormalized vacuum polarization does not rely on special properties of Legendre functions, but rather has been developed in a way that we expect to be applicable to Kerr space-time

Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction

Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.Comment: 4 pages, 3 figure

A note on the Casimir energy of a massive scalar field in positive curvature space

We re-evaluate the zero point Casimir energy for the case of a massive scalar field in $\mathbf{R}^{1}\times\mathbf{S}^{3}$ space, allowing also for deviations from the standard conformal value $\xi =1/6$, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularization of the vacuum energy, as conjectured in a previous publication. Two different, albeit equally valid, ways of doing the analytic continuation are described.Comment: 6 pages, no figure

On Generating Gravity Waves with Matter and Electromagnetic Waves

If a homogeneous plane light-like shell collides head-on with a homogeneous plane electromagnetic shock wave having a step-function profile then no backscattered gravitational waves are produced. We demonstrate, by explicit calculation, that if the matter is accompanied by a homogeneous plane electromagnetic shock wave with a step-function profile then backscattered gravitational waves appear after the collision.Comment: Latex file, 15 pages, accepted for publication in Physical Review

A Maximally Symmetric Vector Propagator

We derive the propagator for a massive vector field on a de Sitter background of arbitrary dimension. This propagator is de Sitter invariant and possesses the proper flat spacetime and massless limits. Moreover, the retarded Green's function inferred from it produces the correct classical response to a test source. Our result is expressed in a tensor basis which is convenient for performing quantum field theory computations using dimensional regularization.Comment: 21 pages, no figures, uses LaTeX 2 epsilon, version 2 has an error in eqn (86) corrected and an updated reference lis

Theoretical description of two ultracold atoms in finite 3D optical lattices using realistic interatomic interaction potentials

A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is treated using an exact diagonalization (configuration-interaction) approach. The orthorhombic symmetry of an optical lattice with three different but orthogonal lattice vectors is explicitly considered as is the Fermionic or Bosonic symmetry in the case of indistinguishable particles.Comment: 19 pages, 5 figure

On the RKKY range function of a one dimensional non interacting electron gas

We show that the pitfalls encountered in earlier calculations of the RKKY range function for a non interacting one dimensional electron gas at zero temperature can be unraveled and successfully dealt with through a proper handling of the impurity potential.Comment: to appear in Phys. Re

High-harmonic generation from arbitrarily oriented diatomic molecules including nuclear motion and field-free alignment

We present a theoretical model of high-harmonic generation from diatomic molecules. The theory includes effects of alignment as well as nuclear motion and is used to predict results for N$_2$, O$_2$, H$_2$ and D$_2$. The results show that the alignment dependence of high-harmonics is governed by the symmetry of the highest occupied molecular orbital and that the inclusion of the nuclear motion in the theoretical description generally reduces the intensity of the harmonic radiation. We compare our model with experimental results on N$_2$ and O$_2$, and obtain very good agreement.Comment: 12 pages, 8 figures, 2 tables; legends revised on Figs. 1,3,4,6 and

Conformal Field Theory Correlators from Classical Scalar Field Theory on AdSd+1AdS_{d+1}

We use the correspondence between scalar field theory on $AdS_{d+1}$ and a conformal field theory on $R^d$ to calculate the 3- and 4-point functions of the latter. The classical scalar field theory action is evaluated at tree level.Comment: 9 pages, LaTeX2e with amsmath, amsfonts packages, section 2 rewritten, references adde