General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space

In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061; quant-ph/9605032], the one dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering multi-dimensional exponential quadratic operator(EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single mode and double-mode EQO through the squeezed operator and the time displacement operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera

Complexified sigma model and duality

We show that the equations of motion associated with a complexified sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process we discover new type of numbers which we called `complexoids' in order to emphasize their close relation with both complex numbers and matroids. It turns out that the complexoids allow to consider the analogue of the complexified sigma-model action but with (1+1)-worldsheet metric, instead of Euclidean-worldsheet metric. Our observations can be useful for further developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio

Duality Symmetry in Kaluza-Klein n+D+dn+D+d Dimensional Cosmological Model

It is shown that, with the only exception of $n=2$, the Einstein-Hilbert action in $n+D+d$ dimensions, with $n$ times, is invariant under the duality transformation $a\to \frac{1}{a}$ and $b\to \frac{1}{b}$, where $a$ is a Friedmann-Robertson-Walker scale factor in $D$ dimensions and $b$ a Brans-Dicke scalar field in $d$ dimensions respectively. We investigate the $2+D+d$ dimensional cosmological model in some detail.Comment: 23 pages, Late

Linearized gravity as a gauge theory

We discuss linearized gravity from the point of view of a gauge theory. In (3+1)-dimensions our analysis allows to consider linearized gravity in the context of the MacDowell-Mansouri formalism. Our observations may be of particular interest in the strong-weak coupling duality for linearized gravity, in Randall-Sundrum brane world scenario and in Ashtekar formalism.Comment: Latex, 13 page

New hydrogen-like potentials

Using the modified factorization method introduced by Mielnik, we construct a new class of radial potentials whose spectrum for l=0 coincides exactly with that of the hydrogen atom. A limiting case of our family coincides with the potentials previously derived by Abraham and MosesComment: 6 pages, latex, 2 Postscript figure

Magnetic noise around metallic microstructures

We compute the local spectrum of the magnetic field near a metallic microstructure at finite temperature. Our main focus is on deviations from a plane-layered geometry for which we review the main properties. Arbitrary geometries are handled with the help of numerical calculations based on surface integral equations. The magnetic noise shows a significant polarization anisotropy above flat wires with finite lateral width, in stark contrast to an infinitely wide wire. Within the limits of a two-dimensional setting, our results provide accurate estimates for loss and dephasing rates in so-called `atom chip traps' based on metallic wires. A simple approximation based on the incoherent summation of local current elements gives qualitative agreement with the numerics, but fails to describe current correlations among neighboring objects.Comment: 10 pages, 9 figures, accepted for publication in J Appl Phys; figures plotted for slightly smaller structur