On Commutative Polarizations

The purpose of this paper is to study finite-dimensional Lie algebras over a field k of characteristic zero which admit a commutative polarization (CP). Among the many results and examples, it is shown that, if k is algebraically closed, the nilradical N of a parabolic subalgebra in A_n and C_n has such a CP. Using this fact a simple closed formula is derived for the index of N.Comment: 34 pages, 2 figures. Submitted to Journal of Algebr

Low-noise microwave polarimeter

Two quarterwave-plate polarizers inserted between rotary waveguide joints transform received signals from arbitrary linear to circular polarizations and then from circular to fixed linear polarizations. Fixed linear polarizations are applied to amplifiers and filters in usual fashion

Electromagnetic counterparts of high-frequency gravitational waves having additional polarization states: distinguishing and probing tensor-mode, vector-mode and scalar-mode gravitons

GWs from extra dimensions, very early universe, and some high-energy astrophysical process, might have at most six polarizations: plus- and cross-type (tensor-mode gravitons), x-, y-type (vector-mode), and b-, l-type (scalar-mode). Peak or partial peak regions of some of such GWs are just distributed in GHz or higher frequency band, which would be optimal band for electromagnetic(EM) response. In this paper we investigate EM response to such high-frequency GWs(HFGWs) having additional polarizations. For the first time we address:(1)concrete forms of analytic solutions for perturbed EM fields caused by HFGWs having all six possible polarizations in background stable EM fields; (2)perturbed EM signals of HFGWs with additional polarizations in three-dimensional-synchro-resonance-system(3DSR system) and in galactic-extragalactic background EM fields. These perturbative EM fields are actually EM counterparts of HFGWs, and such results provide a novel way to simultaneously distinguish and display all possible six polarizations. It is also shown: (i)In EM response, pure cross-, x-type and pure y-type polarizations can independently generate perturbative photon fluxes(PPFs, signals), while plus-, b- and l-type polarizations produce PPFs in different combination states. (ii) All such six polarizations have separability and detectability. (iii)In EM response to HFGWs from extra-dimensions, distinguishing and displaying different polarizations would be quite possible due to their very high frequencies, large energy densities and special properties of spectrum. (iv)Detection band(10^8 to 10^12 Hz or higher) of PPFs by 3DSR and observation range(7*10^7 to 3*10^9 Hz) of PPFs by FAST (Five-hundred-meter-Aperture-Spherical Telescope, China), have a certain overlapping property, so their coincidence experiments will have high complementarity.Comment: 27 pages, 16 figure

Optical gratings induced by field-free alignment of molecules

We analyze the alignment of molecules generated by a pair of crossed ultra-short pump pulses of different polarizations by a technique based on the induced time-dependent gratings. Parallel polarizations yield an intensity grating, while perpendicular polarizations induce a polarization grating. We show that both configurations can be interpreted at moderate intensity as an alignment induced by a single polarized pump pulse. The advantage of the perpendicular polarizations is to give a signal of alignment that is free from the plasma contribution. Experiments on femtosecond transient gratings with aligned molecules were performed in CO2 at room temperature in a static cell and at 30 K in a molecular expansion jet.Comment: 10 pages, 5 figures, submitted to PR

Explicit approximation of the symmetric rearrangement by polarizations

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.Comment: 10 page