How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy

Several years ago we demonstrated that the Casimir energy for perfectly reflecting and imperfectly reflecting parallel plates gravitated normally, that is, obeyed the equivalence principle. At that time the divergences in the theory were treated only formally, without proper regularization, and the coupling to gravity was limited to the canonical energy-momentum-stress tensor. Here we strengthen the result by removing both of those limitations. We consider, as a toy model, massless scalar fields interacting with semitransparent ($\delta$-function) potentials defining parallel plates, which become Dirichlet plates for strong coupling. We insert space and time point-split regulation parameters, and obtain well-defined contributions to the self- energy of each plate, and the interaction energy between the plates. (This self-energy does not vanish even in the conformally-coupled, strong-coupled limit.) We also compute the local energy density, which requires regularization near the plates. In general, the energy density includes a surface energy that resides precisely on the boundaries. This energy is also regulated. The gravitational interaction of this well-defined system is then investigated, and it is verified that the equivalence principle is satisfied.Comment: 14 pages, 4 figure

Probabilistic Super Dense Coding

We explore the possibility of performing super dense coding with non-maximally entangled states as a resource. Using this we find that one can send two classical bits in a probabilistic manner by sending a qubit. We generalize our scheme to higher dimensions and show that one can communicate 2log_2 d classical bits by sending a d-dimensional quantum state with a certain probability of success. The success probability in super dense coding is related to the success probability of distinguishing non-orthogonal states. The optimal average success probabilities are explicitly calculated. We consider the possibility of sending 2 log_2 d classical bits with a shared resource of a higher dimensional entangled state (D X D, D > d). It is found that more entanglement does not necessarily lead to higher success probability. This also answers the question as to why we need log_2 d ebits to send 2 log_2 d classical bits in a deterministic fashion.Comment: Latex file, no figures, 11 pages, Discussion changed in Section

How does Casimir energy fall? III. Inertial forces on vacuum energy

We have recently demonstrated that Casimir energy due to parallel plates, including its divergent parts, falls like conventional mass in a weak gravitational field. The divergent parts were suitably interpreted as renormalizing the bare masses of the plates. Here we corroborate our result regarding the inertial nature of Casimir energy by calculating the centripetal force on a Casimir apparatus rotating with constant angular speed. We show that the centripetal force is independent of the orientation of the Casimir apparatus in a frame whose origin is at the center of inertia of the apparatus.Comment: 8 pages, 2 figures, contribution to QFEXT07 proceeding

Non-linear electrical conduction and broadband noise in charge-ordered rare earth manganate Nd_0.5Ca_0.5MnO_3

Measurements of the dc transport properties and the low-frequency conductivity noise in films of charge ordered Nd_0.5Ca_0.5MnO_3 grown on Si subtrate reveal the existence of a threshold field in the charge ordered regime beyond which strong non linear conduction sets in along with a large broad band conductivity noise. Threshold-dependent conduction disappears as T -> T_{CO}, the charge ordering temperature. This observation suggests that the charge ordered state gets depinned at the onset of the non-linear conduction.Comment: 3 pages of two-column text and 4 eps figure

A theory of wave scatter from an inhomogeneous medium with a slightly rough boundary and its application to sea ice

An analytical theory of electromagnetic wave scattering from an inhomogeneous medium with a slightly rough boundary surface is formulated. The inhomogeneity in the medium is assumed to vary continuously in the vertical direction and to have a small random variation in the horizontal direction. The medium is assumed to consist of two layers. Maxwell's equations are solved by using the small perturbation method together with Fourier transform technique. The resulting differential equations are solved by using WKB and variation of parameter methods. Field amplitudes in each medium are determined by taking boundary conditions into account. The expressions for first order polarized radar backscatter cross-section are obtained. An attempt is made to apply the developed theory to compute sea ice scatter. Numerical calculations are performed for polarized radar backscatter cross-section at two frequencies, 13.3 GHz and 400 MHz. It is shown that WKB method is applicable at both of these frequencies. Theoretical results are compared with the experimental results obtained from NASA Earth Resources Program mission 126. Theoretical results and experimental results are in good agreement

Radar systems for the water resources mission, volume 2

The application of synthetic aperture radar (SAR) in monitoring and managing earth resources was examined. The function of spaceborne radar is to provide maps and map imagery to be used for earth resource and oceanographic applications. Spaceborne radar has the capability of mapping the entire United States regardless of inclement weather; however, the imagery must have a high degree of resolution to be meaningful. Attaining this resolution is possible with the SAR system. Imagery of the required quality must first meet mission parameters in the following areas: antenna patterns, azimuth and range ambiguities, coverage, and angle of incidence

Radar systems for the water resources mission, volume 1

The state of the art determination was made for radar measurement of: soil moisture, snow, standing and flowing water, lake and river ice, determination of required spacecraft radar parameters, study of synthetic-aperture radar systems to meet these parametric requirements, and study of techniques for on-board processing of the radar data. Significant new concepts developed include the following: scanning synthetic-aperture radar to achieve wide-swath coverage; single-sideband radar; and comb-filter range-sequential, range-offset SAR processing. The state of the art in radar measurement of water resources parameters is outlined. The feasibility for immediate development of a spacecraft water resources SAR was established. Numerous candidates for the on-board processor were examined

Radar systems for the water resources mission. Volume 4: Appendices E-I

The use of a scanning antenna beam for a synthetic aperture system was examined. When the resolution required was modest, the radar did not use all the time the beam was passing a given point on the ground to build a synthetic aperture, so time was available to scan the beam to other positions and build several images at different ranges. The scanning synthetic-aperture radar (SCANSAR) could achieve swathwidths of well over 100 km with modest antenna size. Design considerations for a SCANSAR for hydrologic parameter observation are presented. Because of the high sensitivity to soil moisture at angles of incidence near vertical, a 7 to 22 deg swath was considered for that application. For snow and ice monitoring, a 22 to 37 deg scan was used. Frequencies from X-band to L-band were used in the design studies, but the proposed system operated in C-band at 4.75 GHz. It achieved an azimuth resolution of about 50 meters at all angles, with a range resolution varying from 150 meters at 7 deg to 31 meters at 37 deg. The antenna required an aperture of 3 x 4.16 meters, and the average transmitter power was under 2 watts

Radar systems for a polar mission, volume 3, appendices A-D, S, T

Success is reported in the radar monitoring of such features of sea ice as concentration, floe size, leads and other water openings, drift, topographic features such as pressure ridges and hummocks, fractures, and a qualitative indication of age and thickness. Scatterometer measurements made north of Alaska show a good correlation with a scattering coefficient with apparent thickness as deduced from ice type analysis of stereo aerial photography. Indications are that frequencies from 9 GHz upward seem to be better for sea ice radar purposes than the information gathered at 0.4 GHz by a scatterometer. Some information indicates that 1 GHz is useful, but not as useful as higher frequencies. Either form of like-polarization can be used and it appears that cross-polarization may be more useful for thickness measurement. Resolution requirements have not been fully established, but most of the systems in use have had poorer resolution than 20 meters. The radar return from sea ice is found to be much different than that from lake ice. Methods to decrease side lobe levels of the Fresnel zone-plate processor and to decrease the memory requirements of a synthetic radar processor are discussed