15218020
Clear Evasion of the Uncertainty Relation with Very Small Probability
We entertain the idea that the uncertainty relation is not a principle, but rather it is a consequence of quantum mechanics. The uncertainty relation is then a probabilistic statement and can be clearly evaded in processes which occur with a very small probability in a tiny sector of the phase space. This clear evasion is typically realized when one utilizes indirect measurements, and some examples of the clear evasion appear in the system with entanglement though the entanglement by itself is not essential for the evasion. The standard Kennard’s relation and its interpretation remain intact in our analysis. As an explicit example, we show that the clear evasion of the uncertainty relation for coordinate and momentum in the diffraction process discussed by Ballentine is realized in a tiny sector of the phase space with a very small probability. We also examine the uncertainty relation for a two-spin system with the EPR entanglement and show that no clear evasion takes place in this system with the finite discrete degrees of freedom.
118416742
Tunneling Mechanism in Kerr-Newman Black Hole and Dimensional Reduction near the Horizon
It is shown that the derivation of the Hawking radiation from a rotating black hole on the basis of the tunneling mechanism is greatly simplified by using the technique of the dimensional reduction near the horizon. This technique is illustrated for the original derivation by Parikh and Wilczek, but it is readily applied to a variant of the method such as suggested by Banerjee and Majhi.
119239099
Recent Attempts in the Analysis of Black Hole Radiation
In this thesis, we first present a brief review of black hole radiation which is commonly called Hawking radiation. The existence of Hawking radiation by itself is well established by now because the same result is derived by several different methods. On the other hand, there remain several aspects of the effect which have yet to be clarified. We clarify some arguments in previous works on the subject and then attempt to present the more satisfactory derivations of Hawking radiation. To be specific, we examine the analyses in the two recent derivations of Hawking radiation which are based on anomalies and tunneling; both of these derivations were initiated by Wilczek and his collaborators. We then present a simple derivation based on anomalies by emphasizing a systematic use of covariant currents and covariant anomalies combined with boundary conditions which have clear physical meaning. We also extend a variant of the tunneling method proposed by Banerjee and Majhi to a Kerr-Newman black hole by using the technique of the dimensional reduction near the horizon. We directly derive the black body spectrum for a Kerr-Newman black hole on the basis of the tunneling mechanism.We directly derive the black body spectrum for a Kerr-Newman black hole on the basis of the tunneling mechanism.
8012861
HAWKING RADIATION FROM KERR–NEWMAN BLACK HOLE AND TUNNELING MECHANISM
We present the derivation of Hawking radiation by using the tunneling mechanism in a rotating and charged black hole background. We show that the four-dimensional Kerr–Newman metric, which has a spherically nonsymmetric geometry, becomes an effectively two-dimensional spherically symmetric metric by using the technique of the dimensional reduction near the horizon. We can thus readily apply the tunneling mechanism to the nonspherical Kerr and Kerr–Newman metric.
6921270
Ward Identities in the derivation of Hawking radiation from Anomalies
Robinson and Wilczek suggested a new method of deriving Hawking radiation by the consideration of anomalies. The basic idea of their approach is that the flux of Hawking radiation is determined by anomaly cancellation conditions in the Schwarzschild black hole (BH) background. Iso et al. extended the method to a charged Reissner-Nordstroem BH and a rotating Kerr BH, and they showed that the flux of Hawking radiation can also be determined by anomaly cancellation conditions and regularity conditions of currents at the horizon. Their formulation gives the correct Hawking flux for all the cases at infinity and thus provides a new attractive method of understanding Hawking radiation. We present some arguments clarifying for this derivation. We show that the Ward identities and boundary conditions for covariant currents without referring to the Wess-Zumino terms and the effective action are sufficient to derive Hawking radiation. Our method, which does not use step functions, thus simplifies some of the technical aspects of the original formulation.
42818858
Cluster–cluster lensing and the case of Abell 383
Extensive surveys of galaxy clusters motivate us to assess the likelihood of cluster–cluster lensing (CCL), namely, gravitational lensing of a background cluster by a foreground cluster. We briefly describe the characteristics of CCLs in optical, X-ray and Sunyaev–Zel'dovich effect measurements, and calculate their predicted numbers for Λ cold dark matter (ΛCDM) parameters and a viable range of cluster mass functions and their uncertainties. The predicted number of CCLs in the strong-lensing regime varies from several (<10) to as high as a few dozen, depending mainly on whether lensing triaxiality bias is accounted for, through the c–M relation. A much larger number is predicted when taking into account also CCL in the weak-lensing regime. In addition to few previously suggested CCLs, we report a detection of a possible CCL in A383, where background candidate high-z structures are magnified, as seen in deep Subaru observations.
119226694
DYNAMICAL STUDY OF A1689 FROM WIDE-FIELD VLT/VIMOS SPECTROSCOPY: MASS PROFILE, CONCENTRATION PARAMETER, AND VELOCITY ANISOTROPY
We examine the dynamics structure of the rich cluster A1689, combining VLT/VIMOS spectroscopy with Subaru/Suprime-Cam imaging. The radial velocity distribution of ~500 cluster members is bounded by a pair of clearly defined velocity caustics, with a maximum amplitude of ~|4000| km s^(–1) at ≃ 300 h^(–1) kpc, beyond which the amplitude steadily declines, approaching zero velocity at a limiting radius of ~2 h^(–1) Mpc. We derive the three-dimensional velocity anisotropy and galaxy number density profiles using a model-independent method to solve the Jeans equation, simultaneously incorporating the observed velocity dispersion profile, the galaxy counts from deep Subaru imaging, and our previously derived cluster mass profile from a joint lensing and X-ray analysis. The velocity anisotropy is found to be predominantly radial at large radius, becoming increasingly tangential towards the center, in accord with expectations. We also analyze the galaxy data independently of our previous analysis using two different methods: The first is based on a solution of the Jeans equation assuming an Navarro-Frenk-White (NFW) form for the mass distribution, whereas in the second method the caustic amplitude is used to determine the escape velocity. The cluster virial mass derived by both of these dynamical methods is in good agreement with results from our earlier lensing and X-ray analysis. We also confirm the high NFW concentration parameter, with results from both methods combined to yield c_(vir) > 13 (1σ). The inferred virial radius is consistent with the limiting radius where the caustics approach zero velocity and where the counts of cluster members drop off, suggesting that infall onto A1689 is currently not significant.
119160843
1.2 m Shielded Cassegrain Antenna for Close-Packed Radio Interferometer
Interferometric millimeter observations of the cosmic microwave background and clusters of galaxies with arcminute resolutions require antenna arrays with short spacings. Having all antennas co-mounted on a single steerable platform sets limits to the overall weight. A 25 kg lightweight novel carbon-fiber design for a 1.2 m diameter Cassegrain antenna is presented. The finite element analysis predicts excellent structural behavior under gravity, wind, and thermal load. The primary- and secondary-mirror surfaces are aluminum-coated with a thin TiO2 top layer for protection. A low beam sidelobe level is achieved with a Gaussian feed-illumination pattern with edge taper, designed based on feed-horn antenna simulations and verified in a far-field beam-pattern measurement. A shielding baffle reduces interantenna coupling to below ~-135 dB. The overall antenna efficiency, including a series of efficiency factors, is estimated to be around 60%, with major losses coming from the feed spillover and secondary blocking. With this new antenna, a detection rate of about 50 clusters yr-1 is anticipated in a 13-element array operation.
9208829
A New Measure for Weak-Lensing Flexion
We study the possibility of using the octopole moment of gravitationally lensed images as a direct measure of the third-order weak gravitational lensing effect, or the gravitational flexion. It turns out that there is a natural relation between flexion and certain combinations of octopole/higher multipole moments that we call the higher order lensing image's characteristics (HOLICs). This will allow one to measure directly flexion from observable octopole and higher multipole moments of background images. We show based on simulated observations how the use of HOLICs can improve the accuracy and resolution of a reconstructed mass map, in which we assume Gaussian uncertainties in the shape measurements estimated using deep i'-band data of blank fields observed with Suprime-Cam on the Subaru telescope.
119276525
Platform deformation refined pointing and phase correction for the AMiBA hexapod telescope
The Array for Microwave Background Anisotropy (AMiBA) is a radio interferometer for research in cosmology, currently operating 7 0.6m diameter antennas co-mounted on a 6m diameter platform driven by a hexapod mount. AMiBA is currently the largest hexapod telescope. We briefly summarize the hexapod operation with the current pointing error model. We then focus on the upcoming 13-element expansion with its potential difficulties and solutions. Photogrammetry measurements of the platform reveal deformations at a level which can affect the optical pointing and the receiver radio phase. In order to prepare for the 13-element upgrade, two optical telescopes are installed on the platform to correlate optical pointing tests. Being mounted on different locations, the residuals of the two sets of pointing errors show a characteristic phase and amplitude difference as a function of the platform deformation pattern. These results depend on the telescope's azimuth, elevation and polarization position. An analytical model for the deformation is derived in order to separate the local deformation induced error from the real hexapod pointing error. Similarly, we demonstrate that the deformation induced radio phase error can be reliably modeled and calibrated, which allows us to recover the ideal synthesized beam in amplitude and shape of up to 90% or more. The resulting array efficiency and its limits are discussed based on the derived errors.