119187768
Uncertainty Relation and Probability Numerical Illustration
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty product of suitably sampled events with a very small probability. We have shown elsewhere that some examples of the evasion of the uncertainty relation noted in the past are in fact understood in this way. We here numerically illustrate that a very small uncertainty product is realized if one performs a suitable sampling of measured data that occur with a very small probability. We introduce a notion of cyclic measurements. It is also shown that our analysis is consistent with the Landau-Pollak-type uncertainty relation. It is suggested that the present analysis may help reconcile the contradicting views about the “standard quantum limit” in the detection of gravitational waves. Subject Index: 002, 060, 064
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.
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.
118634145
Hawking radiation as tunneling from squashed Kaluza-Klein black hole
We discuss Hawking radiation from a five-dimensional squashed Kaluza-Klein black hole on the basis of the tunneling mechanism. A simple method, which was recently suggested by Umetsu, may be used to extend the original derivation by Parikh and Wilczek to various black holes. That is, we use the two-dimensional effective metric, which is obtained by the dimensional reduction near the horizon, as the background metric. Using the same method, we derive both the desired result of the Hawking temperature and the effect of the backreaction associated with the radiation in the squashed Kaluza-Klein black hole background.
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.
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.
15855827
New Multiply-Lensed Galaxies Identified in ACS/NIC3 Observations of Cl0024+1654, Using an Improved Mass Model
We present an improved strong-lensing analysis of Cl0024+1654 (z = 0.39) using deep Hubble Space Telescope (HST)/Advanced Camera for Surveys (ACS)/NIC3 images, based on 33 multiply-lensed images of 11 background galaxies. These are found with a model that assumes mass approximately traces light, with a low-order expansion to allow for flexibility on large scales. The model is constrained initially by the well-known five-image system (z = 1.675) and refined as new multiply-lensed systems are identified using the model. Photometric redshifts of these new systems are then used to constrain better the mass profile by adopting the standard cosmological relation between redshift and lensing distance. Our model requires only six free parameters to describe well all positional and redshift data. The resulting inner mass profile has a slope of d log M/ dl ogr �− 0.55, consistent with new weak-lensing measurements where the data overlap, at r � 200 kpc/h70. The combined profile is well fitted by a high-concentration Navarro, Frenk & White (NFW) mass profile, Cvir ∼ 8.6 ± 1.6,
14610341
A Method for Weak-Lensing Flexion Analysis by the HOLICs Moment Approach*
We have developed a method for measuring higher order weak-lensing distortions of faint background galaxies, namely, the weak gravitational flexion, by fully extending the Kaiser, Squires, and Broadhurst method to include higher order lensing image characteristics (HOLICs) introduced by Okura, Umetsu, and Futamase. We take into account explicitly the weight function in calculations of noisy shape moments and the effect of higher order point-spread function (PSF) anisotropy, as well as isotropic PSF smearing. Our HOLICs formalism allows accurate measurements of flexion from practical observational data in the presence of a noncircular, anisotropic PSF. We test our method using mock observations of simulated galaxy images and actual, ground-based Subaru observations of the massive galaxy cluster A1689 (z = 0.183). From the high-precision measurements of the spin-1 first flexion, we obtain a high-resolution mass map in the central region of A1689. The reconstructed mass map shows a bimodal feature in the central 4' × 4' region of the cluster. The major, pronounced peak is associated with the brightest cluster galaxy and central cluster members, while the secondary mass peak is associated with a local concentration of bright galaxies. The refined, high-resolution mass map of A1689 demonstrates the power of the generalized weak-lensing analysis techniques for quantitative and accurate measurements of the weak gravitational lensing signal.
46721276
A Possible Route to Spontaneous Reduction of the Heat Conductivity by a Temperature Gradient-driven Instability in Electron-Ion Plasmas
We have shown that there exist low-frequency growing modes driven by a global temperature gradient in electron and ion plasmas by linear perturbation analysis within the framework of plasma kinetic theory. The driving force of the instability is the local deviation of the distribution function from the Maxwell-Boltzmann distribution due to a global temperature gradient. Application of the results to the intracluster medium is being reduced to 5-7 orders of magnitude less than the mean free paths due to Coulomb collisions. This may provide a hint in explaining why hot and cool gas can coexist in the intracluster medium in spite of the very short evaporation timescale due to thermal conduction if the conductivity is the classical Spitzer value. Our results suggest that the realization of the global thermal equilibrium is postponed by the local instability, which is induced for a quicker realization of the local thermal equilibrium state in plasmas. The instability provides a new possibility to create and grow cosmic magnetic fields without any seed magnetic field.
119109989
SUZAKU OBSERVATION OF A1689: ANISOTROPIC TEMPERATURE AND ENTROPY DISTRIBUTIONS ASSOCIATED WITH THE LARGE-SCALE STRUCTURE
We present results of new, deep Suzaku X-ray observations (160 ks) of the intracluster medium (ICM) in A1689 out to its virial radius, combined with complementary data sets of the projected galaxy distribution obtained from the SDSS catalog and the projected mass distribution from our recent comprehensive weak and strong lensing analysis of Subaru/Suprime-Cam and Hubble Space Telescope/Advanced Camera for Surveys observations. Faint X-ray emission from the ICM around the virial radius (r vir ~ 156) is detected at 4.0σ significance, thanks to the low and stable particle background of Suzaku. The Suzaku observations reveal anisotropic gas temperature and entropy distributions in cluster outskirts of r 500 r r vir correlated with large-scale structure of galaxies in a photometric redshift slice around the cluster. The high temperature (~5.4 keV) and entropy region in the northeastern (NE) outskirts is apparently connected to an overdense filamentary structure of galaxies outside the cluster. The gas temperature and entropy profiles in the NE direction are in good agreement, out to the virial radius, with that expected from a recent XMM-Newton statistical study and with an accretion shock heating model of the ICM, respectively. On the contrary, the other outskirt regions in contact with low-density void environments have low gas temperatures (~1.7 keV) and entropies, deviating from hydrostatic equilibrium. These anisotropic ICM features associated with large-scale structure environments suggest that the thermalization of the ICM occurs faster along overdense filamentary structures than along low-density void regions. We find that the ICM density distribution is fairly isotropic, with a three-dimensional density slope of –2.29 ± 0.18 in the radial range of r 2500 r r 500, and with –1.24+0.23 –0.56 in r 500 r r vir, which, however, is significantly shallower than the Navarro, Frenk, and White universal matter density profile in the outskirts, ρ r –3. A joint X-ray and lensing analysis shows that the hydrostatic mass is lower than the spherical-lensing one (~60%-90%), but comparable to a triaxial halo mass within errors, at intermediate radii of 0.6r 2500 r 0.8r 500. On the other hand, the hydrostatic mass within 0.4r 2500 is significantly biased as low as 60%, irrespective of mass models. The thermal gas pressure within r 500 is, at most, ~50%-60% of the total pressure to balance fully the gravity of the spherical-lensing mass, and ~30%-40% around the virial radius. Although these constitute lower limits when one considers the possible halo triaxiality, these small relative contributions of thermal pressure would require additional sources of pressure, such as bulk and/or turbulent motions.
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.