Abstract:
The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can be viewed as two distinct degrees freedom. These, Schwinger's quantum degrees of freedom, are uniquely related to a von Neumann lattices in the phase space that characterizes the Hilbert space and specifies the simultaneous definitions of both (modular) positions and (modular) momenta. The area in phase space for each quantum state in each of these quantum degrees of freedom, is shown to be exactly $h$, Planck's constant.

Abstract:
We consider particular entanglement of two particles whose state vectors are in bases that are mutually unbiased (MUB), i.e. "that exhibit maximum degree of incompatibility" (J.Schwinger,Nat. Ac. Sci. (USA), 1960)). We use this link between entanglement and MUB to outline a protocol for secure key distribution among the parties that share these entangled states. The analysis leads to an association of entangled states and states in an MUB set: both carry the same labels.

Abstract:
The decay rate of late time tails in the Kerr spacetime have been the cause of numerous conflicting results, both analytical and numerical. In particular, there is much disagreement on whether the decay rate of an initially pure multipole moment ${\ell}$ is according to $t^{-(2{\bar\ell}+3)}$, where ${\bar\ell}$ is the least multipole moment whose excitation is not disallowed, or whether the decay rate is according to $t^{-n}$, where $n=n({\ell})$. We do careful 2+1D numerical simulations, and explain the various results. In particular, we show that pure multipole outgoing initial data in either Boyer--Lindquist on ingoing Kerr coordinates on the corresponding slices lead to the same late time tail behavior. We also show that similar initial data specified in terms of the Poisson spherical coordinates lead to the simpler $t^{-(2{\bar\ell}+3)}$ late time tail. We generalize the rule $n=n({\ell})$ to subdominant modes, and also study the behavior of non--axisymmetric initial data. We discuss some of the causes for possible errors in 2+1D simulations, demonstrate that our simulations are free of those errors, and argue that some conflicting past results may be attributed to them.

Abstract:
Three interrelated questions concerning Kerr spacetime late-time scalar-field tails are considered numerically, specifically the evolutions of generic and non-generic initial data sets, the excitation of "up" modes, and the resolution of an apparent paradox related to the superposition principle. We propose to generalize the Barack-Ori formula for the decay rate of any tail multipole given a generic initial data set, to the contribution of any initial multipole mode. Our proposal leads to a much simpler expression for the late-time power law index. Specifically, we propose that the late-time decay rate of the $Y_{\ell m}$ spherical harmonic multipole moment because of an initial $Y_{\ell' m}$ multipole is independent of the azimuthal number $m$, and is given by $t^{-n}$, where $n=\ell'+\ell+1$ for $\ell<\ell'$ and $n=\ell'+\ell+3$ for $\ell\ge\ell'$. We also show explicitly that the angular symmetry group of a multipole does not determine its late-time decay rate.

Abstract:
The late-time tails of a massive scalar field in the spacetime of black holes are studied numerically. Previous analytical results for a Schwarzschild black hole are confirmed: The late-time behavior of the field as recorded by a static observer is given by $\psi(t)\sim t^{-5/6}\sin [\omega (t)\times t]$, where $\omega(t)$ depends weakly on time. This result is carried over to the case of a Kerr black hole. In particular, it is found that the power-law index of -5/6 depends on neither the multipole mode $\ell$ nor on the spin rate of the black hole $a/M$. In all black hole spacetimes, massive scalar fields have the same late-time behavior irrespective of their initial data (i.e., angular distribution). Their late-time behavior is universal.

Abstract:
We study numerically the late-time tails of linearized fields with any spin $s$ in the background of a spinning black hole. Our code is based on the ingoing Kerr coordinates, which allow us to penetrate through the event horizon. The late time tails are dominated by the mode with the least multipole moment $\ell$ which is consistent with the equatorial symmetry of the initial data and is equal to or greater than the least radiative mode with $s$ and the azimuthal number $m$.

Abstract:
An estimate has been made of the masses of heavy hadrons in nonrelativistic quark model, which includes spin and flavor-dependent hyperfine splitting for two quarks. The effect of variation of the wavefunction value at origin and the strong coupling constant, with flavor, has also been included in calculating the mass values.

Abstract:
The accuracy of time-domain solutions of the inhomogeneous Teukolsky equation is improved significantly. Comparing energy fluxes in gravitational waves with highly accurate frequency-domain results for circular equatorial orbits in Schwarzschild and Kerr, we find agreement to within 1% or better, which we believe can be even further improved. We apply our method to orbits for which frequency-domain calculations have a relative disadvantage, specifically high-eccentricity (elliptical and parabolic) "zoom-whirl" orbits, and find the energy fluxes, waveforms, and characteristic strain in gravitational waves.

Abstract:
We consider the importance of the second-order dissipative self force for gravitational wave dephasing for an extreme or intermediate mass ratio system moving along a quasi-circular Schwarzschild orbit. For the first-order self force we use the fully relativistic force in the Lorenz gauge for eternally circular geodesics. The second-order self force is modeled by its 3.5 post Newtonian counterpart. We evolve the system using the osculating orbits method, and obtain the gravitational waveforms, whose phase includes all the terms - within our approximation (and using the self force along circular geodesics) - that are independent of the system's mass ratio. The partial dephasing due to the second-order dissipative self force is substantially smaller than that of the first-order conservative self force, although they are both at the same order in the mass ratio.

Abstract:
Integration of unpredictable renewable power sources into the Grid is leading to the development of wide area control algorithms and smart grid. Smart meters are the first step in the building a smart consumer interface. Much more, however, would be required in building a smart grid than just smart meters. This paper explores the conceptual architecture of smart grid. It highlights the need for additional infrastructure to realize full potential of smart grid. The information presented in this paper is an attempt to uncover what the future in smart grid could be and what infrastructure would be required to tap its potential. As smart grid evolves, more functionality would be built in the constituents. The paper also proposes mathematical basis for some of the controller algorithms.