Quantum Gravity and Black Hole Dynamics in 1+1 Dimensions

We study the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting toy model of the black hole dynamics. The functional measures are explicitly evaluated and the physical state conditions corresponding to the Hamiltonian and the momentum constraints are derived. It is pointed out that the constraints form the Virasoro algebra without central charge. In ADM formalism the measures are very ambiguous, but in our formalism they are explicitly defined. Then the new features which are not seen in ADM formalism come out. A singularity appears at \df^2 =\kappa (>0) , where $\kappa =(N-51/2)/12$ and $N$ is the number of matter fields. Behind the singularity the quantum mechanical region \kappa > \df^2 >0 extends, where the sign of the kinetic term in the Hamiltonian constraint changes. If $\kappa <0$, the singularity disappears. We discuss the quantum dynamics of black hole and then give a suggestion for the resolution of the information loss paradox. We also argue the quantization of the spherically symmetric gravitational system in 3+1 dimensions. In appendix the differences between the other quantum dilaton gravities and ours are clarified and our status is stressed.Comment: phyztex, UT-Komaba 92-14. A few misleading sentences are corrected and some references are adde

On the dynamics of vortex modes within magnetic islands

Recent work investigating the interaction of magnetic islands with micro-turbulence has uncovered the striking observation of large scale vortex modes forming within the island structure [W.A. Hornsby {\it et al.}, Phys. Plasmas {\bf 17} 092301 (2010)]. These electrostatic vortices are found to be the size of the island and are oscillatory. It is this oscillatory behaviour and the presence of turbulence that leads us to believe that the dynamics are related to the Geodesic Acoustic Mode (GAM), and it is this link that is investigated in this paper. Here we derive an equation for the GAM in the MHD limit, in the presence of a magnetic island modified three-dimensional axisymmetric geometry. The eigenvalues and eigenfunctions are calculated numerically and then utilised to analyse the dynamics of oscillatory large-scale electrostatic potential structures seen in both linear and non-linear gyro-kinetic simulations

Vertex Operators in 4D Quantum Gravity Formulated as CFT

We study vertex operators in 4D conformal field theory derived from quantized gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the ultraviolet limit, which mixes positive-metric and negative-metric modes of the gravitational field and thus these modes cannot be treated separately in physical operators. In this paper, we construct gravitational vertex operators such as the Ricci scalar, defined as space-time volume integrals of them are invariant under conformal transformations. Short distance singularities of these operator products are computed and it is shown that their coefficients have physically correct sign. Furthermore, we show that conformal algebra holds even in the system perturbed by the cosmological constant vertex operator as in the case of the Liouville theory shown by Curtright and Thorn.Comment: 26 pages, rewrote review part concisely, added explanation

Making a Universe

For understanding the origin of anisotropies in the cosmic microwave background, rules to construct a quantized universe is proposed based on the dynamical triangulation method of the simplicial quantum gravity. A $d$-dimensional universe having the topology $D^d$ is created numerically in terms of a simplicial manifold with $d$-simplices as the building blocks. The space coordinates of a universe are identified on the boundary surface $S^{d-1}$, and the time coordinate is defined along the direction perpendicular to $S^{d-1}$. Numerical simulations are made mainly for 2-dimensional universes, and analyzed to examine appropriateness of the construction rules by comparing to analytic results of the matrix model and the Liouville theory. Furthermore, a simulation in 4-dimension is made, and the result suggests an ability to analyze the observations on anisotropies by comparing to the scalar curvature correlation of a $S^2$-surface formed as the last scattering surface in the $S^3$ universe.Comment: 27pages,18figures,using jpsj.st

Teleportation and entanglement distillation in the presence of correlation among bipartite mixed states

The teleportation channel associated with an arbitrary bipartite state denotes the map that represents the change suffered by a teleported state when the bipartite state is used instead of the ideal maximally entangled state for teleportation. This work presents and proves an explicit expression of the teleportation channel for the teleportation using Weyl's projective unitary representation of the space of 2n-tuples of numbers from Z/dZ for integers d>1, n>0, which has been known for n=1. This formula allows any correlation among the n bipartite mixed states, and an application shows the existence of reliable schemes for distillation of entanglement from a sequence of mixed states with correlation.Comment: 12 pages, 1 figur

A Tuned and Scalable Fast Multipole Method as a Preeminent Algorithm for Exascale Systems

Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the order of billions of unknowns. That work led to an extremely parallel FMM, scaling to thousands of GPUs or tens of thousands of CPUs. This paper reports on a a campaign of performance tuning and scalability studies using multi-core CPUs, on the Kraken supercomputer. All kernels in the FMM were parallelized using OpenMP, and a test using 10^7 particles randomly distributed in a cube showed 78% efficiency on 8 threads. Tuning of the particle-to-particle kernel using SIMD instructions resulted in 4x speed-up of the overall algorithm on single-core tests with 10^3 - 10^7 particles. Parallel scalability was studied in both strong and weak scaling. The strong scaling test used 10^8 particles and resulted in 93% parallel efficiency on 2048 processes for the non-SIMD code and 54% for the SIMD-optimized code (which was still 2x faster). The weak scaling test used 10^6 particles per process, and resulted in 72% efficiency on 32,768 processes, with the largest calculation taking about 40 seconds to evaluate more than 32 billion unknowns. This work builds up evidence for our view that FMM is poised to play a leading role in exascale computing, and we end the paper with a discussion of the features that make it a particularly favorable algorithm for the emerging heterogeneous and massively parallel architectural landscape

Space-Time and Matter in IIB Matrix Model - gauge symmetry and diffeomorphism -

We pursue the study of the type IIB matrix model as a constructive definition of superstring. In this paper, we justify the interpretation of space-time as distribution of eigenvalues of the matrices by showing that some low energy excitations indeed propagate in it. In particular, we show that if the distribution consists of small clusters of size $n$, low energy theory acquires local SU(n) gauge symmetry and a plaquette action for the associated gauge boson is induced, in addition to a gauge invariant kinetic term for a massless fermion in the adjoint representation of the SU(n). We finally argue a possible identification of the diffeomorphism symmetry with permutation group acting on the set of eigenvalues, and show that the general covariance is realized in the low energy effective theory even though we do not have a manifest general covariance in the IIB matrix model action.Comment: 25 page