On the Penrose Inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.Comment: 4 pages, revtex, no figures. Some comments added. No essential changes. To be published in Phys. Rev. Let

Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

An all-optical buffer based on temporal cavity solitons operating at 10 Gb/s

We demonstrate the operation of an all-optical buffer based on temporal cavity solitons stored in a nonlinear passive fiber ring resonator. Unwanted acoustic interactions between neighboring solitons are suppressed by modulating the phase of the external laser driving the cavity. A new locking scheme is presented that allows the buffer to operate with an arbitrarily large number of cavity solitons in the loop. Experimentally, we are able to demonstrate the storage of 4536 bits of data, written all-optically into the fiber ring at 10 Gb/s, for 1 minute.Comment: 5 pages, 4 figure

How many photons are needed to distinguish two transparencies?

We give a bound on the minimum number of photons that must be absorbed by any quantum protocol to distinguish between two transparencies. We show how a quantum Zeno method in which the angle of rotation is varied at each iteration can attain this bound in certain situations.Comment: 5 pages, 4 figure

Photoproduction off the nucleon revisited: Evidence for a narrow N(1688) resonance?

Revised analysis of $\Sigma$ beam asymmetry for the $\eta$ photoproduction on the free proton reveals a structure at $W\sim 1.69$ GeV. Fit of the experimental data based on the E429 solution of the SAID partial wave analysis suggests a narrow ($\Gamma \leq 25$ MeV) resonance. Possible candidates are $P_{11}, P_{13}$, or $D_{13}$ resonances. The result is considered in conjunction with the recent evidence for a bump-like structure at $W\sim 1.67 - 1.68$ GeV in the quasi-free $\eta$ photoproduction on the neutron.Comment: Contribution to the Workshop on the Physics of the Excited Nucleons NSTAR2007, Bonn, Germany, Sept. 5 - 8 2007. To be published in Eur.Phys.J.

B -> Xs l_i^+ l_j^+ Decays with R-parity Violation

We derive the upper bounds on certain products of R-parity- and lepton-flavor-violating couplings from B \ra X_s {l_i}^+ {l_j}^- decays. These modes of B-meson decays can constrain the product combinations of the couplings with one or more heavy generation indices which are comparable with or stronger than the present bounds. From the studies of the invariant dilepton mass spectrum and the forward backward asymmetry of the emitted leptons we note the possibility of detecting R-parity-violating signals even when the total decay rate due to R-parity violating couplings is comparable with that in the standard model and discriminating two types of R-parity-violating signals. The general expectation of the enhancement of the forward backward asymmetry of the emitted leptons in the minimal supersymmetric standard model with R-parity may be corrupted by R-parity violation.Comment: 10 pages, Revtex, 1 table and 2 figure

Compression and diffusion: a joint approach to detect complexity

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.Comment: 27 pages, 9 figure