Unitarizable representations and fixed points of groups of biholomorphic transformations of operator balls

We show that the open unit ball of the space of operators from a finite dimensional Hilbert space into a separable Hilbert space (we call it "operator ball") has a restricted form of normal structure if we endow it with a hyperbolic metric (which is an analogue of the standard hyperbolic metric on the unit disc in the complex plane). We use this result to get a fixed point theorem for groups of biholomorphic automorphisms of the operator ball. The fixed point theorem is used to show that a bounded representation in a separable Hilbert space which has an invariant indefinite quadratic form with finitely many negative squares is unitarizable (equivalent to a unitary representation). We apply this result to find dual pairs of invariant subspaces in Pontryagin spaces. In the appendix we present results of Itai Shafrir about hyperbolic metrics on the operator ball

D' Production in Heavy Ion Collisions

The production of d' dibaryons in heavy ion collisions due to the elementary process NN -> d' + pion is considered. The cross section NN -> d' + pion is estimated using the vacuum d' width = 0.5 MeV extracted from data on the double charge exchange reactions on nuclei. The d' production rate per single collision of heavy ions is estimated at an incident beam energy of 1 A GeV within the framework of the Quantum Molecular Dynamics transport model. We suggest to analyse the invariant mass spectrum of the NN + pion system in order to search for an abundance of events with the invariant mass of the d' dibaryon. The d' peak is found to exceed the statistical fluctuations of the background at a level of 6 standard deviations for 2 10^5 A central collisions of heavy ions with the atomic number A.Comment: 29 pages including 7 figures, REVTe

Universality Class of Thermally Diluted Ising Systems at Criticality

The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is investigated by finite size scaling techniques using the Monte Carlo method. We find that the critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. Our results agree fairly well with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.Comment: 7 pages, 6 figures, RevTe

Dynamic Scaling in Diluted Systems Phase Transitions: Deactivation trough Thermal Dilution

Activated scaling is confirmed to hold in transverse field induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold but well bellow and above it including the Griffiths-McCoy phase. A novel deactivation phenomena in the Griffiths-McCoy phase is observed using a thermal (in contrast to random) dilution of the system.Comment: 4 pages, 4 figures, RevTe

Excluded Volume Effects in the Quark Meson Coupling Model

Excluded volume effects are incorporated in the quark meson coupling model to take into account in a phenomenological way the hard core repulsion of the nuclear force. The formalism employed is thermodynamically consistent and does not violate causality. The effects of the excluded volume on in-medium nucleon properties and the nuclear matter equation of state are investigated as a function of the size of the hard core. It is found that in-medium nucleon properties are not altered significantly by the excluded volume, even for large hard core radii, and the equation of state becomes stiffer as the size of the hard core increases.Comment: 14 pages, revtex, 6 figure

Using the past to constrain the future: how the palaeorecord can improve estimates of global warming

Climate sensitivity is defined as the change in global mean equilibrium temperature after a doubling of atmospheric CO2 concentration and provides a simple measure of global warming. An early estimate of climate sensitivity, 1.5-4.5{\deg}C, has changed little subsequently, including the latest assessment by the Intergovernmental Panel on Climate Change. The persistence of such large uncertainties in this simple measure casts doubt on our understanding of the mechanisms of climate change and our ability to predict the response of the climate system to future perturbations. This has motivated continued attempts to constrain the range with climate data, alone or in conjunction with models. The majority of studies use data from the instrumental period (post-1850) but recent work has made use of information about the large climate changes experienced in the geological past. In this review, we first outline approaches that estimate climate sensitivity using instrumental climate observations and then summarise attempts to use the record of climate change on geological timescales. We examine the limitations of these studies and suggest ways in which the power of the palaeoclimate record could be better used to reduce uncertainties in our predictions of climate sensitivity.Comment: The final, definitive version of this paper has been published in Progress in Physical Geography, 31(5), 2007 by SAGE Publications Ltd, All rights reserved. \c{opyright} 2007 Edwards, Crucifix and Harriso

Experimental Study of the Shortest Reset Word of Random Automata

In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite synchronizing automaton. The largest automata we considered had 100 states. The results of the experiments allow us to formulate a hypothesis that the length of the shortest reset word of a random finite automaton with $n$ states and 2 input letters with high probability is sublinear with respect to $n$ and can be estimated as $1.95 n^{0.55}.

Two-proton correlations from 158 AGeV Pb+Pb central collisions

The two-proton correlation function at midrapidity from Pb+Pb central collisions at 158 AGeV has been measured by the NA49 experiment. The results are compared to model predictions from static thermal Gaussian proton source distributions and transport models RQMD and VENUS. An effective proton source size is determined by minimizing CHI-square/ndf between the correlation functions of the data and those calculated for the Gaussian sources, yielding 3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are consistent with the data within the error in the correlation peak region.Comment: RevTeX style, 6 pages, 4 figures, 1 table. More discussion are added about the structure on the tail of the correlation function. The systematic error is revised. To appear in Phys. Lett.

Single-photon Transistors Based on the Interaction of an Emitter and Surface Plasmons

A symmetrical approach is suggested (Chang DE et al. Nat Phys 3:807, 2007) to realize a single-photon transistor, where the presence (or absence) of a single incident photon in a ‘gate’ field is sufficient to allow (prevent) the propagation of a subsequent ‘signal’ photon along the nanowire, on condition that the ‘gate’ field is symmetrically incident from both sides of an emitter simultaneously. We present a scheme for single-photon transistors based on the strong emitter-surface-plasmon interaction. In this scheme, coherent absorption of an incoming ‘gate’ photon incident along a nanotip by an emitter located near the tip of the nanotip results in a state flip in the emitter, which controls the subsequent propagation of a ‘signal’ photon in a nanowire perpendicular to the axis of the nanotip