Equilibrium states and invariant measures for random dynamical systems

Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a consistency conditions for such systems, which admit some proper Markov partitions of connected spaces, are introduced, and further sufficient conditions for them are provided. It is shown that every uniformly continuous Markov system associated with a continuous random dynamical system is consistent if it has a dominating Markov chain. A necessary and sufficient condition for the existence of an invariant Borel probability measure for such a non-degenerate system with a dominating Markov chain and a finite (16) is given. The condition is also sufficient if the non-degeneracy is weakened with the consistency condition. A further sufficient condition for the existence of an invariant measure for such a consistent system which involves only the properties of the dominating Markov chain is provided. In particular, it implies that every such a consistent system with a finite Markov partition and a finite (16) has an invariant Borel probability measure. A bijective map between these measures and equilibrium states associated with such a system is established in the non-degenerate case. Some properties of the map and the measures are given.Comment: The article is published in DCDS-A, but without the 3rd paragraph on page 4 (the complete removal of the paragraph became the condition for the publication in the DCDS-A after the reviewer ran out of the citation suggestions collected in the paragraph

Maximal violation of Bell inequalities by position measurements

We show that it is possible to find maximal violations of the CHSH-Bell inequality using only position measurements on a pair of entangled non-relativistic free particles. The device settings required in the CHSH inequality are done by choosing one of two times at which position is measured. For different assignments of the "+" outcome to positions, namely to an interval, to a half line, or to a periodic set, we determine violations of the inequalities, and states where they are attained. These results have consequences for the hidden variable theories of Bohm and Nelson, in which the two-time correlations between distant particle trajectories have a joint distribution, and hence cannot violate any Bell inequality.Comment: 13 pages, 4 figure

Quantum Channels with Memory

We present a general model for quantum channels with memory, and show that it is sufficiently general to encompass all causal automata: any quantum process in which outputs up to some time t do not depend on inputs at times t' > t can be decomposed into a concatenated memory channel. We then examine and present different physical setups in which channels with memory may be operated for the transfer of (private) classical and quantum information. These include setups in which either the receiver or a malicious third party have control of the initializing memory. We introduce classical and quantum channel capacities for these settings, and give several examples to show that they may or may not coincide. Entropic upper bounds on the various channel capacities are given. For forgetful quantum channels, in which the effect of the initializing memory dies out as time increases, coding theorems are presented to show that these bounds may be saturated. Forgetful quantum channels are shown to be open and dense in the set of quantum memory channels.Comment: 21 pages with 5 EPS figures. V2: Presentation clarified, references adde

A Far-UV Spectroscopic Analysis of the Central Star of the Planetary Nebula Longmore 1

We have performed a non-LTE spectroscopic analysis using far-UV and UV data of the central star of the planetary nebula K1-26 (Longmore 1), and found Teff = 120+/-10 kK, logg = 6.7 +0.3/-0.7, and y = 0.10. The temperature is significantly hotter than previous results based on optical line analyses, highlighting the importance of analyzing the spectra of such hot objects at shorter wavelengths. The spectra show metal lines (from, e.g, carbon, oxygen, sulfur, and iron). The signatures of most elements can be fit adequately using solar abundances, confirming the classification of Longmore 1 as a high gravity O(H) object. Adopting a distance of 800 pc, we derive R = 0.04 Rsun, L = 250 Lsun, and M = 0.6 Msun. This places the object on the white dwarf cooling sequence of the evolutionary tracks with an age of ~= 65 kyr.Comment: 14 pages, 4 color figures. Accepted for publication in PAS

Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Comment: 28 pages, 0 figures, 7 table

General graviton exchange graph for four point functions in the AdS/CFT correspondence

In this note we explicitly compute the graviton exchange graph for scalar fields with arbitrary conformal dimension \Delta in arbitrary spacetime dimension d. This results in an analytical function in \Delta as well as in d.Comment: 14 pages, 2 figure

Field and Temperature Dependence of the Superfluid Density in LaO_{1-x}F_xFeAs Superconductors: A Muon Spin Relaxation Study

We present zero field and transverse field \muSR experiments on the recently discovered electron doped Fe-based superconductor LaO_{1-x}F_xFeAs. The zero field experiments on underdoped (x=0.075) and optimally doped (x=0.1) samples rule out any static magnetic order above 1.6 K in these superconducting samples. From transverse field experiments in the vortex phase we deduce the temperature and field dependence of the superfluid density. Whereas the temperature dependence is consistent with a weak coupling BCS s-wave or a dirty d-wave gap function scenario, the field dependence strongly evidences unconventional superconductivity. We obtain the in-plane penetration depth of \lambda_{ab} (0) = 254(2)nm for LaO_{0.9}F_{0.1}FeAs and \lambda_{ab} (0) = 364(8)nm for LaO_{0.925}F_{0.075}FeAs. Further evidence for unconventional superconductivity is provided by the ratio of T_c versus the superfluid density, which is close to the Uemura line of hole doped high-T_c cuprates.Comment: 5 pages, 5 figure

Entanglement, Haag-duality and type properties of infinite quantum spin chains

We consider an infinite spin chain as a bipartite system consisting of the left and right half-chain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the half-chains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases the corresponding state is infinitely entangled in the sense that one copy of the system in such a state is sufficient to distill an infinite amount of maximally entangled qubit pairs. We apply this results to the critical XY model and show that its unique ground state provides a particular example for this type of entanglement.Comment: LaTeX2e, 34 pages, 1 figure (pstricks

Variations in D/H and D/O from New FUSE Observations

We use data obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE) to determine the interstellar abundances of DI, NI, OI, FeII, and H2 along the sigh tlines to WD1034+001, BD+393226, and TD132709. Our main focus is on determining the D/H, N/H, O/H, and D/O ratios along these sightlines, with log N(H) > 20.0, that probe gas well outside of the Local Bubble. Hubble Space Telescope (HST) and International Ultraviolet Explorer (IUE) archival data are used to determine the HI column densities along the WD1034+001 and TD132709 sightlines, respectively. For BD+393226, a previously published N(HI) is used. We find (D/H)x10^5 = 2.14 + 0.53 - 0.45, 1.17 + 0.31 - 0.25, and 1.86 + 0.53 - 0.43, and (D/O)x10^2 = 6.31 + 1.79 - 1.38, 5.62 + 1.61 - 1.31, and 7.59 + 2.17 - 1.76, for the WD1034+001, BD+393226, and TD132709 sightlines, respectively (all 1 si gma). The scatter in these three D/H ratios exemplifies the scatter that has been found by other authors for sightlines with column densities in the range 19.2 < log N(H) < 20.7. The D/H ratio toward WD1034+001 and all the D/O ratios derived here are inconsistent with the Local Bubble value and are some of the highest in the literature. We discuss the implications of our measurements for the determination of the present-epoch abundance of deuterium, and for the different scenarios that try to explain the D/H variations. We present a study of D/H as a function of the average sightline gas density, using the ratios derived in this work as well as ratios from the literature, which suggests that D/H decreases with increasing gas volume density. Similar behaviors by other elements such Fe and Si have been interpreted as the result of depletion into dust grains.Comment: Accepted for publication in the Ap