Binary Reactive Adsorbate on a Random Catalytic Substrate

We study the equilibrium properties of a model for a binary mixture of catalytically-reactive monomers adsorbed on a two-dimensional substrate decorated by randomly placed catalytic bonds. The interacting $A$ and $B$ monomer species undergo continuous exchanges with particle reservoirs and react ($A + B \to \emptyset$) as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For the case of annealed disorder in the placement of the catalytic bonds this model can be mapped onto a classical spin model with spin values $S = -1,0,+1$, with effective couplings dependent on the temperature and on the mean density $q$ of catalytic bonds. This allows us to exploit the mean-field theory developed for the latter to determine the phase diagram as a function of $q$ in the (symmetric) case in which the chemical potentials of the particle reservoirs, as well as the $A-A$ and $B-B$ interactions are equal.Comment: 12 pages, 4 figure

Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional Random Catalytic Substrate

We present an \textit{exactly solvable} model of a monomer-monomer $A + B \to \emptyset$ reaction on a 2D inhomogeneous, catalytic substrate and study the equilibrium properties of the two-species adsorbate. The substrate contains randomly placed catalytic bonds of mean density $q$ which connect neighboring adsorption sites. The interacting $A$ and $B$ (monomer) species undergo continuous exchanges with corresponding adjacent gaseous reservoirs. A reaction $A + B \to \emptyset$ takes place instantaneously if $A$ and $B$ particles occupy adsorption sites connected by a catalytic bond. We find that for the case of \textit{annealed} disorder in the placement of the catalytic bonds the reaction model under study can be mapped onto the general spin $S = 1$ (GS1) model. Here we concentrate on a particular case in which the model reduces to an exactly solvable Blume-Emery-Griffiths (BEG) model (T. Horiguchi, Phys. Lett. A {\bf 113}, 425 (1986); F.Y. Wu, Phys. Lett. A, {\bf 116}, 245 (1986)) and derive an exact expression for the disorder-averaged equilibrium pressure of the two-species adsorbate. We show that at equal partial vapor pressures of the $A$ and $B$ species this system exhibits a second-order phase transition which reflects a spontaneous symmetry breaking with large fluctuations and progressive coverage of the entire substrate by either one of the species.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Secure two-party quantum evaluation of unitaries against specious adversaries

We describe how any two-party quantum computation, specified by a unitary which simultaneously acts on the registers of both parties, can be privately implemented against a quantum version of classical semi-honest adversaries that we call specious. Our construction requires two ideal functionalities to garantee privacy: a private SWAP between registers held by the two parties and a classical private AND-box equivalent to oblivious transfer. If the unitary to be evaluated is in the Clifford group then only one call to SWAP is required for privacy. On the other hand, any unitary not in the Clifford requires one call to an AND-box per R-gate in the circuit. Since SWAP is itself in the Clifford group, this functionality is universal for the private evaluation of any unitary in that group. SWAP can be built from a classical bit commitment scheme or an AND-box but an AND-box cannot be constructed from SWAP. It follows that unitaries in the Clifford group are to some extent the easy ones. We also show that SWAP cannot be implemented privately in the bare model

Optimal simulation of two-qubit Hamiltonians using general local operations

We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems $A$ and $B$ interact by a nonlocal Hamiltonian $H \neq H_A+H_B$. We consider the achievable space of Hamiltonians $H'$ such that the evolution $e^{-iH't}$ can be simulated by the interaction $H$ interspersed with local operations. For any dimensions of $A$ and $B$, and any nonlocal Hamiltonians $H$ and $H'$, there exists a scale factor $s$ such that for all times $t$ the evolution $e^{-iH'st}$ can be simulated by $H$ acting for time $t$ interspersed with local operations. For 2-qubit Hamiltonians $H$ and $H'$, we calculate the optimal $s$ and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of 2-qubit Hamiltonians.Comment: (1) References to related work, (2) protocol to simulate one two-qudit Hamiltonian with another, and (3) other related results added. Some proofs are simplifie

Near-infrared colors of minor planets recovered from VISTA - VHS survey (MOVIS)

The Sloan Digital Sky Survey (SDSS) and Wide-field Infrared Survey Explorer (WISE) provide information about the surface composition of about 100,000 minor planets. The resulting visible colors and albedos enabled us to group them in several major classes, which are a simplified view of the diversity shown by the few existing spectra. We performed a serendipitous search in VISTA-VHS observations using a pipeline developed to retrieve and process the data that corresponds to solar system objects (SSo). The colors and the magnitudes of the minor planets observed by the VISTA survey are compiled into three catalogs that are available online: the detections catalog (MOVIS-D), the magnitudes catalog (MOVIS-M), and the colors catalog (MOVIS-C). They were built using the third data release of the survey (VISTA VHS-DR3). A total of 39,947 objects were detected, including 52 NEAs, 325 Mars Crossers, 515 Hungaria asteroids, 38,428 main-belt asteroids, 146 Cybele asteroids, 147 Hilda asteroids, 270 Trojans, 13 comets, 12 Kuiper Belt objects and Neptune with its four satellites. The colors found for asteroids with known spectral properties reveal well-defined patterns corresponding to different mineralogies. The distributions of MOVIS-C data in color-color plots shows clusters identified with different taxonomic types. All the diagrams that use (Y-J) color separate the spectral classes more effectively than the (J-H) and (H-Ks) plots used until now: even for large color errors (<0.1), the plots (Y-J) vs (Y-Ks) and (Y-J) vs (J-Ks) provide the separation between S-complex and C-complex. The end members A, D, R, and V-types occupy well-defined regions.Comment: 19 pages, 16 figure

DART-RAY: a 3D ray-tracing radiative transfer code for calculating the propagation of light in dusty galaxies

We present DART-Ray, a new ray-tracing 3D dust radiative transfer (RT) code designed specifically to calculate radiation field energy density (RFED) distributions within dusty galaxy models with arbitrary geometries. In this paper, we introduce the basic algorithm implemented in . DART-Ray which is based on a pre-calculation of a lower limit for the RFED distribution. This pre-calculation allows us to estimate the extent of regions around the radiation sources within which these sources contribute significantly to the RFED. In this way, ray-tracing calculations can be restricted to take place only within these regions, thus substantially reducing the computational time compared to a complete ray-tracing RT calculation. Anisotropic scattering is included in the code and handled in a similar fashion. Furthermore, the code utilizes a Cartesian adaptive spatial grid and an iterative method has been implemented to optimize the angular densities of the rays originated from each emitting cell. In order to verify the accuracy of the RT calculations performed by DART-Ray, we present results of comparisons with solutions obtained using the dusty 1D RT code for a dust shell illuminated by a central point source and existing 2D RT calculations of disc galaxies with diffusely distributed stellar emission and dust opacity. Finally, we show the application of the code on a spiral galaxy model with logarithmic spiral arms in order to measure the effect of the spiral pattern on the attenuation and RFED. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society

Progress in noncommutative function theory

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain $W^{*}$-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory

Applying causality principles to the axiomatization of probabilistic cellular automata

Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global evolution G is required to be shift-invariant (it acts the same everywhere) and causal (information cannot be transmitted faster than some fixed number of cells per time step). At least in the classical, reversible and quantum cases, these two top-down axiomatic conditions are sufficient to entail more bottom-up, operational descriptions of G. We investigate whether the same is true in the probabilistic case. Keywords: Characterization, noise, Markov process, stochastic Einstein locality, screening-off, common cause principle, non-signalling, Multi-party non-local box.Comment: 13 pages, 6 figures, LaTeX, v2: refs adde

Violation of Bell's inequalities implies distillability for N qubits

We consider quantum systems composed of $N$ qubits, and the family of all Bell's correlation inequalities for two two-valued measurements per site. We show that if a $N$-qubit state $\rho$ violates any of these inequalities, then it is at least bipartite distillable. Indeed there exists a link between the amount of Bell's inequality violation and the degree of distillability. Thus, we strengthen the interpretation of Bell's inequalities as detectors of useful entanglement.Comment: 6 pages, 3 figures, REVTEX. List of authors extended. Partially rewritten, a rather qualitative explanation of the results. Conclusions unchange