Optical simulation of quantum logic

A constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks with present-day quantum optics technology is a reasonable goal. This technique could be useful for demonstrating basic concepts of simple quantum algorithms or error-correction schemes. The optical analog of a nontrivial three-bit quantum circuit is presented as an illustration

The Formation of Low-Mass Cluster Galaxies and the Universal Initial Galaxy Mass Function

Clusters of galaxies have an observed over-density of low-luminosity systems in comparison to the field, although it is not yet agreed whether this effect is the result of initial galaxy mass functions that vary with environment or galaxy evolutionary effects. In this letter we argue that this over-density is the result of low-mass systems with red colors that are over-populating the faint-end of the observed luminosity function in the nearby rich cluster Abell 0426. We show that the luminosity function of Abell 0426 becomes steeper, from the field value alpha = -1.25+/-0.05 to alpha=-1.44+/-0.04, due to a recently identified population of red low-mass cluster galaxies that are possibly the remnants of dynamical stripped high-mass systems. We further demonstrate, through simple models of stripping effects, how cluster luminosity functions can become artificially steep over time from the production of these low-mass cluster galaxies.Comment: Accepted to ApJ letter

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

Explaining the entropy excess in clusters and groups of galaxies without additional heating

The X-ray luminosity and temperature of clusters and groups of galaxies do not scale in a self-similar manner. This has often been interpreted as a sign that the intracluster medium has been substantially heated by non-gravitational sources. In this paper, we propose a simple model which, instead, uses the properties of galaxy formation to explain the observations. Drawing on available observations, we show that there is evidence that the efficiency of galaxy formation was higher in groups than in clusters. If confirmed, this would deplete the low-entropy gas in groups, increase their central entropy and decrease their X-ray luminosity. A simple, empirical, hydrostatic model appears to match both the luminosity-temperature relation of clusters and properties of their internal structure as well.Comment: 5 pages, 4 figures, accepted in ApJL; added one reference, otherwise unchange

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde

Environmental Dependence of the Fundamental Plane of Galaxy Clusters

Galaxy clusters approximate a planar (FP) distribution in a three-dimensional parameter space which can be characterized by optical luminosity, half-light radius, and X-ray luminosity. Using a high-quality catalog of cluster redshifts, we find the nearest neighbor cluster for those common to an FP study and the cluster catalog. Examining scatter about the FP, we find 99.2% confidence that it is dependent on nearest neighbor distance. Our study of X-Ray clusters finds that those with high central gas densities are systematically closer to neighbor clusters. If we combine results here with those of Fritsch and Buchert, we find an explanation for some of our previous conclusions: Clusters in close proximity to other clusters are more likely to have massive cooling flows because they are more relaxed and have higher central gas densities.Comment: Accepted for publication in Astrophysical Journal Letters. Moderate revisions, including more statistical analysis and discussion. Latex, 7 page

Density profiles and substructure of dark matter halos: converging results at ultra-high numerical resolution

Can N-body simulations reliably determine the structural properties of dark matter halos? Focussing on a Virgo-sized galaxy cluster, we increase the resolution of current ``high resolution simulations'' by almost an order of magnitude to examine the convergence of the important physical quantities. We have 4 million particles within the cluster and force resolution 0.5 kpc/h (0.05% of the virial radius). The central density profile has a logarithmic slope of -1.5, as found in lower resolution studies of the same halo, indicating that the profile has converged to the ``physical'' limit down to scales of a few kpc. Also the abundance of substructure is consistent with that derived from lower resolution runs; on the scales explored, the mass and circular velocity functions are close to power laws of exponents ~ -1.9 and -4. Overmerging appears to be globally unimportant for suhalos with circular velocities > 100 km/s. We can trace most of the cluster progenitors from z=3 to the present; the central object (the dark matter analog of a cD galaxy)is assembled between z=3 and 1 from the merging of a dozen halos with v_circ \sim 300 km/s. The mean circular velocity of the subhalos decreases by ~ 20% over 5 billion years, due to tidal mass loss. The velocity dispersions of halos and dark matter globally agree within 10%, but the halos are spatially anti-biased, and, in the very central region of the cluster, they show positive velocity bias; however, this effect appears to depend on numerical resolution.Comment: 19 pages, 13 figures, ApJ, in press. Text significantly clarifie

The descendents of Lyman Break Galaxies in galaxy clusters: spatial distribution and orbital properties

We combine semi-analytical methods with a ultra-high resolution simulation of a galaxy cluster (of mass 2.3 10^14h-1Msolar, and 4 10^6 particles within its virial radius) formed in a standard CDM universe to study the spatial distribution and orbital properties of the present-day descendents of Lyman Break Galaxies (LBGs). At the present time only five (out of 12) of halos containing LBGs survive as separate entities inside the cluster virial radius. Their circular velocities are in the range 200 - 550 km/sec. Seven halos merged together to form the central object at the very center of the cluster. Using semi-analytical modeling of galaxy evolution we show that descendents of halos containing LBGs now host giant elliptical galaxies. Galaxy orbits are radial, with a pericenter to apocenter ratio of about 1:5. The orbital eccentricities of LBGs descendents are statistically indistinguishable from those of the average galaxy population inside the cluster, suggesting that the orbits of these galaxies are not significantly affected by dynamical friction decay after the formation of the cluster's main body. In this cluster, possibly due to its early formation time, the descendents of LBGs are contained within the central 60% of the cluster virial radius and have an orbital velocity dispersion lower than the global galaxy population, originating a mild luminosity segregation for the brightest cluster members. Mass estimates based only on LBGs descendents (especially including the central cD) reflect this bias in space and velocity and underestimate the total mass of this well virialized cluster by up to a factor of two compared to estimates using at least 20 cluster members.Comment: 6 Pages, 2 Postscript figures. Submitted to Ap