How Rare is the Bullet Cluster?

The galaxy cluster 1E 0657-56 has a bullet-like subcluster that is moving away from the centre of the main cluster at high speed. Markevitch et al. (2004) recently estimated a relative velocity of V_bullet = 4500 +1100/-800 km/s, based on observations of the bow shock in front of the subcluster. The weak lensing analysis of Clowe et al. (2004) indicates that a substantial secondary mass peak is associated with this subcluster. We estimate the likelihood of such a configuration by examining the distribution of subhalo velocities for clusters in the Millennium Run, a large LCDM cosmological simulation. We find that the most massive subhalo has a velocity as high as that of the bullet subcluster in only about 1 out of every 100 cluster-sized halos. This estimate is strongly dependent on the precise velocity adopted for the bullet. One of the ten most massive subhalos has such a high velocity about 40% of the time. We conclude that the velocity of the bullet subcluster is not exceptionally high for a cluster substructure, and can be accommodated within the currently favoured LCDM comogony.Comment: 5 pages, 3 figures, accepted for publication in MNRA

Quantum hypothesis testing with group symmetry

The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound and Stein's lemma, and derive bounds on these quantities in terms of their corresponding statistical distance measures. A special emphasis is put on the comparison of the performances of group-invariant and unrestricted measurements.Comment: 33 page

The law of action and reaction for the effective force in a nonequilibrium colloidal system

We study a nonequilibrium Langevin many-body system containing two 'test' particles and many 'background' particles. The test particles are spatially confined by a harmonic potential, and the background particles are driven by an external driving force. Employing numerical simulations of the model, we formulate an effective description of the two test particles in a nonequilibrium steady state. In particular, we investigate several different definitions of the effective force acting between the test particles. We find that the law of action and reaction does not hold for the total mechanical force exerted by the background particles, but that it does hold for the thermodynamic force defined operationally on the basis of an idea used to extend the first law of thermodynamics to nonequilibrium steady states.Comment: 13 page

General theory for decoy-state quantum key distribution with arbitrary number of intensities

We develop a general theory for quantum key distribution (QKD) in both the forward error correction and the reverse error correction cases when the QKD system is equipped with phase-randomized coherent light with arbitrary number of decoy intensities. For this purpose, generalizing Wang's expansion, we derive a convex expansion of the phase-randomized coherent state. We also numerically check that the asymptotic key generation rates are almost saturated when the number of decoy intensities is three.Comment: This manuscript has been revised extensivel

A Dark Core in Abell 520

The rich cluster Abell 520 (z=0.201) exhibits truly extreme and puzzling multi-wavelength characteristics. It may best be described as a "cosmic train wreck." It is a major merger showing abundant evidence for ram pressure stripping, with a clear offset in the gas distribution compared to the galaxies (as in the bullet cluster 1E 0657-558). However, the most striking feature is a massive dark core (721 h_70 M_sun/L_sun) in our weak lensing mass reconstruction. The core coincides with the central X-ray emission peak, but is largely devoid of galaxies. An unusually low mass to light ratio region lies 500 kpc to the east, and coincides with a shock feature visible in radio observations of the cluster. Although a displacement between the X-ray gas and the galaxy/dark matter distributions may be expected in a merger, a mass peak without galaxies cannot be easily explained within the current collisionless dark matter paradigm. Interestingly, the integrated gas mass fraction (~0.15), mass-to-light ratio (220 h_70 M_sun/L_sun), and position on the X-ray luminosity-temperature and mass-temperature relations are unremarkable. Thus gross properties and scaling relations are not always useful indicators of the dynamical state of clusters.Comment: 10 pages, 5 figures, accepted for publication in the Astrophysical Journal, higher resolution version at http://visav.phys.uvic.ca/~amahdav

Interplay of the Chiral and Large N_c Limits in pi N Scattering

Light-quark hadronic physics admits two useful systematic expansions, the chiral and 1/N_c expansions. Their respective limits do not commute, making such cases where both expansions may be considered to be especially interesting. We first study pi N scattering lengths, showing that (as expected for such soft-pion quantities) the chiral expansion converges more rapidly than the 1/N_c expansion, although the latter nevertheless continues to hold. We also study the Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules of pi N scattering, finding that both fail if the large N_c limit is taken prior to the chiral limit.Comment: 10 pages, ReVTe

Poincar\'{e} gauge theory of gravity

A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most general gravitational Lagrangian density, which is at most quadratic in curvature and torsion tensors and invariant under local Lorentz transformations and under general coordinate transformations, is given. Gravitational field equations are studied in detail, and solutions of the equations for weak gravitational fields are examined for the case with a static, \lq \lq spin"less point like source. We find, among other things, the following: (1)Solutions of the vacuum Einstein equation satisfy gravitational field equations in the vacuum in this theory. (2)For a class of the parameters in the gravitational Lagrangian density, the torsion is \lq \lq frozen" at the place where \lq \lq spin" density of the source field is not vanishing. In this case, the field equation actually agrees with the Einstein equation, when the source field is \lq \lq spin"less. (3)A teleparallel theory developed in a previous paper is \lq \lq included as a solution" in a limiting case. (4)A Newtonian limit is obtainable, if the parameters in the Lagrangian density satisfy certain conditions.Comment: 27pages, RevTeX, OCU-PHYS-15

Asymptotics of Quantum Relative Entropy From Representation Theoretical Viewpoint

In this paper it was proved that the quantum relative entropy $D(\sigma \| \rho)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $\rho$, but is independent of the choice of $\sigma$.Comment: LaTeX2e. 8 pages. The title was changed from "Asymptotic Attainment for Quantum Relative Entropy

Structure formation on the brane: A mimicry

We show how braneworld cosmology with bulk matter can explain structure formation. In this scenario, the nonlocal corrections to the Friedmann equations supply a Weyl fluid that can dominate over matter at late times due to the energy exchange between the brane and the bulk. We demonstrate that the presence of the Weyl fluid radically changes the perturbation equations, which can take care of the fluctuations required to account for the large amount of inhomogeneities observed in the local universe. Further, we show how this Weyl fluid can mimic dark matter. We also investigate the bulk geometry responsible for the scenario.Comment: 7 pages. Matches published versio

New Relations for Excited Baryons in Large N_c QCD

We show that excited baryons in large N_c QCD form multiplets, within which masses are first split at O(1/N_c). The dominant couplings of resonances to various mesons are highly constrained: The N(1535) decays at leading 1/N_c order exclusively to eta-N rather than pi-N, and vice versa for the N(1650). This multiplet structure is reproduced by a simple large N_c quark model, well studied in the literature, that describes resonances as single-quark excitations.Comment: 4 pages, no figures, ReVTeX 4. Includes new discussion of previous work on excited baryon tower