Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

Simple scheme for two-qubit Grover search in cavity QED

Following the proposal by F. Yamaguchi et al.[Phys. Rev. A 66, 010302 (R) (2002)], we present an alternative way to implement the two-qubit Grover search algorithm in cavity QED. Compared with F. Yamaguchi et al.'s proposal, with a strong resonant classical field added, our method is insensitive to both the cavity decay and thermal field, and doesn't require that the cavity remain in the vacuum state throughout the procedure. Moreover, the qubit definitions are the same for both atoms, which makes the experiment easier. The strictly numerical simulation shows that our proposal is good enough to demonstrate a two-qubit Grover's search with high fidelity.Comment: manuscript 10 pages, 2 figures, to appear in Phys. Rev.

Optical Counterpart of the Ultraluminous X-ray Source IC 342 X-1

We present Chandra and HST observations of the ultraluminous X-ray source (ULX) IC 342 X-1. The Chandra and HST images are aligned using two X-ray emitting foreground stars. The astrometry corrected position for X-1 is R.A. = 03h45m55.61s, Decl. = +68d04m55.3s (J2000) with an error circle of 0.2". One extended optical source is found in the error circle, which could be the optical counterpart of X-1. The source shows an extended feature in HST images at long wavelengths, which is likely to be a superposition of two point sources, although it is possible that the dimmer one could be a jet. Both sources are much redder than typical for ULX optical counterparts. The brighter one has an absolute magnitude M_V = -5.2 +/- 0.2 and (B-V)_0 = 0.66 +/- 0.13 and the dimmer star is not detected in B and has (B-V)_0 > 2.1. Their colors are consistent with an F8 to G0 Ib supergiant or a carbon star, respectively. However, it is likely that part or most of the optical emission may be due to X-rays reprocessed by the companion star or the accretion disk. The stellar neighborhood of IC 342 X-1 lacks O stars and has a minimum age of ~10 Myr. This excludes the possibility that the surrounding nebula is powered by an energetic explosion of a single massive star that formed a black hole. We suggest that the nebula is most likely powered by an outflow from the X-ray source.Comment: 10 pages, 8 figures, accepted for publication in Ap

Supersymmetry and the Anomalous Anomalous Magnetic Moment of the Muon

The recently reported measurement of the muon's anomalous magnetic moment differs from the standard model prediction by 2.6 standard deviations. We examine the implications of this discrepancy for supersymmetry. Deviations of the reported magnitude are generic in supersymmetric theories. Based on the new result, we derive model-independent upper bounds on the masses of observable supersymmetric particles. We also examine several model frameworks. The sign of the reported deviation is as predicted in many simple models, but disfavors anomaly-mediated supersymmetry breaking.Comment: 4 pages, 4 figures, version to appear in Phys. Rev. Let

On several families of elliptic curves with arbitrary large Selmer groups

In this paper, we calculate the $\phi (\hat{\phi})-$Selmer groups S^{(\phi)} (E / \Q) and S^{(\hat{\varphi})} (E^{\prime} / \Q) of elliptic curves $y^{2} = x (x + \epsilon p D) (x + \epsilon q D)$ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.Comment: 22 page

Global behavior of cosmological dynamics with interacting Veneziano ghost

In this paper, we shall study the dynamical behavior of the universe accelerated by the so called Veneziano ghost dark energy component locally and globally by using the linearization and nullcline method developed in this paper. The energy density is generalized to be proportional to the Hawking temperature defined on the trapping horizon instead of Hubble horizon of the Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the fate of the universe and present the bifurcation phenomenon of the dynamical system of the universe. It seems that the universe could be dominated by dark energy at present in some region of the parameter space.Comment: 8 pages, 7 figures, accepted for publication in JHE

Generation of N-qubit W state with rf-SQUID qubits by adiabatic passage

A simple scheme is presented to generate n-qubit W state with rf-superconducting quantum interference devices (rf-SQUIDs) in cavity QED through adiabatic passage. Because of the achievable strong coupling for rf-SQUID qubits embedded in cavity QED, we can get the desired state with high success probability. Furthermore, the scheme is insensitive to position inaccuracy of the rf-SQUIDs. The numerical simulation shows that, by using present experimental techniques, we can achieve our scheme with very high success probability, and the fidelity could be eventually unity with the help of dissipation.Comment: to appear in Phys. Rev.