Some symmetry classifications of hyperbolic vector evolution equations

Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations $u_{tx} =f(u,u_t,u_x)$ for an $N$-component vector $u(t,x)$ are considered. In each class we find all scaling-homogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.Comment: Revision of published version, incorporating errata on geometric aspects of the sigma model interpretations in the case of homogeneous space

Three-dimensional Binary Superlattices of Oppositely-charged Colloids

We report the equilibrium self-assembly of binary crystals of oppositely-charged colloidal microspheres at high density. By varying the magnitude of the charge on near equal-sized spheres we show that the structure of the binary crystal may be switched between face-centered cubic, cesium chloride and sodium chloride. We interpret these transformations in terms of a competition between entropic and Coulombic forces

Interferometric CO observations of the ultraluminous IRAS galaxies ARP 220, IC 694/NGC 3690, NGC 6420 and NGC 7469

High resolution CO observations of the IRAS galaxies Arp 220, IC 694/NGC 3690, NGC 6240 and NGC 7469 were made with the Millimeter Wave Interferometer of the Owen Valley Radio Observatory. These yield spatial information on scales of 1 to 5 kpc and allow the separation of compact condensations from the more extended emission in the galaxies. In the case of the obviously interacting system IC 694/NGC 3690 the contributions of each component can be discerned. For that galaxy, and also for Arp 220, the unusually high lumonisities may be produced by nonthermal processes rather than by intense bursts of star formation

Classical and quantum fingerprinting with shared randomness and one-sided error

Within the simultaneous message passing model of communication complexity, under a public-coin assumption, we derive the minimum achievable worst-case error probability of a classical fingerprinting protocol with one-sided error. We then present entanglement-assisted quantum fingerprinting protocols attaining worst-case error probabilities that breach this bound.Comment: 10 pages, 1 figur

Quantum process tomography with coherent states

We develop an enhanced technique for characterizing quantum optical processes based on probing unknown quantum processes only with coherent states. Our method substantially improves the original proposal [M. Lobino et al., Science 322, 563 (2008)], which uses a filtered Glauber-Sudarshan decomposition to determine the effect of the process on an arbitrary state. We introduce a new relation between the action of a general quantum process on coherent state inputs and its action on an arbitrary quantum state. This relation eliminates the need to invoke the Glauber-Sudarshan representation for states; hence it dramatically simplifies the task of process identification and removes a potential source of error. The new relation also enables straightforward extensions of the method to multi-mode and non-trace-preserving processes. We illustrate our formalism with several examples, in which we derive analytic representations of several fundamental quantum optical processes in the Fock basis. In particular, we introduce photon-number cutoff as a reasonable physical resource limitation and address resource vs accuracy trade-off in practical applications. We show that the accuracy of process estimation scales inversely with the square root of photon-number cutoff.Comment: 18 pages, 2 figure

Forming Galaxies with MOND

Beginning with a simple model for the growth of structure, I consider the dissipationless evolution of a MOND-dominated region in an expanding Universe by means of a spherically symmetric N-body code. I demonstrate that the final virialized objects resemble elliptical galaxies with well-defined relationships between the mass, radius, and velocity dispersion. These calculations suggest that, in the context of MOND, massive elliptical galaxies may be formed early (z > 10) as a result of monolithic dissipationless collapse. Then I reconsider the classic argument that a galaxy of stars results from cooling and fragmentation of a gas cloud on a time scale shorter than that of dynamical collapse. Qualitatively, the results are similar to that of the traditional picture; moreover, the existence, in MOND, of a density-temperature relation for virialized, near isothermal objects as well as a mass-temperature relation implies that there is a definite limit to the mass of a gas cloud where this condition can be met-- an upper limit corresponding to that of presently observed massive galaxies.Comment: 9 pages, 9 figures, revised in response to comments of referee. Table added, extended discussion, accepted MNRA

Single-qubit optical quantum fingerprinting

We analyze and demonstrate the feasibility and superiority of linear optical single-qubit fingerprinting over its classical counterpart. For one-qubit fingerprinting of two-bit messages, we prepare `tetrahedral' qubit states experimentally and show that they meet the requirements for quantum fingerprinting to exceed the classical capability. We prove that shared entanglement permits 100% reliable quantum fingerprinting, which will outperform classical fingerprinting even with arbitrary amounts of shared randomness.Comment: 4 pages, one figur

Probing for evolutionary links between local ULIRGs and QSOs from NIR spectroscopy

We present a study of the dynamical evolution of Ultraluminous Infrared Galaxies (ULIRGs), merging galaxies of infrared luminosity >10^12 L_sun. During our Very Large Telescope large program, we have obtained ISAAC near-infrared, high-resolution spectra of 54 ULIRGs (at several merger phases) and 12 local Palomar-Green QSOs to investigate whether ULIRGs go through a QSO phase during their evolution. One possible evolutionary scenario is that after nuclear coalescence, the black hole radiates close to Eddington to produce QSO luminosities. The mean stellar velocity dispersion that we measure from our spectra is similar (~160 km/s) for 30 post-coalescence ULIRGs and 7 IR-bright QSOs. The black holes in both populations have masses of order 10^7-10^8 M_sun (calculated from the relation to the host dispersion) and accrete at rates >0.5 Eddington. Placing ULIRGs and IR-bright QSOs on the fundamental plane of early-type galaxies shows that they are located on a similar region (that of moderate-mass ellipticals), in contrast to giant ellipticals and radio-loud QSOs. While this preliminary comparison of the ULIRG and QSO host kinematical properties indicates that (some) ULIRGs may undergo a QSO phase in their evolutionary history before they settle down as ellipticals, further data on non-IR excess QSOs are necessary to test this scenario.Comment: To appear in the "QSO Host Galaxies: Evolution and Environment" conference proceedings; meeting held in Leiden, August 200

Reductions of integrable equations on A.III-type symmetric spaces

We study a class of integrable non-linear differential equations related to the A.III-type symmetric spaces. These spaces are realized as factor groups of the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to this symmetric space as an element of the reduction group and restrict generic Lax operators to this symmetric space. The symmetries of the Lax operator are inherited by the fundamental analytic solutions and give a characterization of the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc