Adiabatic Computation - A Toy Model

We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $\alpha$ parameter which emulates many-variables constrains in the classical computational problem. The proposed model presents, in the $s-\alpha$ plane, a line of first order quantum phase transition that ends at a second order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap and the entanglement content of the ground state.Comment: 7 pages, 8 figure

Presentations: from Kac-Moody groups to profinite and back

We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on both

Geometry of entangled states, Bloch spheres and Hopf fibrations

We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit overall phase degree of freedom. For the two qubits case, the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf fibration, with S3 fibres and a S4 base. A main striking result is that suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.

Entanglement in a first order quantum phase transition

The phase diagram of spins 1/2 embedded in a magnetic field mutually interacting antiferromagnetically is determined. Contrary to the ferromagnetic case where a second order quantum phase transition occurs, a first order transition is obtained at zero field. The spectrum is computed for a large number of spins and allows one to study the ground state entanglement properties which displays a jump of its concurrence at the critical point.Comment: 4 pages, 3 EPS figure

Proposed Revisions to the Strength-Reduction Factor for Axially Loaded Members

Modifications correct anomalies for nonprestressed reinforced concrete members subjected to flexure and axial load

Revealing the Young Starburst in Haro 3 with Radio and Infrared Imaging

The Wolf-Rayet galaxy Haro 3 (Mrk 35, NGC 3353) was observed at the near-IR and radio wavelengths as part of ongoing program to study the earliest stages of starbursts. These observations confirm that the current episode of star formation is dominated by a single region (region A). While there are knots of recent (~10 Myr) star formation outside of region A, the sources of ionizing radiation as observed in both radio and Br-gamma observations are almost exclusively associated with region A. The derived ionizing flux implies a star formation rate of ~0.6 solar masses per year localized within a radius of ~0.1 kpc. A comparison with observations from HST indicates that one or more of the star clusters in region A are optically obscured. The star clusters in region A have ages at least as young as ~5 Myr, and possibly as young as ~0.1 Myr. The star cluster that appears to be the youngest also exhibits a near-IR excess in its colors, possibly indicating natal dust in very close proximity to the ionizing stars. The difference between optical- and radio-determined ionizing fluxes as well as the near-IR colors indicate an average extinction value of A_V ~2.5 in region A. The total stellar mass associated with the current starburst in region A is inferred from both the near-IR and radio observations to be ~10^6 solar masses. The other main stellar concentrations observed in the near-IR (Regions B1 and B2) are somewhat older than region A, with ages ~8-10 Myr, and the near-IR observations indicate they have stellar masses of ~8x10^4 and ~2x10^4 solar masses, respectively.Comment: 17 pages, 3 figures, to appear in AJ August 200

Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model

It is of high interest, in the context of Adiabatic Quantum Computation, to better understand the complex dynamics of a quantum system subject to a time-dependent Hamiltonian, when driven across a quantum phase transition. We present here such a study in the Lipkin-Meshkov-Glick (LMG) model with one variable parameter. We first display numerical results on the dynamical evolution across the LMG quantum phase transition, which clearly shows a pronounced effect of the spectral avoided level crossings. We then derive a phenomenological (classical) transition model, which already shows some closeness to the numerical results. Finally, we show how a simplified quantum transition model can be built which strongly improve the classical approach, and shed light on the physical processes involved in the whole LMG quantum evolution. From our results, we argue that the commonly used description in term of Landau-Zener transitions is not appropriate for our model.Comment: 7 pages, 5 figures; corrected reference

On the distortion of twin building lattices

We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-isometric embedding. As a consequence, we provide an estimate of the quasi-flat rank of these lattices, which implies that there are infinitely many quasi-isometry classes of finitely presented simple groups. In an appendix, we describe how non-distortion of lattices is related to the integrability of the structural cocycle

Thermal Excitation of Broadband and Long-range Surface Waves on SiO 2 Submicron Films

We detect thermally excited surfaces waves on a submicron SiO 2 layer, including Zenneck and guided modes in addition to Surface Phonon Polaritons. The measurements show the existence of these hybrid thermal-electromagnetic waves from near-(2.7 $\mu$m) to far-(11.2 $\mu$m) infrared. Their propagation distances reach values on the order of the millimeter, several orders of magnitude larger than on semi-infinite systems. These two features, spectral broadness and long range propagation, make these waves good candidates for near-field applications both in optics and thermics due to their dual nature.Comment: Applied Physics Letters, American Institute of Physics, 201