Quantum walks based on an interferometric analogy

There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walk operates with continuous time. Here a third model for a quantum walk is proposed, which is based on an analogy to optical interferometers. It is a discrete-time model, and the unitary operator that advances the walk one step depends only on the local structure of the graph on which the walk is taking place. No quantum coin is introduced. This type of walk allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Walks on the line and cycle are discussed in some detail, and a probability current for these walks is introduced. The relation to the coined quantum walk is also discussed. The paper concludes by showing how to define these walks for a general graph.Comment: Latex,18 pages, 5 figure

Scattering in an environment

The cross section of elastic electron-proton scattering taking place in an electron gas is calculated within the Closed Time Path method. It is found to be the sum of two terms, one being the expression in the vacuum except that it involves dressing due to the electron gas. The other term is due to the scattering particles-electron gas entanglement. This term dominates the usual one when the exchange energy is in the vicinity of the Fermi energy. Furthermore it makes the trajectories of the colliding particles more consistent and the collision more irreversible, rendering the scattering more classical in this regime.Comment: final version to appear in Phys. Rev.

Modeling broadband X-ray absorption of massive star winds

We present a method for computing the net transmission of X-rays emitted by shock-heated plasma distributed throughout a partially optically thick stellar wind from a massive star. We find the transmission by an exact integration of the formal solution, assuming that the emitting plasma and absorbing plasma are mixed at a constant mass ratio above some minimum radius, below which there is assumed to be no emission. This model is more realistic than either the slab absorption associated with a corona at the base of the wind or the exospheric approximation that assumes that all observed X-rays are emitted without attenuation from above the radius of optical depth unity. Our model is implemented in XSPEC as a pre-calculated table that can be coupled to a user-defined table of the wavelength dependent wind opacity. We provide a default wind opacity model that is more representative of real wind opacities than the commonly used neutral interstellar medium (ISM) tabulation. Preliminary modeling of \textit{Chandra} grating data indicates that the X-ray hardness trend of OB stars with spectral subtype can largely be understood as a wind absorption effect.Comment: 9 pages, 9 figures. Includes minor corrections made in proof

Phase Transition Study of Superconducting Microstructures

The presented results are part of a feasibility study of superheated superconducting microstructure detectors. The microstructures (dots) were fabricated using thin film patterning techniques with diameters ranging from $50\mu$m up to $500\mu$m and thickness of $1\mu$m. We used arrays and single dots to study the dynamics of the superheating and supercooling phase transitions in a magnetic field parallel to the dot surface. The phase transi- tions were produced by either varying the applied magnetic field strength at a constant temperature or changing the bath temperature at a constant field. Preliminary results on the dynamics of the phase transitions of arrays and single indium dots will be reported.Comment: 7pages in LaTex format, five figures available upon request by [email protected], preprint Bu-He 93/

Current-density functional for disordered systems

The effective action for the current and density is shown to satisfy an evolution equation, the functional generalization of Callan-Symanzik equation. The solution describes the dependence of the one-particle irreducible vertex functions on the strength of the quenched disorder and the annealed Coulomb interaction. The result is non-perturbative, no small parameter is assumed. The a.c. conductivity is obtained by the numerical solution of the evolution equation on finite lattices in the absence of the Coulomb interaction. The static limit is performed and the conductivity is found to be vanishing beyond a certain threshold of the impurity strength.Comment: final version, 28 pages, 17 figures, to appear in Phys. Rev.

Molecular diversity of arbuscular mycorrhizal fungi and patterns of host association over time and space in a tropical forest

We have used molecular techniques to investigate the diversity and distribution of the arbuscular mycorrhizal (AM) fungi colonizing tree seedling roots in the tropical forest on Barro Colorado Island (BCI), Republic of Panama. In the first year, we sampled newly emergent seedlings of the understory treelet Faramea occidentalis and the canopy emergent Tetragastris panamensis, from mixed seedling carpets at each of two sites. The following year we sampled surviving seedlings from these cohorts. The roots of 48 plants were analysed using AM fungal-specific primers to amplify and clone partial small subunit (SSU) ribosomal RNA gene sequences. Over 1300 clones were screened for random fragment length polymorphism (RFLP) variation and 7% of these were sequenced. Compared with AM fungal communities sampled from temperate habitats using the same method, the overall diversity was high, with a total of 30 AM fungal types identified. Seventeen of these types have not been recorded previously, with the remainder being similar to types reported from temperate habitats. The tropical mycorrhizal population showed significant spatial heterogeneity and nonrandom associations with the different hosts. Moreover there was a strong shift in the mycorrhizal communities over time. AM fungal types that were dominant in the newly germinated seedlings were almost entirely replaced by previously rare types in the surviving seedlings the following year. The high diversity and huge variation detected across time points, sites and hosts, implies that the AM fungal types are ecologically distinct and thus may have the potential to influence recruitment and host composition in tropical forests

Space-time evolution of electron cascades in diamond

Here we describe model calculations to follow the spatio-temporal evolution of secondary electron cascades in diamond. The band structure of the insulator has been explicitly incorporated into the calculations as it affects ionizations from the valence band. A Monte-Carlo model was constructed to describe the path of electrons following the impact of a single electron of energy E 250 eV. The results show the evolution of the secondary electron cascades in terms of the number of electrons liberated, the spatial distribution of these electrons, and the energy distribution among the electrons as a function of time. The predicted ionization rates (5-13 electrons in 100 fs) lie within the limits given by experiments and phenomenological models. Calculation of the local electron density and the corresponding Debye length shows that the latter is systematically larger than the radius of the electron cloud. This means that the electron gas generated does not represent a plasma in a single impact cascade triggered by an electron of E 250 eV energy. This is important as it justifies the independent-electron approximation used in the model. At 1 fs, the (average) spatial distribution of secondary electrons is anisotropic with the electron cloud elongated in the direction of the primary impact. The maximal radius of the cascade is about 50 A at this time. As the system cools, energy is distributed more equally, and the spatial distribution of the electron cloud becomes isotropic. At 90 fs maximal radius is about 150 A. The Monte-Carlo model described here could be adopted for the investigation of radiation damage in other insulators and has implications for planned experiments with intense femtosecond X-ray sources.Comment: 26 pages, latex, 13 figure

Partial Transmutation of Singularities in Optical Instruments

Some interesting optical instruments such as the Eaton lens and the Invisible Sphere require singularities of the refractive index for their implementation. We show how to transmute those singularities into harmless topological defects in anisotropic media without the need for anomalous material properties

Renormalization Group and Universality

It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$ scalar field theory. Our equations are superior compared with the usual approach which retains only the contributions that are non-vanishing in the ultraviolet regime. We find an indication for the existence of relevant operators at the infrared fixed point, contrary to common expectations. This result makes the sufficiency of using only renormalizable coupling constants in parametrizing the long distance phenomena questionable.Comment: 32pp in plain tex; revised version to appear in PR