Remarks on the multi-species exclusion process with reflective boundaries

We investigate one of the simplest multi-species generalizations of the one dimensional exclusion process with reflective boundaries. The Markov matrix governing the dynamics of the system splits into blocks (sectors) specified by the number of particles of each kind. We find matrices connecting the blocks in a matrix product form. The procedure (generalized matrix ansatz) to verify that a matrix intertwines blocks of the Markov matrix was introduced in the periodic boundary condition, which starts with a local relation [Arita et al, J. Phys. A 44, 335004 (2011)]. The solution to this relation for the reflective boundary condition is much simpler than that for the periodic boundary condition

Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries

The one-dimensional partially asymmetric simple exclusion process with open boundaries is considered. The stationary state, which is known to be constructed in a matrix product form, is studied by applying the theory of q-orthogonal polynomials. Using a formula of the q-Hermite polynomials, the average density profile is computed in the thermodynamic limit. The phase diagram for the correlation length, which was conjectured in the previous work[J. Phys. A {\bf 32} (1999) 7109], is confirmed.Comment: 24 pages, 6 figure

Transport of interface states in the Heisenberg chain

We demonstrate the transport of interface states in the one-dimensional ferromagnetic Heisenberg model by a time dependent magnetic field. Our analysis is based on the standard Adiabatic Theorem. This is supplemented by a numerical analysis via the recently developed time dependent DMRG method, where we calculate the adiabatic constant as a function of the strength of the magnetic field and the anisotropy of the interaction.Comment: minor revision, final version; 13 pages, 4 figure

On Matrix Product Ground States for Reaction-Diffusion Models

We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a coagulation-decoagulation model explicit four-dimensional representations are given and exact expressions for various physical quantities are recovered. We also find the general structure of $n$-point correlation functions at the phase transition.Comment: LaTeX source, 7 pages, no figure

An Extended Network Model with a Packages Diffusion Process

The dynamics of a packages diffusion process within a selforganized network is analytically studied by means of an extended $f$% -spin facilitated kinetic Ising model (Fredrickson-Andersen model) using a Fock-space representation for the master equation. To map the three component system (active, passive and packages cells) onto a lattice we apply two types of second quantized operators. The active cells correspond to mobile states whereas the passive cells correspond to immobile states of the Fredrickson-Andersen model. An inherent cooperativity is included assuming that the local dynamics and subsequently the local mobilities are restricted by the occupation of neighboring cells. Depending on a temperature-like parameter $h^{-1}$ (interconnectivity) the diffusive process of the packages (information) can be almost stopped, thus we get a well separation of the time regimes and a quasi-localization for the intermediate range at low temperatures.Comment: 13 pages and 1 figur

Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability

The reaction process $A+B->C$ is modelled for ballistic reactants on an infinite line with particle velocities $v_A=c$ and $v_B=-c$ and initially segregated conditions, i.e. all A particles to the left and all B particles to the right of the origin. Previous, models of ballistic annihilation have particles that always react on contact, i.e. pair-reaction probability $p=1$. The evolution of such systems are wholly determined by the initial distribution of particles and therefore do not have a stochastic dynamics. However, in this paper the generalisation is made to $p<1$, allowing particles to pass through each other without necessarily reacting. In this way, the A and B particle domains overlap to form a fluctuating, finite-sized reaction zone where the product C is created. Fluctuations are also included in the currents of A and B particles entering the overlap region, thereby inducing a stochastic motion of the reaction zone as a whole. These two types of fluctuations, in the reactions and particle currents, are characterised by the `intrinsic reaction rate', seen in a single system, and the `extrinsic reaction rate', seen in an average over many systems. The intrinsic and extrinsic behaviours are examined and compared to the case of isotropically diffusing reactants.Comment: 22 pages, 2 figures, typos correcte

Status of a DEPFET pixel system for the ILC vertex detector

We have developed a prototype system for the ILC vertex detector based on DEPFET pixels. The system operates a 128x64 matrix (with ~35x25 square micron large pixels) and uses two dedicated microchips, the SWITCHER II chip for matrix steering and the CURO II chip for readout. The system development has been driven by the final ILC requirements which above all demand a detector thinned to 50 micron and a row wise read out with line rates of 20MHz and more. The targeted noise performance for the DEPFET technology is in the range of ENC=100 e-. The functionality of the system has been demonstrated using different radioactive sources in an energy range from 6 to 40keV. In recent test beam experiments using 6GeV electrons, a signal-to-noise ratio of S/N~120 has been achieved with present sensors being 450 micron thick. For improved DEPFET systems using 50 micron thin sensors in future, a signal-to-noise of 40 is expected.Comment: Invited poster at the International Symposium on the Development of Detectors for Particle, AstroParticle and Synchrotron Radiation Experiments, Stanford CA (SNIC06) 6 pages, 12 eps figure

Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process

We study the one dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida, Evans, Hakim and Pasquier [J. Phys. A 26, 1493 (1993)] have shown that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra, closely related to the deformed oscillator-algebra. We construct all finite dimensional irreducible representations of this algebra. This enables us to compute the stationary bulk density as well as all correlation lengths for the ASEP on a set of special curves of the phase diagram.Comment: 18 pages, Latex, 1 EPS figur

Electronic correlation effects and the Coulomb gap at finite temperature

We have investigated the effect of the long-range Coulomb interaction on the one-particle excitation spectrum of n-type Germanium, using tunneling spectroscopy on mechanically controllable break junctions. The tunnel conductance was measured as a function of energy and temperature. At low temperatures, the spectra reveal a minimum at zero bias voltage due to the Coulomb gap. In the temperature range above 1 K the Coulomb gap is filled by thermal excitations. This behavior is reflected in the temperature dependence of the variable-range hopping resitivity measured on the same samples: Up to a few degrees Kelvin the Efros-Shkovskii ln$R \propto T^{-1/2}$ law is obeyed, whereas at higher temperatures deviations from this law are observed, indicating a cross-over to Mott's ln$R \propto T^{-1/4}$ law. The mechanism of this cross-over is different from that considered previously in the literature.Comment: 3 pages, 3 figure

Applying psychological type theory to cathedral visitors : a case study of two cathedrals in England and Wales

This study employs Jungian psychological type theory to profile visitors to Chester Cathedral in England and St Davids Cathedral in Wales. Psychological type theory offers a fourfold psychographic segmentation of visitors, distinguishing between introversion and extraversion, sensing and intuition, thinking and feeling, and judging and perceiving. New data provided by 157 visitors to Chester Cathedral (considered alongside previously published data provided by 381 visitors to St Davids Cathedral) demonstrated that these two cathedrals attract more introverts than extraverts, more sensers than intuitives, and more judgers than perceivers, but equal proportions of thinkers and feelers. Comparison with the population norms demonstrated that extraverts and perceivers are significantly under-represented among visitors to these two cathedrals. The implications of these findings are discussed both for maximising the visitor experiences of those already attracted to these cathedrals and for discovering ways of attracting more extraverts and more perceivers to explore these cathedrals