On the universal Representation of the Scattering Matrix of Affine Toda Field Theory

By exploiting the properties of q-deformed Coxeter elements, the scattering matrices of affine Toda field theories with real coupling constant related to any dual pair of simple Lie algebras may be expressed in a completely generic way. We discuss the governing equations for the existence of bound states, i.e. the fusing rules, in terms of q-deformed Coxeter elements, twisted q-deformed Coxeter elements and undeformed Coxeter elements. We establish the precise relation between these different formulations and study their solutions. The generalized S-matrix bootstrap equations are shown to be equivalent to the fusing rules. The relation between different versions of fusing rules and quantum conserved quantities, which result as nullvectors of a doubly q-deformed Cartan like matrix, is presented. The properties of this matrix together with the so-called combined bootstrap equations are utilised in order to derive generic integral representations for the scattering matrix in terms of quantities of either of the two dual algebras. We present extensive case-by-case data, in particular on the orbits generated by the various Coxeter elements.Comment: 57 page

Weak disorder expansion for localization lengths of quasi-1D systems

A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength

Understanding and Improving the Wang-Landau Algorithm

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a stage of initial accumulation, and the statistical error is found to scale as $\sqrt{\ln f}$ with the modification factor $f$. This has implications for strategies for obtaining fast convergence.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Collective Diffusion and a Random Energy Landscape

Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different equations in case of an arbitrary occupation number per lattice site or in a system under exclusion. Based on scaling arguments it will be demonstrated that both systems belong below the critical dimension $d_c$ to the same universality class leading to anomalous diffusion in the long time limit. The dynamical exponent $z$ can be calculated by an $\epsilon = d_c-d$ expansion. Above the critical dimension we discuss the differences in the diffusion constant for sufficient high temperatures. For a random potential we find a higher mobility for systems with exclusion.Comment: 15 pages, no figure

Approaches and tools to manipulate the carbonate chemistry

Although the chemistry of ocean acidifi cation is very well understood (see chapter 1), its impact on marine organisms and ecosystems remains poorly known. The biological response to ocean acidifi cation is a recent field of research, the fi rst purposeful experiments have only been carried out as late as the 1980s (Agegian, 1985) and most were not performed until the late 1990s. The potentially dire consequences of ocean acidifi cation have attracted the interest of scientists and students with a limited knowledge of the carbonate chemistry and its experimental manipulation. Perturbation experiments are one of the key approaches used to investigate the biological response to elevated p(CO2). Such experiments are based on measurements of physiological or metabolic processes in organisms and communities exposed to seawater with normal and altered carbonate chemistry. The basics of the carbonate chemistry must be understood to perform meaningful CO2 perturbation experiments (see chapter 1). Briefl y, the marine carbonate system considers € CO2 ∗(aq) [the sum of CO2 and H2CO3], € HCO3 −, € CO3 2−, H+, € OH− , and several weak acid-base systems of which borate-boric acid (€ B(OH)4 − , B(OH)3) is the most important. As discussed by Dickson (chapter 1), if two components of the carbonate chemistry are known, all the other components can be calculated for seawater with typical nutrient concentrations at given temperature, salinity, and pressure. One of the possible pairs is of particular interest because both components can be measured with precision, accuracy, and are conservative in the sense that their concentrations do not change with temperature or pressure. Dissolved inorganic carbon (DIC) is the sum of all dissolved inorganic carbon species while total alkalinity (AT) equals € [HCO3 − ] + 2 € [CO3 2− ] + € [B(OH)4 − ] + € [OH− ] - [H+] + minor components, and refl ects the excess of proton acceptors over proton donors with respect to a zero level of protons (see chapter 1 for a detailed defi nition). AT is determined by the titration of seawater with a strong acid and thus can also be regarded as a measure of the buffering capacity. Any changes in any single component of the carbonate system will lead to changes in several, if not all, other components. In other words, it is not possible to vary a single component of the carbonate system while keeping all other components constant. This interdependency in the carbonate system is important to consider when performing CO2 perturbation experiments. To adjust seawater to different p(CO2) levels, the carbonate system can be manipulated in various ways that usually involve changes in AT or DIC. The goal of this chapter is (1) to examine the benefi ts and drawbacks of various manipulation methods used to date and (2) to provide a simple software package to assist the design of perturbation experiments

Herschel photometric observations of the low metallicity dwarf galaxy NGC 1705

We present Herschel SPIRE and PACS photometeric observations of the low metallicity (Z ~ 0.35 Z_☉) nearby dwarf galaxy, NGC 1705, in six wavelength bands as part of the Dwarf Galaxy Survey guaranteed time Herschel key program. We confirm the presence of two dominant circumnuclear IR-bright regions surrounding the central super star cluster that had been previously noted at mid-IR wavelengths and in the sub-mm by LABOCA. On constructing a global spectral energy distribution using the SPIRE and PACS photometry, in conjunction with archival IR measurements, we note the presence of an excess at sub-mm wavelengths. This excess suggests the presence of a significant cold dust component within NGC 1705 and was modeled as an additional cold component in the SED. Although alternative explanations for the sub-mm excess beyond 350 μm, such as changes to the dust emissivity cannot be ruled out, the most likely explanation for the observed submillimetre excess is that of an additional cold dust component

Current reversal and exclusion processes with history-dependent random walks

A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate by breaking and reforming lattice bonds. We determine the steady-state current on a ring, and find current-reversal as a function of particle density. This phenomenon is attributed to the non-local interaction between the walkers through their trails, which originates from strong correlations between the dynamics of the particles and the lattice. We rationalize our findings within an effective description in terms of quasi-particles which we call front barriers. Our analytical results are complemented by stochastic simulations.Comment: 5 pages, 6 figure

Mapping the interstellar medium in galaxies with Herschel/SPIRE

The standard method of mapping the interstellar medium in a galaxy, by observing the molecular gas in the CO 1-0 line and the atomic gas in the 21-cm line, is largely limited with current telescopes to galaxies in the nearby universe. In this letter, we use SPIRE observations of the galaxies M99 and M100 to explore the alternative approach of mapping the interstellar medium using the continuum emission from the dust. We have compared the methods by measuring the relationship between the star-formation rate and the surface density of gas in the galaxies using both methods. We find the two methods give relationships with a similar dispersion, confirming that observing the continuum emission from the dust is a promising method of mapping the interstellar medium in galaxies