Equational reasoning with context-free families of string diagrams

String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout rewriting. However, one often wishes to express not just single equations, but entire families of equations between diagrams of arbitrary size. To do this we define a class of context-free grammars, called B-ESG grammars, that are suitable for defining entire families of string graphs, and crucially, of string graph rewrite rules. We show that the language-membership and match-enumeration problems are decidable for these grammars, and hence that there is an algorithm for rewriting string graphs according to B-ESG rewrite patterns. We also show that it is possible to reason at the level of grammars by providing a simple method for transforming a grammar by string graph rewriting, and showing admissibility of the induced B-ESG rewrite pattern.Comment: International Conference on Graph Transformation, ICGT 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21145-9_

First-Order Insulator-to-Metal Mott Transition in the Paramagnetic 3D System GaTa4Se8

The nature of the Mott transition in the absence of any symmetry braking remains a matter of debate. We study the correlation-driven insulator-to-metal transition in the prototypical 3D Mott system GaTa4Se8, as a function of temperature and applied pressure. We report novel experiments on single crystals, which demonstrate that the transition is of first order and follows from the coexistence of two states, one insulating and one metallic, that we toggle with a small bias current. We provide support for our findings by contrasting the experimental data with calculations that combine local density approximation with dynamical mean-field theory, which are in very good agreement.Comment: 5 pages and 4 figures. Supplemental material: 2 pages, 2 figure

Transfer of Spectral Weight in Spectroscopies of Correlated Electron Systems

We study the transfer of spectral weight in the photoemission and optical spectra of strongly correlated electron systems. Within the LISA, that becomes exact in the limit of large lattice coordination, we consider and compare two models of correlated electrons, the Hubbard model and the periodic Anderson model. The results are discussed in regard of recent experiments. In the Hubbard model, we predict an anomalous enhancement optical spectral weight as a function of temperature in the correlated metallic state which is in qualitative agreement with optical measurements in $V_2O_3$. We argue that anomalies observed in the spectroscopy of the metal are connected to the proximity to a crossover region in the phase diagram of the model. In the insulating phase, we obtain an excellent agreement with the experimental data and present a detailed discussion on the role of magnetic frustration by studying the $k-$resolved single particle spectra. The results for the periodic Anderson model are discussed in connection to recent experimental data of the Kondo insulators $Ce_3Bi_4Pt_3$ and $FeSi$. The model can successfully explain the different energy scales that are associated to the thermal filling of the optical gap, which we also relate to corresponding changes in the density of states. The temperature dependence of the optical sum rule is obtained and its relevance for the interpretation of the experimental data discussed. Finally, we argue that the large scattering rate measured in Kondo insulators cannot be described by the periodic Anderson model.Comment: 19 pages + 29 figures. Submitted to PR

Comment on low-temperature transport properties of non-stoichiometric La_{0.95-x}Sr_{x}MnO_{3}

In a recent paper (Michalopolou A., Syskakis E. and Papastaikoudis C., 2001 J. Phys.: Cond. Mat. 13, 11615) the authors reported on the measurements of electrical resistivity and specific heat at zero magnetic field carried out on polycrystalline non-stoichiometric La_{0.95-x}Sr_{x}MnO_{3} manganites.In particular, they attributed the low temperature behavior of resistivity (shallow minimum and slight upturn at lowest temperatures) to 3D electron-electron interaction enhanced by disorder, using results of numerical fittings of the dependencies of resistivity on temperature in the interval 4.2 -- 40 K. We argue that such an analysis may be not valid for polycrystalline manganites where relatively strong grain boundary effects might mask weak contribution of quantum effects to low temperature resistivity. The crucial test of applicability of the theory of quantum corrections to conductivity in this case is the resistive measurements under non-zero magnetic field.Comment: pdf, 6 pages, submitted to J. Phys.: Cond. Matte

Optical Conductivity in Mott-Hubbard Systems

We study the transfer of spectral weight in the optical spectra of a strongly correlated electron system as a function of temperature and interaction strength. Within a dynamical mean field theory of the Hubbard model that becomes exact in the limit of large lattice coordination, we predict an anomalous enhancement of spectral weight as a function of temperature in the correlated metallic state and report on experimental measurements which agree with this prediction in $V_2O_3$. We argue that the optical conductivity anomalies in the metal are connected to the proximity to a crossover region in the phase diagram of the model.Comment: 12 pages and 4 figures, to appear in Phys. Rev. Lett., v 75, p 105 (1995

Typical-Medium Theory of Mott-Anderson Localization

The Mott and the Anderson routes to localization have long been recognized as the two basic processes that can drive the metal-insulator transition (MIT). Theories separately describing each of these mechanisms were discussed long ago, but an accepted approach that can include both has remained elusive. The lack of any obvious static symmetry distinguishing the metal from the insulator poses another fundamental problem, since an appropriate static order parameter cannot be easily found. More recent work, however, has revisited the original arguments of Anderson and Mott, which stressed that the key diference between the metal end the insulator lies in the dynamics of the electron. This physical picture has suggested that the "typical" (geometrically averaged) escape rate from a given lattice site should be regarded as the proper dynamical order parameter for the MIT, one that can naturally describe both the Anderson and the Mott mechanism for localization. This article provides an overview of the recent results obtained from the corresponding Typical-Medium Theory, which provided new insight into the the two-fluid character of the Mott-Anderson transition.Comment: to be published in "Fifty Years of Anderson localization", edited by E. Abrahams (World Scientific, Singapore, 2010); 29 pages, 22 figures

Band-width control in a perovskite-type 3d^1 correlated metal Ca_1-xSr_xVO_3. II. Optical spectroscopy investigation

Optical conductivity spectra of single crystals of Ca_1-xSr_xVO_3 have been studied to elucidate how the electronic behavior depends on the strength of the electron correlation without changing the nominal number of electrons per vanadium atom. The effective mass deduced by the analysis of the Drude-like contribution do not show critical enhancement, even though the system is close to the Mott transition. Besides the Drude-like contribution, two anomalous features were observed in the optical conductivity spectra of the intraband transition within the 3d band. These features can be assigned to transitions involving the incoherent and coherent bands near the Fermi level. The large spectral weight redistribution in this system, however, does not involve a large mass enhancement.Comment: 12 pages in a Phys. Rev. B camera-ready format with 16 EPS figures embedded. LaTeX 2.09 source file using "camera.sty" and "prbplug.sty" provided by N. Shirakawa. For OzTeX (Macintosh), use "ozfig.sty" instead of "psfig.sty". "ozfig.sty" can be also obtained by e-mail request to N. Shirakawa: . Submitted to Phys. Rev. B. See "Part I (by Inoue et al.)" at cond-mat/980107

Complex patterns of global spread in invasive insects: eco-evolutionary and management consequences

The advent of simple and affordable tools for molecular identification of novel insect invaders and assessment of population diversity has changed the face of invasion biology in recent years. The widespread application of these tools has brought with it an emerging understanding that patterns in biogeography, introduction history and subsequent movement and spread of many invasive alien insects are far more complex than previously thought. We reviewed the literature and found that for a number of invasive insects, there is strong and growing evidence that multiple introductions, complex global movement, and population admixture in the invaded range are commonplace. Additionally, historical paradigms related to species and strain identities and origins of common invaders are in many cases being challenged. This has major consequences for our understanding of basic biology and ecology of invasive insects and impacts quarantine, management and biocontrol programs. In addition, we found that founder effects rarely limit fitness in invasive insects and may benefit populations (by purging harmful alleles or increasing additive genetic variance). Also, while phenotypic plasticity appears important post-establishment, genetic diversity in invasive insects is often higher than expected and increases over time via multiple introductions. Further, connectivity among disjunct regions of global invasive ranges is generally far higher than expected and is often asymmetric, with some populations contributing disproportionately to global spread. We argue that the role of connectivity in driving the ecology and evolution of introduced species with multiple invasive ranges has been historically underestimated and that such species are often best understood in a global context

Metal-insulator transition in a doubly orbitally degenerate model with correlated hopping

In the present paper we propose a doubly orbitally degenerate narrow-band model with correlated hopping. The peculiarity of the model is taking into account the matrix element of electron-electron interaction which describes intersite hoppings of electrons. In particular, this leads to the concentration dependence of the effective hopping integral. The cases of the strong and weak Hund's coupling are considered. By means of a generalized mean-field approximation the single-particle Green function and quasiparticle energy spectrum are calculated. Metal-insulator transition is studied in the model at different integer values of the electron concentration. With the help of the obtained energy spectrum we find energy gap width and criteria of metal-insulator transition.Comment: minor revisions, published in Phys. Rev.