On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J, and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices, and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Friedel oscillations in one-dimensional metals: From Luttinger`s theorem to the Luttinger liquid

Charge density and magnetization density profiles of one-dimensional metals are investigated by two complementary many-body methods: numerically exact (Lanczos) diagonalization, and the Bethe-Ansatz local-density approximation with and without a simple self-interaction correction. Depending on the magnetization of the system, local approximations reproduce different Fourier components of the exact Friedel oscillations. (C) 2008 Elsevier B.V. All rights reserved.

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Passage of radiation through wormholes of arbitrary shape

We study quasinormal modes and scattering properties via calculation of the S matrix for scalar and electromagnetic fields propagating in the background of spherically symmetric and axially symmetric traversable Lorentzian wormholes of a generic shape. Such wormholes are described by the general Morris-Thorne ansatz. The properties of quasinormal ringing and scattering are shown to be determined by the behavior of the wormhole's shape function b(r) and shift factor Phi(r) near the throat. In particular, wormholes with the shape function b(r), such that b(dr) approximate to 1, have very long-lived quasinormal modes in the spectrum. We have proved that the axially symmetric traversable Lorentzian wormholes, unlike black holes and other compact rotating objects, do not allow for superradiance. As a by-product we have shown that the 6th order WKB formula used for scattering problems of black or wormholes gives quite high accuracy and thus can be used for quite accurate calculations of the Hawking radiation processes around various black holes.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Transport-Regional Equity Issue Revisited

Almeida E. S. de, Haddad E. A. and Hewings G. J. D. Transport-regional equity issue revisited, Regional Studies. The objective of this paper is to analyse the relationship between transport and regional equity in Minas Gerais, Brazil. Furthermore, the existence of a trade-off between economic performance and regional equity is investigated as well. To do so, the paper develops a spatial computable general equilibrium model based on Brocker and Schneider`s approach of 2002 to implement comparative static analysis, explicitly incorporating iceberg transportation costs. Four activities are modelled, namely production, final demand, transportation and exports. Two production factors are assumed: labour and other factors. The model has 12 domestic regions and three external regions. Four counterfactual experiments are developed based on decreases in transportation costs due to a `distance shortening`. The main findings indicate that if the transport infrastructure improvement is focused only among poor regions, the promotion of regional equity is insignificant. If the transport infrastructure improvement links are concentrated among rich regions, there is an increase in regional income inequalities. However, if the improvements are targeted to the roads linking poor regions and rich ones, there is greater promotion of regional equity. The same result will occur when improvements are made to all road links of the state. [image omitted] Almeida E. S. de, Haddad E. A. et Hewings G. J. D. La question du rapport entre le transport et l`equilibre regional vue sous un jour nouveau, Regional Studies. Cet article cherche a analyser le rapport entre le transport et l`equilibre regional en Minas Gerais au Bresil. En outre, on examine la presence d`un echange entre la performance economoique et l`equilibre regional. Pour le faire, on construit un modele geographique de l`equilibre general a utiliser sur ordinateur fonde sur l`approche de Brockner et Schneider en 2002 afin de mettre en oeuvre une analyse statique comparative qui comprend explicitement les frais de transport iceberg. On modelise quatre activites, a savoir, la production, la demande finale, le transport et l`exportation. On fait deux suppositions quant aux facteurs de production: la main-d`oevre et d`autres facteurs. Le modele embrasse douze regions internes et trois regions externes. On fait quatre experiences paradoxales fondees sur la baisse des frais de transport due a une `reduction des distances`. Les principaux resultats indiquent que si l`amelioration de l`equipement de transport ne porte que sur les regions defavorisees, la promotion de l`equilibre regional s`avere negligeable. Si l`amelioration de l`equipement de transport focalise les regions riches, il s`avere un creusement des ecarts des revenus regionaux. Cependant, si les ameliorations ciblent les routes qui relient les regions defavorisees aux regions riches, il s`avere une plus grande promotion de l`equilibre regional. Il en va de meme pour la situation ou on a apporte des amenagements a toutes les liaisons routieres de l`etat. Modele geographique de l`equilibre general a utiliser sur ordinateur Equilibre regional Peformance economique Frais de transport Almeida E. S. de, Haddad E. A. und Hewings G. J. D. Die Wiederaufnahme der Frage von Verkehrswesen im Verhaltnis zu regionaler Fairness, Regional Studies. Dieser Aufsatz beabsichtigt, die Beziehung zwischen Verkehrswesen und regionaler Fairness in Minas Gerais (Brasilien) zu analysieren und zugleich auch das Vorkommen von Einbussen entweder bei wirtschaftlicher Leistung der regionaler Fairness zu untersuchen. Zu diesem Zwecke wird ein auf dem Ansatz von Brocker und Schneider (2002) aufbauendes raumliches komputables allgemeines Gleichgewichtsmodell entwickelt, um vergleichende statistische Analysen durchzufuhren, wobei verborgene `Eisberg`-Transportkosten ausdrucklich berucksichtigt werden. Es werden vier Unternehmenstatigk eiten aufgefuhrt: Herstellung, Nachfrage, Transportwesen und Exporte, und zwei Produktionsfaktoren vorausgesetzt: Arbeitskrafte und andere Faktoren. Das Modell umfasst zwolf Inlandsregionen und drei externe Regionen. Es werden vier gegensatzliche Experimente entwickelt, die auf einer Abnahme der Transportkosten infolge einer `Verkurzung der Entfernungen` beruhen. Die Hauptbefunde weisen darauf hin, dass die Forderung regionaler Fairness unbedeutend bleibt, wenn die Verbesserungen der Transportinfrastruktur sich nur auf minderbemittelte Regionen konzentrieren; werden die Verbesserungen der Verbindungen der Transportinfrastruktur in wohlhabenden Regionen durchgefuhrt, so nehmen regionale Einkommensunterschiede zu. Wenn die Verbesserungen jedoch auf Strassen abzielen, die wohlhabende Regionen mit weniger bemittelten verbinden, wird regionale Fairness starker gefordert. Das gleiche Ergebnis wird sich einstellen, wenn Verbesserungen an allen Strassenverbindungen des Staates vorgenommen werden. Raumliches, komputables, allgemeines Gleichgewichtsmodell Regionale Fairness Wirtschaftsleistung Transportkosten Almeida E. S. de, Haddad E. A. y Hewings G. J. D. Revisando el tema de la igualdad del transporte en las regiones, Regional Studies. El objetivo de este documento es analizar la relacion entre el transporte y la igualdad regional en Minas Gerais, Brasil. Asimismo investigamos la existencia de una compensacion entre el rendimiento economico y la igualdad regional. Para ello desarrollamos un modelo de equilibrio general computable y espacial basado en el enfoque de Brocker y Schneider en 2002 para hacer un analisis estatico y comparativo, explicitamente incorporando los costes ocultos de transporte. Se modelan cuatro actividades: la produccion, la demanda final, el transporte y las exportaciones. Suponemos que existen dos factores de produccion: mano de obra y otros factores. En este modelo, existen doce regiones internas y tres regiones externas. Desarrollamos cuatro experimentos contrafactuales basados en la disminucion de los costes de transporte debido a una `acortamiento de las distancias`. Los principales resultados indican que si la mejora de la infraestructura del transporte se centra solo entre las regiones mas pobres, el fomento de la igualdad regional es insignificante. Si los enlaces de la mejora de la infraestructura del transporte se concentran en las regiones ricas, aumentan las desigualdades de ingresos regionales. Sin embargo, si se mejoran los enlaces de carreteras entre las regiones pobres y ricas, se fomenta mejor la igualdad regional. El mismo resultado ocurre cuando se mejoran los enlaces de todas las carreteras del estado. Modelo de equilibrio general computable y espacial Igualdad regional Rendimiento economico Costes de transporte.

EXACT AND QUASI-EXACT MODELS OF STRANGE STARS

We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

A Hopping Mechanism for Cargo Transport by Molecular Motors on Crowded Microtubules

Most models designed to study the bidirectional movement of cargos as they are driven by molecular motors rely on the idea that motors of different polarities can be coordinated by external agents if arranged into a motor-cargo complex to perform the necessary work Gross, Hither and yon: a review of bidirectional microtubule-based transport (Gross in Phys. Biol. 1:R1-R11, 2004). Although these models have provided us with important insights into these phenomena, there are still many unanswered questions regarding the mechanisms through which the movement of the complex takes place on crowded microtubules. For example (i) how does cargo-binding affect motor motility? and in connection with that-(ii) how does the presence of other motors (and also other cargos) on the microtubule affect the motility of the motor-cargo complex? We discuss these questions from a different perspective. The movement of a cargo is conceived here as a hopping process resulting from the transference of cargo between neighboring motors. In the light of this, we examine the conditions under which cargo might display bidirectional movement even if directed by motors of a single polarity. The global properties of the model in the long-time regime are obtained by mapping the dynamics of the collection of interacting motors and cargos into an asymmetric simple exclusion process (ASEP) which can be resolved using the matrix ansatz introduced by Derrida (Derrida and Evans in Nonequilibrium Statistical Mechanics in One Dimension, pp. 277-304, 1997; Derrida et al. in J. Phys. A 26: 1493-1517, 1993).

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Static Hopfions in the extended Skyrme-Faddeev model

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is an extension of the Skyrme-Faddeev model by the addition of a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled non-linear partial differential equations in two variables by a successive over-relaxation (SOR) method. We construct numerical solutions with Hopf charge up to four, and calculate their analytical behavior in some limiting cases. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms. Their energies and sizes tend to zero as that combination approaches a particular special value. We calculate the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and find that it vanishes at that same special value of the coupling constants. In addition, the model presents an integrable sector with an in finite number of local conserved currents which apparently are not related to symmetries of the action. In the intersection of those two special sectors the theory possesses exact vortex solutions (static and time dependent) which were constructed in a previous paper by one of the authors. It is believed that such model describes some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and our results may be important in identifying important structures in that strong coupling regime.

Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies`s extension

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is the extended Skyrme-Faddeev model with a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled nonlinear partial differential equations in two variables by a successive over-relaxation method. We construct numerical solutions with the Hopf charge up to 4. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms.