Row transfer matrix functional relations for Baxter's eight-vertex and six-vertex models with open boundaries via more general reflection matrices

The functional relations of the transfer matrices of fusion hierarchies for six- and eight-vertex models with open boundary conditions have been presented in this paper. We have shown the su(2) fusion rule for the models with more general reflection boundary conditions, which are represented by off-diagonal reflection matrices. Also we have discussed some physics properties, which are determined by the functional relations. Finally, the intertwining relation between the reflection K-matrices for the vertex and SOS models is discussed.     

Exact solution for the spin-s XXZ quantum chain with non-diagonal twists

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon which a Bethe ansatz calculation can be constructed, in contrast to the well-known case of periodic boundary conditions. In this paper we show how the transfer matrix eigenvalue expression for the spin-s XXZ chain twisted by the charge-conjugation matrix can in fact be obtained. The technique used is the generalization to spin-s of the functional relation method based on “pair propagation through a vertex”. The Bethe ansatz-type equations obtained reduce, in the case of lattice size N = 1, to those recently found for the Hofstadter problem of Bloch electrons on a square lattice in a magnetic field.     

Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions

We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that interactions up to ? ⁶-tensorial type are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.     

Renormalizability conditions for almost-commutative geometries

We formulate conditions for almost-commutative (spacetime) manifolds under which the asymptotically expanded spectral action is renormalizable. These conditions are of a graph-theoretical nature, involving the Krajewski diagrams that classify such geometries. This applies in particular to the Standard Model of particle physics, giving a graph-theoretical argument for its renormalizability. A promising potential application is in the selection of physical (renormalizable) field theories described by almost-commutative geometries, thereby going beyond the Standard Model.     

A multifractal study of wave functions in 1-D quasicrystals

Using multifractal analysis we study extended, self-similar and non-self-similar type of wave functions in the Fibonacci model. Extended states arising due to commutation of transfer matrices for certain blocks of atoms in quasiperiodic systems are shown to have the same signature as the Bloch states in terms of the singularity spectrum withf(α)=α=1. Numerically, however, the extended states show a typical multifractal behaviour for finite chain lengths. Finite size scaling corrections yield results consistent with that obtained analytically. The self-similar states at the band edges show a multifractal behaviour and they are energy dependent in the case of blocks of atoms arranged in a Fibonacci sequence. For non-self-similar states we obtain a non-monotonic behaviour off(α) as a function of the chain length. We also show that in cases where extended states exist, the cross-over from extended to non-self-similar states in gradual.     

Quantum-state transfer through long-range correlated disordered channels

We study quantum-state transfer in XX spin-1/2 chains where both communicating spins are weakly coupled to a channel featuring disordered on-site magnetic fields. Fluctuations are modeled by long-range correlated sequences with self-similar profile obeying a power-law spectrum. We show that the channel is able to perform almost perfect quantum-state transmissions even in the presence of significant amounts of disorder provided the degree of those correlations is strong enough, with the cost of having long transfer times and unavoidable timing errors. Still, we show that the lack of mirror symmetry in the channel does not affect much the likelihood of having high-quality outcomes. Our results suggest that coexistence between localized and delocalized states can diminish effects of static perturbations in solid-state devices for quantum communication.     

Electrons on one-dimensional quasi-lattices

Electronic properties in one-dimensional quasi-lattices constructed by the Fibonacci substitution rule are studied numerically. Examining the generation dependence of the substitution, we find that the gross band structure is generation independent and self-similar and that the ratio of the number of the eigenvalues contained in each band tends to the golden mean with the generation. The spatial variations of the wave functions with various energies are self-similar. Other class of the quasi-lattice is briefly discussed to highlight generality of our conclusions.     

Noncompact <Emphasis Type="Italic">sl</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) Spin Chains: BGG-Resolution,Q-Operators and Alternating Sum Representation for Finite-Dimensional Transfer Matrices

We study properties of transfer matrices in the sl(N) spin chain models. The transfer matrices with an infinite-dimensional auxiliary space are factorized into the product of N commuting Baxter Q{\mathcal{Q}}-operators. We consider the transfer matrices with auxiliary spaces of a special type (including the finite-dimensional ones). It is shown that they can be represented as the alternating sum over the transfer matrices with infinite- dimensional auxiliary spaces. We show that certain combinations of the Baxter Q{\mathcal{Q}}-operators can be identified with the Q-functions, which appear in the Nested Bethe Ansatz.     

Diagonalisation of finite-size corner transfer matrices and related spin chains

We study Baxter's corner transfer matrices for anisotropic Ising models of finite size. They are related to spin one-half chains with coefficients which increase linearly along the chain. The operators are diagonalised with the help of special polynomials and the eigenvalue spectrum is discussed. The relation to the infinite lattice limit is outlined.     

Superspace approach to quantum gauge theories

We present an approach to quantum gauge theories formulated entirely on a superspace. We show that at the classical level the field equations are the same as in the usual Minkowski-space approach. In particular the a-flatness conditions, which represent the BRS and anti-BRS covariance in the usual approach, appear as field equations. We show that the theory is renormalizable and the a-flatness conditions are stable under renormalization. We speculate about the relevance of this approach to the confinement problem.     

Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy

We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the Andrews-Baxter-Forrester (ABF) models, for which we obtain diagonal, elliptic solutions to the reflection equations, and find that the double-row transfer matrices satisfy functional equations with the same form as in the case of periodic boundary conditions.     

On the vacuum states for non-commutative gauge theory

Candidates for renormalizable gauge theory models on Moyal spaces constructed recently have non-trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which form a global symmetry group for the action. We compute the explicit expression in position space for these vacuum configurations in two and four dimensions.     

A physical explanation for the origin of self-similar magnetoconductance fluctuations in semiconductor billiards

We report quantum-mechanical calculations which replicate the self-similar magnetoconductance fluctuations observed in recent experiments on semiconductor Sinai billiards. We interpret these fluctuations by considering the mixed stable-chaotic classical dynamics of electrons in the billiard. In particular, we show that the fluctuation patterns are dominated by individual stable orbits. The scaling characteristics of the self-similar fluctuations depend on the geometry of the associated stable orbit. We find that our analysis is insensitive to the details of the potential landscape, and is applicable to real devices with a wide range of soft-wall profiles. We show that our analysis also provides a possible explanation for the distinct series of magnetoconductance fluctuations observed in recent experiments on carbon nanotubes.     

Open Hecke chains and free fermions

We consider integrable open-chain models formulated in terms of generators of Hecke algebra. The algebraic analogs of Sklyanin’s commutative transfer matrices are considered for these models. The spectrum of Hamiltonians for open Hecke chains of finite size is deduced for special representations of the Hecke algebra.     

Supersymmetric models with minimal flavor violation and their running

We revisit the formulation of the principle of minimal flavor violation (MFV) in the minimal supersymmetric extension of the standard model, both at moderate and large tan β, and with or without new CP-violating phases. We introduce a counting rule which keeps track of the highly hierarchical structure of the Yukawa matrices. In this manner, we are able to control systematically which terms can be discarded in the soft SUSY breaking part of the Lagrangian. We argue that for the implementation of this counting rule, it is convenient to introduce a new basis of matrices in which both the squark (and slepton) mass terms as well as the trilinear couplings can be expanded. We derive the RGE for the MFV parameters and show that the beta functions also respect the counting rule. For moderate tan β, we provide explicit analytic solutions of these RGE and illustrate their behavior by analyzing the neighborhood (also switching on new phases) of the SPS-1a benchmark point. We then show that even in the case of large tan β, the RGE remain valid and that the analytic solutions obtained for moderate tan β still allow us to understand the most important features of the running of the parameters, as illustrated with the help of the SPS-4 benchmark point.     

Probing Si and Ti Based Sol-Gel Matrices by Fluorescence Techniques

The photophysical behavior of several probes incorporated in sol-gel–derived matrices (both monoliths and thin films) has been studied using steady-state and time-resolved fluorescence, along with fluorescence anisotropy to study the matrix structure and to elucidate probe-matrix interactions. The probes studied include laser and solvatochromic dyes along with porphyrins and phthalocyanines. It was found that spectral shifts, time-resolved decays, and quantum yields depend on the type of matrix and its preparation conditions combined with the drying time and the nature of retained solvent, which can be added to act as an anticracking agent. The differences between the results in the TiO₂ matrix, where electron transfer is most probably present, and SiO₂ are shown.     

Linearization of the interaction principle: Analytic Jacobians in the “Radiant” model

In this paper we present a new linearization of the Radiant radiative transfer model. Radiant uses discrete ordinates for solving the radiative transfer equation in a multiply-scattering anisotropic medium with solar and thermal sources, but employs the adding method (interaction principle) for the stacking of reflection and transmission matrices in a multilayer atmosphere. For the linearization, we show that the entire radiation field is analytically differentiable with respect to any surface or atmospheric parameter for which we require Jacobians (derivatives of the radiance field). Derivatives of the discrete ordinate solutions are based on existing methods developed for the LIDORT radiative transfer models. Linearization of the interaction principle is completely new and constitutes the major theme of the paper. We discuss the application of the Radiant model and its linearization in the Level 2 algorithm for the retrieval of columns of carbon dioxide as the main target of the Orbiting Carbon Observatory (OCO) mission.     

Self-similarity and scaling of wave function for binary quasiperiodic chains associated with quadratic irrationals

By establishing the correspondence between the substitution rule (aa ⁿb; ba) and the transformation on the value of =tan by1/(n+) in the cut-and-project (CP) method, it is proved that the necessary and sufficient conditions for a binary quasiperiodic (QP) sequence made by the CP method to be self-similar is that is a quadratic irrational (QI) number. And, vice versa, the necessary condition for a binary self-similar sequence generated by the substitution rule to be obtainable by the CP method is that the corresponding substitution rule can be rewritten as a simple composition of transformations with the type (aa ⁿb; ba). To illustrate some physical properties of the self-similar QP chains associated with QI numbers, we analyze the scaling behaviour of the wave function atE=0 for an off-diagnonal tight-binding model. It is shown that the wave function atE=0 grows at most by a power-law for the QP lattices, characterized by a special class of QI numbers. For the QP chains associated with general QI numbers, with the same logic, the typical scaling behaviour of the wave function is conjectured to be the same.     

Are nonrenormalizable gauge theories renormalizable?

We raise the issue whether gauge theories, that are not renormalizable in the usual powercounting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of terms in the bare action. We find that a theory is renormalizable in this sense if the a priori constraints that we impose on the form of the bare action correspond to the cohomology of the BRST-transformations generated by the action. Recent cohomology theorems of Bamich, Brandt, and Henneaux are used to show that conventionally nomenormalizable theories of Yang-Mills fields (such as quantum chromodynamics with heavy quarks integrated out) and/or gravitation are renormalizable in the modern sense.     

Flexible polymers and thin rods far from equilibrium: buckling dynamics

We investigate the dynamics of the classical Euler buckling instability of compressed objects such as flexible molecular chains and thin rods moving in a viscous medium. We find that flexible chains undergo a coarsening process self-similar in time. They develop a wavelike pattern whose amplitude and wavelength grow in time. We relate the buckling dynamics to phase ordering phenomena. The role of the order parameter here is played by the chain slope with respect to the straight initial chain configuration.