Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Euclideanization, topological theories, higher dimensions and all that

It is shown that the euclideanized Yukawa theory, with the Dirac fermion belonging to an irreducible representation of the Lorentz group, is not bounded from below. A one parameter family of supersymmetric actions is presented which continuously interpolates between the N = 2 SSYM and the N = 2 supersymmetric topological theory. In order to obtain a theory which is bounded from below and satisfies Osterwalder-Schrader positivity, the Dirac fermion should belong to a reducible representation of the Lorentz group and the scalar fields have to be reinterpreted as the extra components of a higher dimensional vector field.

Noncommutative vortices and instantons from generalized Bose operators

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.

Magnetic structures and magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied by neutron powder diffraction

The magnetic structures and the magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied using neutron powder diffraction are reported. Magnetic phase transitions are identified at T-N(Fe/Mn) approximate to 295K where a paramagnetic-to-antiferromagnetic transition occurs in the Fe/Mn sublattice, T-SR(Fe/Mn) approximate to 26K where a spin-reorientation transition occurs in the Fe/Mn sublattice and T-N(R) approximate to 2K where Tb-ordering starts to manifest. At 295 K, the magnetic structure of the Fe/Mn sublattice in TbFe0.5Mn0.5O3 belongs to the irreducible representation Gamma(4) (G(x)A(y)F(z) or Pb'n'm). A mixed-domain structure of (Gamma(1) + Gamma(4)) is found at 250K which remains stable down to the spin re-orientation transition at T-SR(Fe/Mn) approximate to 26K. Below 26K and above 250 K, the majority phase (>80%) is that of Gamma(4). Below 10K the high-temperature phase Gamma(4) remains stable till 2K. At 2 K, Tb develops a magnetic moment value of 0.6(2) mu(B)/f.u. and orders long-range in F-z compatible with the Gamma(4) representation. Our study confirms the magnetic phase transitions reported already in a single crystal of TbFe0.5Mn0.5O3 and, in addition, reveals the presence of mixed magnetic domains. The ratio of these magnetic domains as a function of temperature is estimated from Rietveld refinement of neutron diffraction data. Indications of short-range magnetic correlations are present in the low-Q region of the neutron diffraction patterns at T < T-SR(Fe/Mn). These results should motivate further experimental work devoted to measure electric polarization and magnetocapacitance of TbFe0.5Mn0.5O3. (C) 2016 AIP Publishing LLC.

Magnetic structures and magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied by neutron powder diffraction

The magnetic structures and the magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied using neutron powder diffraction are reported. Magnetic phase transitions are identified at T-N(Fe/Mn) approximate to 295K where a paramagnetic-to-antiferromagnetic transition occurs in the Fe/Mn sublattice, T-SR(Fe/Mn) approximate to 26K where a spin-reorientation transition occurs in the Fe/Mn sublattice and T-N(R) approximate to 2K where Tb-ordering starts to manifest. At 295 K, the magnetic structure of the Fe/Mn sublattice in TbFe0.5Mn0.5O3 belongs to the irreducible representation Gamma(4) (G(x)A(y)F(z) or Pb'n'm). A mixed-domain structure of (Gamma(1) + Gamma(4)) is found at 250K which remains stable down to the spin re-orientation transition at T-SR(Fe/Mn) approximate to 26K. Below 26K and above 250 K, the majority phase (>80%) is that of Gamma(4). Below 10K the high-temperature phase Gamma(4) remains stable till 2K. At 2 K, Tb develops a magnetic moment value of 0.6(2) mu(B)/f.u. and orders long-range in F-z compatible with the Gamma(4) representation. Our study confirms the magnetic phase transitions reported already in a single crystal of TbFe0.5Mn0.5O3 and, in addition, reveals the presence of mixed magnetic domains. The ratio of these magnetic domains as a function of temperature is estimated from Rietveld refinement of neutron diffraction data. Indications of short-range magnetic correlations are present in the low-Q region of the neutron diffraction patterns at T < T-SR(Fe/Mn). These results should motivate further experimental work devoted to measure electric polarization and magnetocapacitance of TbFe0.5Mn0.5O3. (C) 2016 AIP Publishing LLC.

Magnetic structures and magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied by neutron powder diffraction

The magnetic structures and the magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied using neutron powder diffraction are reported. Magnetic phase transitions are identified at T-N(Fe/Mn) approximate to 295K where a paramagnetic-to-antiferromagnetic transition occurs in the Fe/Mn sublattice, T-SR(Fe/Mn) approximate to 26K where a spin-reorientation transition occurs in the Fe/Mn sublattice and T-N(R) approximate to 2K where Tb-ordering starts to manifest. At 295 K, the magnetic structure of the Fe/Mn sublattice in TbFe0.5Mn0.5O3 belongs to the irreducible representation Gamma(4) (G(x)A(y)F(z) or Pb'n'm). A mixed-domain structure of (Gamma(1) + Gamma(4)) is found at 250K which remains stable down to the spin re-orientation transition at T-SR(Fe/Mn) approximate to 26K. Below 26K and above 250 K, the majority phase (>80%) is that of Gamma(4). Below 10K the high-temperature phase Gamma(4) remains stable till 2K. At 2 K, Tb develops a magnetic moment value of 0.6(2) mu(B)/f.u. and orders long-range in F-z compatible with the Gamma(4) representation. Our study confirms the magnetic phase transitions reported already in a single crystal of TbFe0.5Mn0.5O3 and, in addition, reveals the presence of mixed magnetic domains. The ratio of these magnetic domains as a function of temperature is estimated from Rietveld refinement of neutron diffraction data. Indications of short-range magnetic correlations are present in the low-Q region of the neutron diffraction patterns at T < T-SR(Fe/Mn). These results should motivate further experimental work devoted to measure electric polarization and magnetocapacitance of TbFe0.5Mn0.5O3. (C) 2016 AIP Publishing LLC.

Magnetic structures and magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied by neutron powder diffraction

The magnetic structures and the magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied using neutron powder diffraction are reported. Magnetic phase transitions are identified at T-N(Fe/Mn) approximate to 295K where a paramagnetic-to-antiferromagnetic transition occurs in the Fe/Mn sublattice, T-SR(Fe/Mn) approximate to 26K where a spin-reorientation transition occurs in the Fe/Mn sublattice and T-N(R) approximate to 2K where Tb-ordering starts to manifest. At 295 K, the magnetic structure of the Fe/Mn sublattice in TbFe0.5Mn0.5O3 belongs to the irreducible representation Gamma(4) (G(x)A(y)F(z) or Pb'n'm). A mixed-domain structure of (Gamma(1) + Gamma(4)) is found at 250K which remains stable down to the spin re-orientation transition at T-SR(Fe/Mn) approximate to 26K. Below 26K and above 250 K, the majority phase (>80%) is that of Gamma(4). Below 10K the high-temperature phase Gamma(4) remains stable till 2K. At 2 K, Tb develops a magnetic moment value of 0.6(2) mu(B)/f.u. and orders long-range in F-z compatible with the Gamma(4) representation. Our study confirms the magnetic phase transitions reported already in a single crystal of TbFe0.5Mn0.5O3 and, in addition, reveals the presence of mixed magnetic domains. The ratio of these magnetic domains as a function of temperature is estimated from Rietveld refinement of neutron diffraction data. Indications of short-range magnetic correlations are present in the low-Q region of the neutron diffraction patterns at T < T-SR(Fe/Mn). These results should motivate further experimental work devoted to measure electric polarization and magnetocapacitance of TbFe0.5Mn0.5O3. (C) 2016 AIP Publishing LLC.

Mode characteristics for equilateral triangle optical resonators

Mode characteristics of equilateral triangle resonators (ETRs) are analyzed based on the symmetry operation of the point group C-3v. The results show that doubly degenerate eigenstates can be reduced to the A(1) and A(2) representations of C-3v, if the longitudinal mode number is a multiple of 6; otherwise, they form the E irreducible representation Of C-3v. And the one-period length for the mode light ray is half of the perimeter of the ETR. Mode Q-factors are calculated by the finite-difference time-domain (FDTD) technique and compared with those calculated from far-field emission based on the analytical near-field pattern for TE and TM modes. The results show that the far-field emission based on the analytical field distribution can be used to estimate the mode Q-factor, especially for TM modes. FDTD numerical results also show that Q-factor of TE modes reaches maximum value as the longitudinal mode number is a multiple of 7. In addition, photoluminescence spectra and measured Q-factors are presented for fabricated ETR with side lengths of 20 and 30 mu m, and the mode wavelength intervals are compared with the analytical results.

Plethysms and interacting boson models

A short review of the plethysm technique aiming to its application in finding branching rules for the reduction of an irreducible representation of a group under the restriction to one of its subgroups is given. The algebraic structure of the interacting boson model and some of its extensions is given together with the branching rules needed to classify their basis states, obtained by the use of plethysms. (C) 2003 American Institute of Physics.

Localizability in de Sitter space

An analogue of the Newton-Wigner position operator is defined for a massive neutral scalar field in de Sitter space. The one-particle subspace of the theory, consisting of positive-energy solutions of the Klein-Gordon equation selected by the Hadamard condition, is identified with an irreducible representation of the de Sitter group. Postulates of localizability analogous to those written by Wightman for fields in Minkowski space are formulated on it, and a unique solution is shown to exist. Representations in both the principal and the complementary series are considered. A simple expression for the time evolution of the Newton-Wigner operator is presented.

Multiparameter twisted Weyl algebras

We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras. (C) 2011 Elsevier Inc. All rights reserved.

Coupled Nonlinear Ginzburg-Landau and Mechanics Model for Martensitic Transformations in Polycrystals

Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.

On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.

On the renormalization flow representation of field theory and some applications

In this thesis we discuss a representation of quantum mechanics and quantum and statistical field theory based on a functional renormalization flow equation for the one-particle-irreducible average effective action, and we employ it to get information on some specific systems.