Universal deformations of reductive Lie algebras

We construct multiparameter quantizations of reductive Lie algebras which have the property of universality within a certain class of deformations. The universal deformations can be defined so that the algebra structure on each simple component is the same as that of the standard one-parameter quantization, the remaining parameters being relegated to the coalgebra structure. We discuss an example in which only the latter parameters appear, as a special case of deformations of a semisimple algebra whose simple components remain classical. Deformations are defined as algebras over power series rings and it is essential to require them to be torsion free to secure the universality. The Poincaré-Birkhoff-Witt theorem and the torsion freeness are established for the universal deformation on the basis of results on the representation theory of the deformed algebras.     

QFT on homothetic Killing twist deformed curved spacetimes

We study the quantum field theory (QFT) of a free, real, massless and curvature coupled scalar field on self-similar symmetric spacetimes, which are deformed by an abelian Drinfel’d twist constructed from a Killing and a homothetic Killing vector field. In contrast to deformations solely by Killing vector fields, such as the Moyal-Weyl Minkowski spacetime, the equation of motion and Green’s operators are deformed. We show that there is a *-algebra isomorphism between the QFT on the deformed and the formal power series extension of the QFT on the undeformed spacetime. We study the convergent implementation of our deformations for toy-models. For these models it is found that there is a *-isomorphism between the deformed Weyl algebra and a reduced undeformed Weyl algebra, where certain strongly localized observables are excluded. Thus, our models realize the intuitive physical picture that noncommutative geometry prevents arbitrary localization in spacetime.     

Quasi-Hopf Deformations of Quantum Groups

The search for elliptic quantum groups leads to a modified quantum Yang–Baxter relation and to a special class of quasi-triangular quasi-Hopf algebras. This Letter calculates deformations of standard quantum groups (with or without spectral parameter) in the category of quasi-Hopf algebras. An earlier investigation of the deformations of quantum groups, in the category of Hopf algebras, showed that quantum groups are generically rigid: Hopf algebra deformations exist only under some restrictions on the parameters. In particular, affine Kac–Moody algebras are more rigid than their loop algebra quotients and only the latter (in the case of sl(n)) can be deformed to elliptic Hopf algebras. The generalization to quasi-Hopf deformations lifts this restriction. The full elliptic quantum groups (with central extension) associated with sl(n) are thus quasi-Hopf algebras. The universal R-matrices satisfy a modified Yang–Baxter relation and are calculated more or less explicitly. The modified classical Yang–Baxter relation is obtained and the elliptic solutions are worked out explicitly.The same method is used to construct the Universal R-matrices associated with Felder's quantization of the Knizhnik–Zamolodchikov–Bernard equation, to throw some light on the quasi-Hopf structure of conformal field theory and (perhaps) the Calogero–Moser models.     

Directional emission from weakly eccentric resonators

It is shown that when a circular resonator is deformed in a nonintegrable way, a symmetry breaking of escaping rays occurs which can dramatically modulate the outgoing wave even for small perturbations. The underlying mechanism does not occur in integrable models for which the ray families can be computed exactly and is described in this Letter on the basis of canonical perturbation theory. Emission from deformed resonators is currently of immense practical interest in the context of whispering-gallery optical resonances of dielectric cavities, and the approach outlined here promises simple analytical characterizations in the important case of small deformations.     

Kolmogorov-Arnold-Moser transition and laser action on scar modes in semiconductor diode lasers with deformed resonators

Measurements of the optical spectra of semiconductor injection lasers with deformed cylinder resonators show strong indications of the classical Kolmogorov-Arnold-Moser transition from integrability to chaos for devices with small deformation. At larger deformation, evidence for laser action on scar modes is obtained. The diode lasers operate with TE polarization, resulting in laser action on (partially) chaotic whispering-gallery modes for all deformations.     

Semiclassical interpretation of the gross-shell structure in deformed nuclei

An analysis of the classical closed orbits in the infinitely deep elongated ellipsoidal well is given with respect to their relevance to the gross-shell structure of the single-particle spectra in deformed nuclei. It is shown that the deformed-shape gross-shells responsible for the ground state deformations, as well as those responsible for the fission intermediate states, find a reasonable explanation in terms of the semiclassical three-dimensional quantization involving the planar orbits in the axis-of-symmetry plane and the simplest three-dimensional orbits which appear at large distortions. The former are found important for the ground state shapes. The results are also compared with the harmonic oscillator model.     

Speckle interferometry for measurement of continuous deformations

Improvements of a method for measurement of continuous displacements and deformations with digital phase shifting speckle pattern interferometry are presented. The method is based on an algorithm that, with the knowledge of the initial phase, only needs one image at a time to evaluate continuos phase changes due to object deformations. In the improved method, the initial random phase of the speckle pattern is evaluated using a number of phase-shifted images before the deformation under study. This is used for increasing the accuracy of the initial phase estimation and reducing influences from image noise and other measurement disturbances. The phase-shifted speckle patterns are used as references for comparison with the speckle patterns of the deformed object, thereby increasing the reliability and accuracy of the phase estimations of the deformed patterns. The technique can be used for measuring deformations such as transients and other dynamic events, heat expansion as well as other phenomena where it is difficult to accomplish phase shifting during deformation.     

Minimal parabolic quantum groups in twist deformations

Study of parabolic twist deformations in the exponential coordinates faces serious difficulties. We demonstrate how to deal with this problem using the dual-group approach. The properties of the deformed symmetries can be easily disclosed when the deformed costructure is formulated in the dual-group terms.     

Embedded random matrix ensembles for complexity and chaos in finite interacting particle systems

Universal properties of simple quantum systems whose classical counter parts are chaotic, are modeled by the classical random matrix ensembles and their interpolations/deformations. However for finite interacting many-particle systems such as atoms, molecules, nuclei and mesoscopic systems (atomic clusters, helium droplets, quantum dots, etc.) for wider range of phenomena, it is essential to include information such as particle number, number of single-particle orbits, lower particle rank of the interaction, etc. These considerations led to resurgence of interest in investigating in detail the so-called embedded random matrix ensembles and their various deformed versions. Besides giving a overview of the basic results of embedded ensembles for the smoothed state densities and transition matrix elements, recent progress in investigating these ensembles with various deformations, for deriving a statistical mechanics (with relationships between quantum chaos, thermalization, phase transitions and Fock space localization, etc.) for isolated finite systems with few particles is briefly discussed. These results constitute new progress in deriving a basis for statistical spectroscopy (introduced and applied in nuclear structure physics and more recently in atomic physics) and its domains of applicability.     

Partial α-decay half-lives of ground to ground and ground to excited states of Thorium family

Partial half-lives and Q-values of allowed α-decay for Thorium family are evaluated by using the WKB approximation. In order to calculate the partial half-lives, transition probabilities from ground to ground and ground to excited states of daughter nuclei are obtained. The α-decay potential barrier includes deformed volume, surface, and Coulomb parts in the deformed liquid drop model (DLDM), deformed Woods-Saxon nuclear potential and centrifugal term. The quadrupole and the hexadecapole deformations are considered in the calculations. Calculated half-lives are compared to the results of other theoretical models as well as experimental data. Comparison of the present study and other theoretical methods with experimental data indicated that the predicted half-lives using current approach are well agreed with the experimental data than results of UMADAC and CPPMDN theoretical models. Moreover, the evaluated half-lives correspond well with the Geiger-Nuttall empirical formula.     

Shell phenomena in mesoscopic systems: From nuclei to quantum dots

The evolution of shape parameters and giant dipole and octupole resonances in rotating nuclei, the role of main classical orbits for deformed systems with octupole and hexadecapole deformations, the occurence of magic numbers under a perpendicular magnetic field in small quantum dots are discussed from the point of view of the manifestation of shell effects in a finite Fermi system. Presented by R.G. Nazmitdinov at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Angular quantization and form factors in massive integrable models

We discuss an application of the method of angular quantization to the reconstruction of form factors of local fields in massive integrable models. The general formalism is illustrated with examples of the Klein-Gordon, sinh-Gordon and Bullough-Dodd models. For the latter two models the angular quantization approach makes it possible to obtain free field representations for form factors of exponential operators. We discuss an intriguing relation between the free field representations and deformations of the Virasoro algebra. The deformation associated with the Bullough-Dodd models appears to be different from the known deformed Virasoro algebra.     

Calculation of nuclear rotational energies

Rotational energies are calculated for nuclei in the deformed regions both at the ground state and at very high deformations. The single-particle Hamiltonian includes both quadrupole and hexadecapole deformations.     

变形碳纳米管的研究

给出了一些用透射电子显微镜观察到的变形碳纳米管结果，它们在形态上可以分为径向形变和轴向形变两类．这种在氩气氛电弧放电阴极沉积物中生成的变形纳米管，可以用我们建议的模型定性地加以解释 关键词：     

Light nuclei near neutron and proton drip lines in relativistic mean-field theory

We have made a detailed study of the ground-state properties of nuclei in the light-mass region with atomic numbers Z = 10–22 in the framework of the relativistic mean-field (RMF) theory. The nonlinear σω model with scalar self-interaction has been employed. The RMF calculations have been performed in an axially deformed configuration using the force NL-SH. We have considered nuclei about the stability line as well as those close to proton and neutron drip lines. It is shown that the RMF results provide good agreement with the available empirical data. The RMF predictions also show reasonably good agreement with those of the mass models. It is observed that nuclei in this mass region are found to possess strong deformations and exhibit shape changes all along the isotopic chains. The phenomenon of shape coexistence is found to persist near the stability line as well as near the drip lines. It is shown that the magic number N = 28 is quenched strongly, thus enabling the corresponding nuclei to assume strong deformations. Nuclei near the neutron and proton drip lines in this region are also shown to be strongly deformed.     

Classical simulations of heavy-ion fusion reactions and weakly-bound projectile breakup reactions

Heavy-ion collision simulations in various classical models are discussed. Heavy-ion reactions with spherical and deformed nuclei are simulated in a classical rigid-body dynamics (CRBD) model which takes into account the reorientation of the deformed projectile. It is found that the barrier parameters not only on the initial orientations of the deformed nucleus, but also on the collision energy and the moment of inertia of the deformed nucleus. Maximum reorientation effect occurs at near- and below-barrier energies for light deformed nuclei. Calculated fusion cross-sections for ²⁴Mg + ²⁰⁸Pb reaction are compared with a static-barrier-penetration model (SBPM) calculation to see the effect of reorientation. Heavy-ion reactions are also simulated in a 3-stage classical molecular dynamics (3S-CMD) model in which the rigid-body constraints are relaxed when the two nuclei are close to the barrier thus, taking into account all the rotational and vibrational degrees of freedom in the same calculation. This model is extended to simulate heavy-ion reactions such as⁶Li + ²⁰⁹Bi involving the weakly-bound projectile considered as a weakly-bound cluster of deuteron and ⁴He nuclei, thus, simulating a 3-body system in 3S-CMD model. All the essential features of breakup reactions, such as complete fusion, incomplete fusion, no-capture breakup and scattering are demonstrated.     

Neutron component deformations,folding models and Satchler's theorem

The identity, proved by Satchler, between a folded quadrupole moment and the underlying nuclear quadrupole moment has been exploited in order to survey deformed optical model and folding model calculations. We find reasonable agreement for light nuclei between e.m. and nuclear deformations, and for heavy nuclei the following alternative holds: either the folding model for nucleons breaks down in a manner not understood, or, heavy nuclei have much greater deformations of the proton component than of the neutron component for the hexadecapole degree of freedom. In addition we show that α-particle folding models appear to break down completely for heavier nuclei.     

Thermodynamic stability of the structure of a deformed Fe-C solid solution

An analysis is made of the thermodynamic stability of the dislocation structure in polycrystalline samples of Fe-C, deformed under conditions of high rates and hydrostatic pressures, based on experimental and theoretical data concerning the internal energy and on diffractometer measurements of the broadening of x-ray lines. The method of deformation calorimetry was used to determine the internal energy in a wide range of deformations. A theoretical model is proposed for estimating the change in internal energy in deformed alloys. An investigation is made of the dependence of the interdislocation interaction parameter on the deformation rate for different stressed state-schemes and large plastic deformations. It is shown that the relative quantity δU/A is correlated in a wide range of deformations with the relative root-mean-square distortions of the crystal lattice of the deformed solid solution. The mechanisms for the accumulation of energy in deformed solid solutions having a body-centered cubic lattice are considered. Don State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 77–83.     

Modified Smoothed Particle Hydrodynamics (MSPH) basis functions for meshless methods,and their application to axisymmetric Taylor impact test

The Modified Smoothed Particle Hydrodynamics (MSPH) method proposed earlier by the authors and applied to the analysis of transient two-dimensional (2-D) heat conduction, 1-D transient simple shearing deformations of a thermoviscoplastic material, 1-D wave propagation in a functionally graded plate, and 2-D elastodynamic crack propagation is extended to the analysis of axisymmetric deformations of a thermoviscoplastic material. In the MSPH method, different shape functions are used to find kernel estimates of the function, and of its first and second derivatives. It differs from the classical finite element method in which derivatives of a function are usually obtained by differentiating the shape function used to approximate the function. It is shown that results computed with the MSPH method for the Noh problem agree well with its analytical solution. The MSPH basis functions can be used in any meshless method to numerically solve either static or dynamic problems. The method is then applied to analyze transient deformations of a cylindrical rod impacting at normal incidence a rigid smooth stationary flat plate. The computed solution is found to agree very well with those obtained by analyzing axisymmetric and 3-D transient deformations of the rod with the commercial code LS-DYNA. The final length of the deformed rod, the final radius of the impacted face, and the final length of the relatively undeformed portion of the rod for twelve test configurations computed with the MSPH method are also found to agree well with their corresponding experimental values.     

Octupole Deformations of Even-Even Rn,Th, and U Nuclei in Relativistic Mean Field Theory

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field （RAS-RMF） model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from neaxly-spherical （N = 130） shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only^222,224 Rn axe oetupole deformed and the octupole deformations for them are small. However, more nuclei （N ≌ 134 148） in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant （｜β3｜- 0.1 or even larger）.