Symmetric bifurcations and phenomena of polarization symmetry breaking in a single-mode gas laser

An analysis is carried out of the optical cavities whose natural modes have the form of Gaussian beams with complex astigmatism. In the case of coincident eigenvalues of the cavity ray matrix, the wave beams were found to be determined not only by the geometrical optics characteristics of a cavity, but also by additional cavity-independent parameters. A detailed analysis is given for the fundamental mode of such cavities. Concrete cavities possessing these properties are noted.     

Broken colour symmetry and liberated quarks

We present and discuss a quark model of hadrons, in which local SU(3) gauge symmetry is completely broken and yet asymptotic freedom is presented. There is no infrared slavery in this model, and isolated quarks are free to exist. Colour becomes a global symmetry which is only approximate under SU(3) but nearly exact under SU(2) × U(1), as far as the usual hadron spectroscopy is concerned.     

Broken conformal symmetry and hadronic scaling

High energy, large momentum transfer hadronic reactions are studied in the framework of broken conformal symmetry. Hadrons lie on almost linear Regge trajectories. Inclusive cross section scale as $\text{～s}{}^{\mathrm{?2}}\text{(}\text{q}{}^2{}_{\mathrm{<mtext>T</mtext>}}\text{s)}{}^{\mathrm{?4}}$. Large rates of heavy particle production are predicted.     

Broken quantum symmetry and confinement phases in planar physics

Many two-dimensional physical systems have symmetries which are mathematically described by quantum groups (quasitriangular Hopf algebras). In this Letter we introduce the concept of a spontaneously broken Hopf symmetry and show that it provides an effective tool for analyzing a wide variety of phases exhibiting many distinct confinement phenomena.     

Theory of polarization phenomena in the hyper-Raman effect

This paper describes a general theory of the polarization state of hyper-Raman emission. In particular an examination is made of the azimuth and ellipticity of hyper-Raman scattered radiation relative to that of a general elliptically polarized source.

It is shown that a distinction may be made between infra-red active and inactive vibrations in the hyper-Raman effect by an analysis of the ellipticity of the scattered light. For a circularly polarized source, the scattering from infra-red inactive vibrations exhibits full reversal of circularity; infra-red active vibrations scatter with no change in circularity. In hyper-Rayleigh scattering a similar analysis is given for non-polar and polar molecules.     

Simple kinetic model of symmetry breaking

We consider a dynamical system described by a set of random variablesN| _i(t) and depending on a parameterR controlling its stability. IfR < R _c the system is stable and theN _i have some symmetry properties in the statistical sense (i.e., with respect to time averaging). IfR > R _c the system is unstable and the nonlinear dynamics of theN _i may lead to an asymptotic stationary state which does not possess the symmetries of the stable system. We show that the dynamics of symmetry breaking resembles a phase transition in the limit of many variables.     

Thermal expansion and kinetic coefficients of crystals

Electrical (ρ) and thermal (W) resistivities and thermal expansion coefficient (β) of Cu, Zn, Al, Pb, Ni, β-brass, Al₂O₃, NaCl, Si, SiO₂(∥), and SiO₂(⊥) were simultaneously measured with standard four-probe, absolute steady-state, and quartz dilatometer techniques. Measurements of Ni and β-brass were performed at temperatures from 300 to 1100 K and measurements of all other samples were made between 90 and 500 K. This temperature range includes the range below and above the Debye temperature (T_D). The total uncertainties of the specific electrical and thermal resistivities and thermal expansion coefficient (TEC) measurements are 0.5%, 3.0%, and (1.5-4.0%), respectively. The universal linear relationship between the electrical and thermal resistivities and βΤ over the wide temperature range was found experimentally. Using the Landau criterion for convection development for ideal phonon and electron gases in the solids, the universal relations, ρ^ph/ρ^*≡βT and W^ph/W^*≡βT (where ρ^ph is the phonon electrical resistivity, is the characteristic electrical resistivity, W^ph is the phonon thermal resistivity, and W^*=k_BG/qc_p is the characteristic thermal resistivity) between relative phonon electrical and phonon thermal resistivities and βΤ were derived. The derived universal relations provide a new method for estimating the kinetic coefficients (electrical and thermal resistivities) from TEC measurements.     

Calculation of the spin-lattice coupling coefficients in cubic symmetry

The relationships between spin-lattice coupling coefficients G₁₁, G₄₄ in cubic symmetry and the zero-field splittings in low symmetry have been put forward and hence the simple methods of calculating these coefficients from the formulae of zero-field splittings are given. According to these, the coefficient G₄₄ can be obtained very easily from two cases, one from the derivative of zero-field splitting D in trigonal symmetry with respect to the bonding angle β and another from the derivative of splitting E in rhombic symmetry with respect to the angle θ. So, one can, in a certain degree, check whether the formulae of D in trigonal field and E in rhombic field based on different mechanisms and models are consistent and reliable by comparing the formulae of G₄₄ obtained from the two cases.     

Tensor interactions and polarization phenomena in heavy-ion scattering

Elastic and inelastic scattering of ⁷Li by ⁵⁸Ni at E_lab = 14.2 and 20.3 MeV is investigated theoretically, special emphasis being laid on polarization phenomena. A parameter-independent study shows second-rank tensor interactions to be the main origin of tensor analyzing powers for both elastic and inelastic scattering. Coupled-channel (CC) calculations using cluster-folding interactions which include the tensor terms are found to be successful in reproducing the data for cross sections and vector and tensor analyzing powers, when projectile excitation effects are sufficiently taken into account. Scattering of ⁶Li by ⁵⁸Ni at E_lab = 20.0 MeV is also investigated by the CC calculation, where successes similar to the ⁷Li case are obtained in understanding experimental data.     

Broken time‐reversal symmetry scattering at the Anderson transition

We study numerically the statistical properties of some scattering quantities for the Power‐law Banded Random Matrix model at criticality in the absence of time‐reversal symmetry, with a small number of single‐channel leads attached to it. We focus on the average scattering matrix elements, the conductance probability distribution, and the shot noise power as a function of the effective bandwidth b of the model. We find a smooth transition from insulating‐ to metallic‐like behavior in the scattering properties of the model by increasing b. We contrast our results with existing random matrix theory predictions.     

Deformation dependence of symmetry energy coefficients of nuclei

Based on the semi-classical Thomas-Fermi approximation together with the Skyrme energy-density functional, we study the deformation dependence of symmetry energy coefficients of finite nuclei. The symmetry energy coefficients of nuclei with mass number A = 40, 100, 150, 208 are extracted from two-parameter parabola fitting to the calculated energy per particle. We find that the symmetry energy coefficients decrease with the increase of nuclear quadrupole deformations, which is mainly due to the isospin dependence of the difference between the proton and neutron surface diffuseness. Large deformations of nuclei can cause the change of the symmetry energy coefficient by about 0.5 Me V and the influence of nuclear deformations on the symmetry energy coefficients is more evident for light and intermediate nuclei.     

Investigation of covariant properties and symmetry of kinetic equations

A group of transformations is found, relative to which linear hyperparabolic equations are covariant. Differential operators of first-order symmetry are constructed, and are used to separate the variables in some particular cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 46–52, December, 1976.     

Broken spin symmetry approach to chemical reactivity and magnetism of graphenium species

The basic problem of weak interaction between odd electrons in graphene and silicene is considered in the framework of the broken spin symmetry approach. This approach exhibits the peculiarities of the odd-electron behavior via both enhanced chemical reactivity and magnetism.     

Comment on symmetry properties of the linear Enskog kinetic operators

The one-particle average consistent with the structure of the revised Enskog theory is introduced. Symmetry properties of the linear kinetic operators reflecting those of theN-particle pseudo-Liouville operators are derived, implying a recently proved symmetry of kinetic expressions for equilibrium time correlation functions.     

Spatial-temporal dispersion of the kinetic coefficients near the Anderson transition

A generalization of the Vollhardt-Wölfle localization theory is proposed to make it possible to study the spatial-temporal dispersion of the kinetic coefficients of a d-dimensional disordered system in the low-frequency, long-wavelength range (ω?_F and q?k _F ). It is shown that the critical behavior of the generalized diffusion coefficient D(q,ω) near the Anderson transition agrees with the general Berezinskii-Gor’kov localization criterion. More precisely, on the metallic side of the transition the static diffusion coefficient D(q,0) vanishes at a mobility threshold λ _c common for all q: D(q, 0)∝t=(λ _c ?λ)/λ _c →0, where λ=1/(2π?_F τ) is a dimensionless coupling constant. On the insulator side, q≠0 D(q,ω)∝?iω as ω→0 for all finite q. Within these limits, the scale of the spatial dispersion of D(q,ω) decreases in proportion to t in the metallic phase and in proportion to ωξ ², where ξ is the localization length, in the insulator phase until it reaches its lower limit ～λ _F. The suppression of the spatial dispersion of D(q,ω) near the Anderson transition up to the atomic scale confirms the asymptotic validity of the Vollhardt-Wölfle approximation: D(q,ω)?D(ω) as |t|→0 and ω→0. By contrast, the scale of the spatial dispersion of the electrical conductivity in the insulator phase is of order of the localization length and diverges in proportion to |t|^?v as |t|→0.     

Theory of spin polarization phenomena in atomic and molecular photoeffects

A compact invariant expression for the angular distribution of photoelectrons formed as a result of photoionization of axisymmetrically polarized atoms and molecules, including optically active molecules, is derived from the general symmetry considerations and using a recently developed bipolar harmonic reduction technique. In the angular distribution of photoelectrons, as well as in the total photoionization cross section, the dependence on all the geometric parameters is separated completely. The polarization of ionizing radiation can be arbitrary, with the partial polarization being specified by the Stokes parameters. The expression for the angular distribution of photoelectrons escaping from an atomic-molecular system oriented in the first order also determines the structure of the expression for the photoionization cross section of an unpolarized system with allowance for the spin polarization of a photoelectron or a photoion with the spin 1/2. The roles played by circular dichroism, chirality, etc., in the process of photoionization of oriented and aligned systems are analyzed in detail.     

Electrode kinetic phenomena of solid state ionic devices

With the development of functional materials with high ionic and combined ionicelectronic conductivity, the engineering of interfaces became prerequisite. Technological applications demand combinations of materials with different electrical properties to form junctions. The occurring kinetic electrode phenomena play a significant role to the overall performance and may be rate determining. We show here the significance of the equilibration between platinum and the solid electrolyte with respect to the response time in potentiometric oxygen sensors. Fundamental aspects of voltage generation are discussed as well, and the response time is correlated to the equilibration along the contact zone between platinum and the electrolyte. A common problem of potentiometric devices for gas sensing applications is the cross sensitivity to species other than those under detection. The proposed kinetic method based on the theta concept is investigated for selective detection in the presence of a multiple number of complex gases by employing a single electrochemical cell. Information from current-voltage plots is converted to generate complex plane plot for the Fourier coefficients. The various polarizations under the applied electric perturbation are modelled and compared to experimental data for the determination of the rate determining processes.