Commutator Representations of Covariant Differential Calculi on Quantum Groups

Let (, d) be a first-order differential *-calculus on a *-algebra . We say that a pair (, F) of a *-representation of on a dense domain of a Hilbert space and a symmetric operator F on gives a commutator representation of if there exists a linear mapping : L( ) such that (adb) = (a)i[F, (b) ], a, b . Among others, it is shown that each left-covariant *-calculus of a compact quantum group Hopf *-algebra has a faithful commutator representation. For a class of bicovariant *-calculi on , there is a commutator representation such that F is the image of a central element of the quantum tangent space. If is the Hopf *-algebra of the compact form of one of the quantum groups SL _q (n+1), O _q (n), Sp _q (2n) with real trancendental q, then this commutator representation is faithful.     

Two-Frequency Mutual Coherence Function of Millimeter Wave in Rain

In this paper, the general formulations of two-frequency mutual coherence function, , for a pulse wave propagating in random discrete media are summarized. The relations of the amplitudes and phases of the to _d are given by Ishimaru et al, based on average particle in cloud and rain. In practice, since the particles sizes in random discrete media are in a size distribution spectrum, the ought to be derived from a particles size distribution. Based on an approximately solution, we describe these examples of millimeter waves (94, 220GHz) pulse propagating in rain and show that the 's amplitudes and phases obvious varies as rainfall and frequency. For a kind of rain, considering raindrops size distribution and average raindrop size, respectively, the 's amplitudes and phases are calculated. The numerical results show that the differences between the results calculated by raindrops size spectrum and by average size are remarkable, especially for heavy rainfall. Therefore, It is shown that the calculated by a particles size distribution is more reasonable than by average size. For the numerical analyses, particles size distribution ought to be adopted. This study is important for us to provide adequate bandwidths to achieve high-rate pulse communications and improve MMW radar system performances and atmospheric remote-sensing techniques.     

Group actions on C*-algebras, 3-cocycles and quantum field theory

We study group extensions , where acts on a C^*-algebraA. Given a twisted covariant representation ,V of the pairA, we construct 3-cocycles on with values in the centre of the group generated byV(). These 3-cocycles are obstructions to the existence of an extension of byV() which acts onA compatibly with . The main theorems of the paper introduce a subsidiary invariant which classifies actions of onV() and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant and the 3-cocycle.     

Pseudo-Jahn-Teller effect in tetragonal local centers

The shape of the light absorption band by a local tetragonal center at the transition _{1 5}(x, y) is investigated in a semiclassical approximation. In addition to interaction with fully-symmetric (₁), Jahn-Teller (₃, ₄) vibrations, inter-action is also taken into account with vibrations ₅, which admix an electron level ₄(z) to the electronic state ₅, which is separated from ₅ by the energetic gap . An analytic computation of the band shape is performed in the first order of the expansion of the form function in ^–1. An asymmetric two-hump band is obtained, where the long-wave maximum always has higher intensity than the shortwave maximum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 62–67, December, 1987.     

Anomaly of the soft-mode damping function near phase-transition points due to interaction with acoustic phonons

An expression is derived for the anomalous part (T, ) of the soft-mode damping function due to third-order interaction between critical optical phonons and acoustic phonons. It is shown that in crystals with a large elastic viscosity the damping function of critical phonons can have stronger temperature anomalies near phase-transition points. The frequency dispersion of () is investigated; it is found that the damping is a maximum at =_o for the soft-mode vibrational dynamics and at =0 for the relaxational dynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–49, March, 1982.     

A General-Relativistic Fermat Principle for Extended Light Sources and Extended Receivers

In an arbitrary Lorentzian manifold, we fix a spacelike submanifold P and a timelike submanifold . We interpret P as (the surface of) a light source at a particular instant of time, and we interpret as the history of (the surface of) a receiver. We prove the following version of Fermat's principle. Among all lightlike curves from P to , the lightlike geodesics which are perpendicular to P and spatially perpendicular to are characterized by stationary arrival time. Here, the arrival time is defined with the help of an arbitrary time function on . Moreover, we show that the second variation of the arrival time at a stationary point is characterized by a Morse index theorem.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Radiative Decay of Vector Meson V → Pγ in the Spinor Strong Interaction Theory

The spinor strong interaction theory recentlydeveloped is applied to the radiative decay of atwo-quark vector meson into pseudoscalar meson V P. Expression of the decay rate isderived in this first-principle theory without assumptionand free parameter. The ratio (D^*0 D⁰)/(D^*+ D⁺) is correctly predicted. Theorders of magnitude of the radiative decay rates of B*,D*, K*, and estimated from this expression areconsistent with data. Very fast mesons have a smallersize then do mesons at rest, similar to Lorentzcontraction in laboratory space.     

Differential algebras for quantum groups of type B, C, and D

We study higher order bicovariant differential calculi on the quantum groups O_q(N) and Sp _q (N). We show that the second antisymmetrizer exterior algebra _u is the quotient of the universal exterior algebra _u by the principal ideal generated by . Here denotes the unique up to scalars biinvariant 1-form. Moreover is central in _u and _u is an inner differential calculus. We show that the quadratic dual to the left-invariant algebra _{s L} is isomorphic to the reflection equation algebra. Let be an arbitrary left-covariant first order differential calculus. We show that the dimension of the space of left-invariant 2-forms in the universal exterior algebra equals the number of linearly independent quadratic-linear relations in the quantum tangent space.     

A Sum Rule for the Two-Dimensional Two-Component Plasma

In a two-dimensional, two-component plasma, the second moment of the density correlation function has the simple value {12[1–(/4)]²}^–1, where is the dimensionless coupling constant. This result is derived by using analogies with critical systems.     

The electronic structure of Rhodium: Angle-resolved studies of photoelectron and secondary electron emission

We report electron spectroscopic studies of the Rh(111) surface, with the aim to obtain bulk band-structure information. We have measured normal photoemision using tunable synchrotron radiation in the range of photon energies between 11 eV and 55 eV, and angle-dependent photoemission along the LUX and LKL azimuths using the He resonance lines (=21.2 eV, 40.8 eV). To complement these data, we studied angleresolved secondary electron emission after excitation with electrons and photons. We derive parts of the one-electron energy dispersionE(k) along L, and determine the energies of several bulk critical points (in eV):E(> ₇₊/₈₊)=–2.75±0.10,E(> ₈₊=–0.85±0.10,E(> _7–=16.1±0.5,E(> _6–/> _8–)=20.5±0.5,E(X ₇₊)=–5.0±0.1,E(L ₆₊)=–5.6±0.5,E(L ₆₊/L ₄₊₊₅₊)=–2.65±0.10,E(L ₆₊)=9.0±0.5 eV. Our results are compared to several available band structure calculations.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Thickness dependence of the spin- and angle-resolved photoemission of ultrathin,epitaxial Ni(111)/W(110) layers

The thickness dependence of the magnetic band structure of ultrathin, epitaxial Ni(111)/W(110) layers has been studied by spin and angle-resolved photoemission spectroscopy. The changes of the spin-resolved photoemission intensities upon reducing the layer thickness depend strongly on the wavevector along the -L line of the Brillouin zone. The measured exchange splitting atk 1/3(-L) andk 1/2(-L) is found to be independent of the layer thickness for layers consisting of 3 or more atomic layers, while decreases rapidly with the layer thickness atk2/3(-L). This behavior is very similar to the temperature dependence of the spin-resolved photoemission spectra of bulk Ni(111) at the samek-points.     

Radiation effects in the production and decay of ψ mesons by leptons

A new expression _e is obtained for resonance in the reaction e⁺e^– ar ^+– with allowance for the radiative corrections, which also contain the emission of hard photons by the final leptons and the final value of the energy resolution E. An expression is obtained for the total probability of radiative lepton decay. A numerical analysis of the experimental data is made for the reaction ^+–, and the parameters e⁺e^– (3, 1) e⁺e^–, and _e ² /, _e, and are determined for (3, 1) resonance-with allowance for the radiative corrections.This paper was read (November 17–21, 1975) at a session on high-energy physics of the Department of Nuclear Physics of the Academy of Sciences of the USSR.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–34, March, 1977.     

Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases

A feature of a conducting phase at low density is that there is a singularity in the fugacity expansion of the pressure, whereas the same expansion in the insulating phase gives an analytic series. The Yang-Lee characterization of a phase transition thus implies that in the conducting phase the zeros of the grand partition function must pinch the real axis in the complex scaled fugacity () plane at =0, whereas in the insulating phase a neighborhood of =0 must be zero free. Exact and numerical calculations are presented which suggest that for two-component log-potential lattice gases in one dimension with dimensionless coupling, the zeros pinch the point =0 for<2, while for2 a neighborhood of =0 is zero free. The conductor-insulator transition therefore takes place at=2 independent of the density and other parameters in the model.     

The magnetic behavior of CeB6: Comparison between elastic and inelastic neutron scattering,initial susceptibility and high-field magnetization

We report measurements of the elastic and inelastic neutron scattering, initial susceptibility and high-field magnetization on thoroughly prepared poly- and single crystalline samples of CeB₆. Part of these experiments have been performed at temperatures down to 60 mK and magnetic fields up to 70 kØe. Our neutron-diffraction data provide the first proof that CeB₆ is an antiferromagnet belowT _N2K as has been suggested by previous bulk experiments. The reduced value of the low-temperature magnetic moment both below and aboveT _N points to the existence of a Kondo effect of the ₇ crystal-field (CF) ground state of Ce³⁺. From the low-temperature width of the quasielastic neutron line, the Kondo temperature is inferred to beT _K3 K. The thermal variation of the initial susceptibility (forT>20K) is semiquantitatively explained invoking, besides the Kondo effect, a ₇- ₈ CF splitting of 70 K and magnetic interactions, which are about 10 times stronger between ₈ states than those between ₇ states. This large ₈- ₈ exchange interaction is also assumed to account for the most striking result of this work, i.e. the lack of any CF-transition peak up to 44 meV in our inelastic neutron-scattering spectra.     

On the decay width of multiply measured unstable state

In the case of multiple measurements we have found that there is nonzero decay width () (even for bound states) and that, for relatively long time intervals separating successive measurements, () tends like ^–k (k 1 according to the investigated model) to the asymptotic value _o for unstable states and to zero for bound states. We have shown that the detector efficiencyZ 1 is responsible for this effect and that the evolution operator acting in the considered subspace of states should be renormalized to avoid this effect. As an illustration we have considered electromagnetic levels in the Coulomb field as an example of unstable states.     

Higher order differential calculus on SL q(N)

Let be a bicovariant first order differential calculus on a Hopf algebra . There are three possibilities to construct a differential N ₀-graded Hopf algebra which contains as its first order part. In all cases is a quotient = /J of the tensor algebra by some suitable ideal. We distinguish three possible choices _u J, _s J, and _W J, where the first one generates the universal differential calculus (over ) and the last one is Woronowicz' external algebra. Let q be a transcendental complex number and let be one of the N ²-dimensional bicovariant first order differential calculi on the quantum group SL _q(N). Then for N 3 the three ideals coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant k-forms. In this case each bi-invariant form is closed. In case of 4D _± calculi on SL _q(2) the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed.     

From monotonic to oscillatory decay of correlations: Analytical approximation for the two-dimensional,one-component plasma

An approximate evaluation of the pair distribution and the structure factor is performed analytically for the two-dimensional, one-component plasma at any value of the coupling constant. The approximate distribution remains positive and satisfies three sum rules, including the compressibility one. When 0 or 2, exact results are found. At=2 the transition from monotonie (<2) to oscillatory (>2) decay of correlations takes place. Comparison with the Monte Carlo simulations shows good agreement for 0<<4.     

Conversion of hyperons in nuclear matter

The width of the N N conversion for hyperons in nuclear matter is calculated on the basis of the one-boson exchange model. It turns out that there is a substantial compensation of the contributions of different mesons to the conversion amplitude. As a result, is reduced by roughly a factor of two as compared to the value from the exchange of only a pion. Without taking the Pauli principle into account, we obtain = 15–25 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–7, December 1983.