New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes

A new infinite series of Einstein metrics is constructed explicitly on S²×S³, and the non-trivial S³-bundle over S², containing infinite numbers of inhomogeneous ones. They appear as a certain limit of 5-dimensional AdS Kerr black holes. In the special case, the metrics reduce to the homogeneous Einstein metrics studied by Wang and Ziller. We also construct an inhomogeneous Einstein metric on the non-trivial S^d–2-bundle over S² from a d-dimensional AdS Kerr black hole. Our construction is a higher dimensional version of the method of Page, which gave an inhomogeneous Einstein metric on      

Universal Teichmüller Space and DiffS 1/S 1

We point out that the coset space DiffS ¹/S ¹ is a dense complex submanifold of the Universal Teichmüller SpaceS of compact Riemann spaces of genus g1. A holomorphic map ofS into the inifinite dimensional Segal diskD ₁ is constructed. This is the Universal analogue of the map of Teichmüller spaces into the Siegel disk provided by the period matrix. The Kähler potential for the general homogenous metric on DiffS ¹/S ¹ is computed explicitly using the map intoD ₁. Some applications to string theory are discussed.This work was supported in part by the U.S. Department of Energy Contract No. DE-AC02-76ER13065     

Simplification of the Hamilton-Jacobi functional of general relativity

In follow-up of an earlier paper by Komar it is shown that the Lagrangian of general relativity can be chosen so thatS=p ^mng_mnd³x. This result holds without the requirement of special boundary conditions.Supported in part by the U.S. Air Force under Grant No. AF-AFOSR 68-1524 to Yeshiva University and Contract No. ARL F 33615-70-C-1110 to Syracuse University.     

Collisional redistribution of energy in the infrared spectrum of potassium vapor under two-photon excitation

The cascade decay of the 6S(4D) levels of the potassium atom, 6S(4D)-5P-5S(3D)-4P, following two-photon excitation of potassium vapor (4S-4P-6S) is investigated experimentally. The dependences of 11 resonant IR line intensities on potassium and buffer gas densities are presented. It is shown that the presence of buffer gas leads to collisional redistribution of radiation, causing suppression of some lines and production of new ones.     

Induced emission from a sodium Rydberg atom in a microwave cavity

Results are presented from an experiment on the observation of an induced microwave transition 37P-37S in sodium Rydberg atoms under the action of 30 thermal photons in a microwave cavity. The measured value of the transition rate (4±1.5)×10⁴ s⁻¹ agrees with the calculated value. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 413–416 (25 March 1999)     

Calculation of the minimum scattering field of an arbitrary antenna by its directivity pattern

A rigorous statistically closed expression has been obtained to calculate the elements of the polarization scattering matrix S _p which describes the quadratically minimum scattering field of an arbitrary passive matched antenna. The elements S _p are analytically expressed only through the complex vector pattern of the antenna.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 8, pp. 1026–1035, August, 1996.     

On the solution of some vertex models using factorizableS matrices

The intimate connection between factorizableS matrices and some vertex models in two dimensions (to be reviewed here) is exploited to show that the knowledge of theS matrix not only allows us to define a solvable vertex modelá la Zamolodchikov, but often to write down the free energy by inspection. The prototype for discussion is Baxter's eight-vertex model generated by Zamolodchikov's Z₄ S matrix. The method is then applied to a hitherto unsolved 19-vertex model, based on the isospin-1S matrix of Zamolidchikov and Fateev, and agreement is checked to fourth order in a perturbation series. The possibility of molding other problems like theq-state Potts model into this framework is considered.Research supported in part by NSF grant No. INT 8117361.     

Different mechanisms of nucleation and self-organization of droplets in ferroelectric smectic membranes

New mechanisms of droplet nucleation and self-organization in ferroelectric membranes are described. The droplets may be accompanied by different number of topological defects (zero, one, two) whose location may be on the droplet boundary or in the membrane. Nucleation and self-organization of droplets with total topological charge S = 0 , S = + 1 and S = - 1 were investigated. We found that an S = - 1 topological defect may be the center of both droplet nucleation and chain formation. This mechanism of chaining drastically differs from the droplet self-organization described earlier which is realized by attraction of droplet-defect pairs. Our observations demonstrate new possibilities for manipulating the inclusions and their self-organization in smectic membranes.     

Differential entropy and tiling

This paper relates the differential entropy of a sufficiently nice probability density functionp on Euclideann-space to the problem of tilingn-space by the translates of a given compact symmetric convex setS with nonempty interior. The relationship occurs via the concept of the epsilon entropy ofn-space under the norm induced byS, with probability induced byp. An expression is obtained for this entropy as approaches 0, which equals the differential entropy ofp, plusn times the logarithm of 2/, plus the logarithm of the reciprocal of the volume ofS, plus a constantC(S) depending only onS, plus a term approaching zero with. The constantC(S) is called the entropic packing constant ofS; the main results of the paper concern this constant. It is shown thatC(S) is between 0 and 1; furthermore,C(S) is zero if and only if translates ofS tile all ofn-space.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Photochemistry of thiophene‐S‐oxide derivatives

Photolysis of substituted thiophene‐S‐oxides in solution results in the formation of either the corresponding thiophene or furan, in addition to uncharacterized materials. No good rationalization is available for the choice of which pathway may predominate, but it is demonstrated that the photolysis of 2,5‐bistrimethylsilylthiopene‐ S‐oxide produces O(³P) in the same manner as the well‐established photolysis of dibenzothiophene‐S‐oxide. Copyright © 2008 John Wiley & Sons, Ltd.     

A Finitely Additive State Criterion for the Completeness of Inner Product Spaces

We show that an inner product space S (real, complex or quaternion) is complete if, and only if, the system of all orthogonally closed subspaces in S, denoted by F(S), admits at least one finitely additive state which is not vanishing on the set of all finite dimensional subspaces of S. Although it gives only a partial solution to the problem formulated by Pták on the existence of a finitely additive state on F(S) for incomplete S, this gives an important insight into the structure of the set of states on F(S). This criterion has no analogue whatsoever in E(S), the system of splitting subspaces of S.     

The effect of the electric field on the spectral line shape

The effect of the external electric field on the spectral line shape under conditions of a uniform population of magnetic sublevels is studied in the density matrix formalism. The line shapes of spontaneous radiation for the atomic 4¹P₁-2¹S₀, 4³D₁-2³P₀, 4³S₁-2³P₀, 4³P₁-2³S₁, 4³D₁-2³P₁, and 4³S₁-2³P₁ transitions ofHe are calculated. The electric field is shown to be responsible for the spectral line shape asymmetry. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 23–28, November, 1999.     

A spin-3/2 Ising model on a square lattice

The spin-3/2 Ising model described by the most general Hamiltonian with up-down symmetry, −βH=Σ_〈ij〉{JS _i S _j +KS ₂ ⁱ S ₂ ^j +LS ₃ ⁱ S ₃ ^j +M/2(S _i S ₃ ^j +S _j S ₃ ⁱ )}−ΔΣ_i S ₂ ⁱ , is investigated on a square lattice. It is shown that this model is reducible to an eight-vertex model on a surface in the parameter space spanned by the coupling constants J, K, L, and M. It is shown that this model is equivalent to an exactly solvable free fermion model along two lines in the parameter space. Consequently, the critical behavior and, in particular, the critical temperature for the second-order phase transitions of the model is found exactly. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 270–275 (25 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Quantum theory of particles with spin zero and one half in external fields

The unitary (pseudo unitary) time-evolution operator for a particle with spin half (zero) in an external time-dependent electromagnetic (scalar) field is used to generate a Bogoliubov automorphism on the algebra of the free in field. For the case of an electric external field (scalar field) a finite expression for _out is given and theS-matrix constructed. The latter is unitary and implements the Bogoliubov automorphism. Theorems by Shale and Stinespring are rederived.Supported in part by the U.S. Atomic Energy Commission under Contract No. AT-30-1-3829.     

Resonance behavior of a K S K S system near the mass 1775 MeV

The preliminary results of an investigation of a system of two K _S mesons in the mass interval 1600–1950 MeV are reported. The events were obtained on a 6-m magnetic spark spectrometer at ITEP in π ⁻ p interactions at 40 GeV, using a neutral trigger which suppressed both charged particles and γ rays. A peak of width ≃30 MeV with statistical significance not lower than six standard deviations is observed with momentum transfer selection |tu|0.23 GeV² near the mass 1775 MeV of the K _S K _S system. The observed phenomena can be interpreted as the existence of one resonance with the indicated parameters, or two narrower resonances. In the latter case, their masses are 1768±1.5 and 1787±1.5 MeV. The widths of these states are comparable to the mass resolution of the spectrometer (∼5 MeV). Estimates of the product σ ⋅BR(K _S K _S ) give ∼1.5 and 2.5 nb, respectively, for the first and second states. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 727–731 (25 November 1998)     

EPR Investigations on Molecular Orientation of Paramagnetic Liquid Crystals in a Surface-Stabilized Liquid Crystal Cell: Studies on a Smectic C or Chiral Smectic C Phase

By electron paramagnetic resonance spectroscopy we investigated the molecular orientation in a surface-stabilized liquid crystal (LC) cell, which includes a racemic (±) or an enantiomerically enriched (S,S) paramagnetic LC, (2S,5S)-2,5-dimethyl-2-tridecyloxyphenyl-5-[4-(4-tridecyloxy-benzenecarbonyloxy)phenyl]pyrrolidine-1-oxy (2), whose spin source is fixed inside the rigid core. For both the smectic C (SmC) phase of (±)-2 and the chiral smectic C (SmC^*) phase of (S,S)-2 in a surface-stabilized LC cell (antiparallel configuration, thickness of 4 μm), the profile of the observed g-value as a function of the angle between the applied magnetic field and the cell plane could be explained by the orientation model, where, with some disordering, the molecules align uniformly with the direction which tilts from the normal line of the smectic layer being orthogonal to the rubbing direction on the cell surface. We divided the effect from the disordering into two parts, one of which is concerning the direction of the molecular long axis and the other is concerning the rotation around the molecular long axis. As a result of the analysis, the SmC^* phase gave quite lower ordering concerning the direction of the molecular long axis and a little lower ordering concerning the rotation around the molecular long axis than the SmC phase at the same temperature (80 °C). The obtained lower ordering in the SmC^* phase is probably due to the chirality that would result in the formation of a helical superstructure in a bulky state. Authors' address: Yohei Noda, Laboratory of Electron Spin Chemistry, Department of Chemistry, Graduate School of Science, Kyoto University, 606-8502 Kyoto, Japan     

Exact solution of the multichannel Kondo problem,scaling, and integrability

In this work we give the exact solution of the model describing the scattering of conduction electrons by an impurity in the orbital singlet state (so-calledn- channel Kondo problem). Depending on the relation between the impurity spinS and the number of electron scattering channelsn, the model behaves differently at low energies. At 2S the effective charge increases to infinity at low energies, whereas atn > 2S it tends to a finite fixed point. The model under study is the first example of the one-dimensional quantum field theory exhibiting scaling behavior.     

On the prosaic origin of the double poles in the sine-GordonS-matrix

We show that the apparently exotic double poles in the sine-GordonS-matrix are nothing but ordinary anomalous thresholds.This research was supported in part by the National Science Foundation under Grant No. PHY77-22864Max Kade Foundation Fellow. On leave of absence from the Institut für Theoretische Physik, Freie Universität Berlin, Federal Republic of Germany     

Decay-mode independent searches for new scalar bosons with the OPAL detector at LEP

This paper describes topological searches for neutral scalar bosons S⁰ produced in association with a Z⁰ boson via the Bjorken process at centre-of-mass energies of 91 GeV and 183-209 GeV. These searches are based on studies of the recoil mass spectrum of and events and on a search for with and S or photons. They cover the decays of the S⁰ into an arbitrary combination of hadrons, leptons, photons and invisible particles as well as the possibility that it might be stable. No indication for a signal is found in the data and upper limits on the cross section of the Bjorken process are calculated. Cross-section limits are given in terms of a scale factor k with respect to the Standart Model cross section for the Higgs-strahlung process . These results can be interpreted in general scenarios independently of the decay modes of the S⁰. The examples considered here are the production of a single new scalar particle with a decay width smaller than the detector mass resolution, and for the first time, two scenarios with continuous mass distributions, due to a single very broad state or several states close in mass. Received: 13 March 2002 / Published online: 19 February 2003     

Temperature dependence of the elastic constants and Debye temperatures of NaCl and KCl single crystals

A pulsed ultrasonic method has been used to measure the temperature dependences of the elastic moduli, the constants C_ik and S_ik , the anisotropy factors, the bulk moduli, and the Poisson ratios over the temperature range 300-120 ° K for NaCl and over the range 300-80 ° K for KCl. The Debye temperatures of these compounds are calculated from the elastic constants extrapolated to 0 ° K.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 22–28, June, 1970.