Laser spectroscopy of the 1s HFS of H-like ions at a bunched beam in the storage ring ESR

The investigation of the 1s HFS provides a good possibility for testing QED effects in a combination of a strong electric and magnetic field. Here, we report about the laserspectroscopic measurements of the ground state hyperfine splitting in ²⁰⁷Pb⁸¹⁺. To handle this M1-transition in the infrared optical regime with its long lifetime, we developed a new detection technique using a bunched ion beam. For the observation of fluorescence light, a new mirror system is adapted to the emission characteristics from an ion beam at relativistic velocities. This revised version was published online in July 2006 with corrections to the Cover Date.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Hydroxyl ion conduction in ytterbium-doped strontium cerate at T<580 K in H2O/air atmosphere

Open circuit voltage (OCV) measurements in H₂O/air concentration cells at T<580 K using Yb-doped SrCeO₃ electrolyte indicate that under these conditions, protons are transported through the electrolyte as -ve ions, possibly as hydroxyl (OH⁻) ions. The H⁺ ionic transport, which is generally reported, becomes the dominant mode for H₂O/air concentration cells at temperatures greater than 750 K or when H₂O/air electrodes are replaced by H₂/Ar, and the anomalous OCV sign disappears. The combination of low temperature and the presence of hydrogen and oxygen as provided by the H₂O/air system appears to be necessary for the postulated hydroxyl ion electrode reactions to take place. In addition to OCV measurements, results from impedance spectroscopy are used to provide evidence in support of the suggested hydroxyl ion mode of protonic transport under the specified conditions. These findings are directly relevant in the development of novel humidity sensors in the temperature range 450–580K and is reported in a separate paper in this conference. Paper presented at the 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Italy, Sept. 15–22, 1996     

Thoms Effect as Influenced by the Concentration and Molecular Parameters of the Cationic Copolymer of Acrylamide

The Thoms effect observed with water-soluble cationic copolymer of acrylamide was studied in relation to the concentration, molecular weight, and molecular weight polydispersity of the polymeric additive, with its composition and composition polydispersity being constant.     

Characters of irreducibleG-modules and cohomology ofG/P for the lie supergroupG=Q(N)

We prove a character formula for any finite-dimensional irreducible representationV of the “queer” Lie superalgebra g=q(n). It expresses chV in terms of the multiplicities of the irreducible g-subquotients of the cohomology groups of certain dominant g-bundles on the Π-symmetric projective spaces (i.e., on the homogeneous superspacesG/P whose reduced space is a projective space, whereG=Q(n)). We also establish recurrent relations for the above multiplicities, and this enables us to compute explicitly chV for any givenV. This provides a complete solution to the Kac character problem for the Lie superalgebraq(n). Finally, we consider the particular cases ofq(2), q(3), andq(4) in which we compare the new character formula with the generic character formula of [12]. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 41, Algebraic Geometry-7, 1997.     

On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Logarithmic temperature dependence of the conductivity of the two-dimensional metal

We report on the first observation and studies of a weak delocalizing logarithmic temperature dependence of the conductivity, which causes the conductivity of the 2D metal to increase as T decreases down to 16 mK. The prefactor of the logarithmic dependence is found to decrease gradually with density, to vanish at a critical density n _c , 2∼2×10¹² cm⁻², and then to have the opposite sign at n>n _c ,2. The second critical density sets the upper limit on the existence region of the 2D metal, whereas the conductivity at the critical point, G _c ,2∼120e ²/h, sets an upper (low-temperature) limit on its conductivity. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 497–501 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.