A Reduction Theorem for Highest Weight Modules over Toroidal Lie Algebras

Let be a toroidal Lie algebra corresponding to a semisimple Lie algebra We describe all Borel subalgebras of which contain the Cartan subalgebra where is a fixed Cartan subalgebra of We show that each such Borel subalgebra determines a parabolic decomposition where is a proper toroidal subalgebra of and Our first main result is that, for any weight which does not vanish on , an arbitrary subquotient of the Verma module is induced from its submodule of invariant vectors. This reduces the study of subquotients of to the study of subquotients of Verma modules over . We then introduce categories and and their respective blocks and corresponding to a central charge which is nonzero on . Our second main result is that the functors of induction and invariants are mutually inverse equivalences of the category and the full subcategory of whose objects are generated by their invariants.     

Sideband cooling while preserving coherences in the nuclear spin state in group-II-like atoms

We propose a method for laser cooling group-II-like atoms without changing the quantum state of their nuclear spins, thus preserving coherences that are usually destroyed by optical pumping in the cooling process. As group-II-like atoms have a (1)S(0) closed-shell ground state, nuclear spin and electronic angular momentum are decoupled, allowing for their independent manipulation. The hyperfine interaction that couples these degrees of freedom in excited states can be suppressed through the application of external magnetic fields. Our protocol employs resolved-sideband cooling on the forbidden clock transition, (1)S(0) --> (3)P(0), with quenching via coupling to the rapidly decaying (1)P(1) state, deep in the Paschen-Back regime. This makes it possible to laser cool neutral atomic qubits without destroying the quantum information stored in their nuclear spins, as shown in two examples, (171)Yb and (87)Sr.     

Memory-function conductivity formula and transport coefficients in underdoped cuprates

The two-band memory-function conductivity formula is derived from the quantum kinetic equation in the pseudogap state of underdoped cuprates. The conduction electrons are described by using the adiabatic version of the nested Fermi liquid model, and the effects of Mott correlations are taken into account phenomenologically. The linear dependence of the low-temperature effective number of conduction electrons on the doping level δ (for not too large δ) is found to be in agreement with experimental observation. The momentum distribution function turns out to play an important role in describing temperature effects. The closing of the antiferromagnetic pseudogap at temperatures of the order of room temperature is shown to be a direct consequence of a relatively large width of the quasiparticle peak in this distribution function. The coupling of conduction electrons to external magnetic fields is included in the two-band transport equations in the usual semiclassical way. It is shown that the low-temperature Hall number is proportional to δ as well (again for not too large δ) and that it exhibits singular behaviour when the Fermi surface changes from the hole-like shape into the electron-like shape.     

Exoelectron emission from solid nitrogen

Solid nitrogen was investigated by activation spectroscopy methods – thermally stimulated luminescence and thermally stimulated exoelectron emission (TSL and TSEE) in combination with luminescence analysis. TSEE from solid nitrogen pre-irradiated by an electron beam was measured and investigated for the first time. A set of peaks both in TSL and TSEE were observed. It was found that one of the peaks in the TSEE curve is caused by release of electrons in the course of the α-β phase transition of solid nitrogen. The corresponding activation energy was estimated.     

Grüneisen parameter of NaCl at high compressions

A new method of determining the pressure dependence of the Grüneisen parameter is described. The measurements were carried out on NaCl to 33 kbar at room temperature using an end-loaded piston-cylinder apparatus. A fluid cell arrangement with Bridgman unsupported area seals was used. Changes of sample temperature associated with small adiabatic pressure changes were measured and the Grüneisen parameter could be calculated from the thermodynamic relationship $\text{γ = (}\text{K}{}_{\mathrm{s}}\text{T}\text{)(}\text{?T}\text{?P}\text{)}{}_{\mathrm{s}}$ where K_s is the adiabatic bulk modulus. Our results are in excellent agreement with those reported by Roberts and Ruppin [1] who calculated the pressure dependence of γ from thermodynamic and ultrasonic data and in excellent agreement with those reported by Hardy and Karo [2] who carried out a lattice-dynamical calculation.     

Die Stabilität der Kobalt(II)- und Kupfer(II)-Komplexe mit α-, β- und γ-Aminobutyrat

Stability constants of cobalt(II) and copper(II) complexes with α-, β-, and γ-aminobutyrate as well as the protonation constants of these ligands have been determined by potentiometric titration. ΔG ^? values, computed from the stability constants, increase in the orderAABA. The increase in ΔG ^? AABA→BABA amounts approx. 15 per cent. The same difference was observed for α- and β-alaninato complexes with various transition metal ions.     

Near infrared electronic spectrum of TCNQ mono-valent anion

The high resolution near infrared electronic spectrum of TCNQ anion dissolved in 2-methyltetrahydrofuran glass at 77 K has been determined. The absorption bands are interpreted as simple progressions of two molecular vibrations in a single electronic excited state with ν₀₀ = 11661 cm^?1. The molecular vibrations (ω′₁ = 1264 ± 3 cm^?1, ω′₂ = 335 ± 3 cm^?1) of the vibrational progression agree well with observed Raman active transitions. The experimental data do not require the presence of two electronic transitions in the 1.3 to 2.1 eV region, contrary to what had been assumed previously on the basis of less well resolved room temperature spectra.     

A Synthesis of Prostaglandins: Strategy and Reality

The prostaglandin synthesis developed in the Woodward Research Institute at Basel serves to provide an unusual look behind the scenes. A candid account is presented of the sometimes tortuous chronological sequence of ideas and experiments during work on a challenging synthesis.