On invariant subspaces and eigenfunctions of regular Hecke operators on spaces of multiple theta constants

Invariant subspaces and eigenfunctions of regular Hecke operators acting on spaces spanned by products of even number of Igusa theta constants with rational characteristics are constructed. For some of the eigenfunctions of genuses g=1 and g=2, corresponding zeta functions of Hecke and Andrianov are explicitly calculated.     

The Trifluoromethyl Anion

First evidence for the existence of free trifluoromethyl anion CF₃^? has been obtained. The 3D‐caged potassium cation in [K(crypt‐222)]⁺ is inaccessible to CF₃^?, thus rendering it uncoordinated (“naked”). Ionic [K(crypt‐222)]⁺ CF₃^? has been characterized by single‐crystal X‐ray diffraction, solution NMR spectroscopy, DFT calculations, and reactivity toward electrophiles.     

Homogeneous nucleophilic radiofluorination and fluorination with phosphazene hydrofluorides

A series of phosphazenium hydrofluorides, P(1)(tBu)·[(18/19)F]HF, P(1)(tOct)·[(18/19)F]HF, P(2)(Et)·[(18/19)F]HF, and P(4)(tBu)·[(18/19)F]HF, was synthesized. The radioactive phosphazenium [(18)F]hydrofluorides were obtained by the one-step formation and trapping of gaseous [(18)F]HF with the respective phosphazene bases. The [(19)F] isotopomers were prepared from the corresponding phosphazene bases and Et(3)N·3HF. Under the design of experiment (DoE)-optimized conditions, P(2)(Et)·HF and P(4)(tBu)·HF fluorinated alkyl chlorides, bromides, and pseudohalides in 76-98% yield, but gave lower yields with iodides and electron-deficient arenes. DoE models showed that fluorination can be performed in glass vessels, and that the reactivity of P(2)(Et)·HF and P(4)(tBu)·HF is dominated by solvent polarity but is insensitive to water to at least 2 equiv. In contrast, P(1)(tBu)·HF and P(1)(tOct)·HF were unstable towards autofluorolysis. DFT calculations were performed to rationalize this finding in terms of diminished steric bulk, higher Parr's electrophilicity, and chemical hardness of P(1)(R)H(+). The corresponding radiofluorination reaction gave no valid DoE model but displayed similar substrate scope. High specific activity and excellent radiochemical yields with various pseudohalides (81-91%) suggest that the proposed radiofluorination methodology can complement the current [(18)F]KF/Kryptofix methods, particularly in the areas for which nonpolar reaction conditions are required.     

Peculiarities of the complexation of copper and silver adducts of a 3,5-bis(trifluoromethyl)pyrazolate ligand with organoiron compounds

Interaction of the copper, {[3,5-(CF(3))(2)Pz]Cu}(3), and silver, {[3,5-(CF(3))(2)Pz]Ag}(3), macrocycles [3,5-(CF(3))(2)Pz = 3,5-bis(trifluoromethyl)pyrazolate] with cyclooctatetraeneiron tricarbonyl, (cot)Fe(CO)(3), was investigated by IR and NMR spectroscopy for the first time. The formation of 1:1 complexes was observed at low temperatures in hexane. The composition of the complexes (1:1) and their thermodynamic characteristics in hexane and dichloromethane were determined. The π-electron system of (cot)Fe(CO)(3) was proven to be the sole site of coordination in solution and in the solid state. However, according to the single-crystal X-ray data, the complex has a different (2:1) composition featuring the sandwich structure. The complexes of ferrocene with copper and silver macrocycles have a columnar structure (X-ray data).     

Photochromism in single nitrogen-vacancy defect in diamond

Photochromism in single nitrogen-vacancy optical centers in diamond is demonstrated. Time-resolved optical spectroscopy shows that intense irradiation at 514 nm switches the nitrogen-vacancy defects to the negative form. This defect state relaxes back to the neutral form under dark conditions. Temporal anticorrelation of photons emitted by the different charge states of the optical center unambiguously indicates that the nitrogen-vacancy defect accounts for both 575 nm and 638 nm emission bands. Possible mechanism of photochromism involving nitrogen donors is discussed. PACS 61.72.-y;61.72.Ji;03.67.-a     

A quantum computer based on NV centers in diamond: Optically detected nutations of single electron and nuclear spins

In an effort to realize a two-bit processor for a quantum computer on the basis of single nitrogen-vacancy defect centers (NV centers) in diamond, the optically detected nutations of the electron spin of a single NV center in the ground state and of the nuclear spin of a ¹³C atom located at a diamond lattice site nearest to the NV center are studied. The photodynamics of NV and NV + ¹³C centers under different temperatures and optical excitation conditions is discussed. A seven-level model of a center excited by radiation from an Ar⁺ laser at room temperature is proposed. On the basis of this model, the experimental spectra of optically detected electron paramagnetic and electron-nuclear double resonances of single NV and NV + ¹³C centers in diamond nanocrystals, as well as experimental data on the optically detected nutations of the electron and nuclear spins of these centers caused by the actions of pulsed microwave and radiofrequency fields, respectively, are interpreted.     

Form factors,deformed Knizhnik-Zamolodchikov equations and finite-gap integration

We study the limit of asymptotically free massive integrable models in which the algebra of nonlocal charges turns into affine algebra. The form factors of fields in that limit are described by KZ equations on level 0. We show the limit to be connected with finite-gap integration of classical integrable equations.     

Magnetic measurement of transport AC losses in Bi-2223/Ag tapes

Magnetic nature of the losses in superconducting wire carrying AC current implies that it should be possible to determine these losses in a contactless way. Ribbon-like samples are quite favorable for such an experiment, because a notable portion of magnetic flux related to losses ‘escapes' the sample volume and can be detected by an appropriate pick-up coil. In this case, a model describing the AC current penetration into the tape, based, e.g., on the critical state model, allows one to derive the losses from the pick-up coil signal. Because this signal is proportional to the number of coil turns, extension of the accessible range of measured voltages (and losses) can be achieved. We demonstrate the data obtained on a 1 cm long portion of a low-loss multifilamentary tape carrying AC current with frequency 35 Hz. The pick-up coil technique allowed us to reach loss level more than one order below the experimental limit for direct measurements.