Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil

For a generalized Zakharov-Shabat system in which the matrix potential is a polynomial in the spectral parameter a generating operator is constructed which makes it possible to compactly write out the nonlinear evolution equations (NEE) connected with the system. The eigenfunctions of the generating operator — the squares of solutions of the original system — are found. The Hamiltonian property of the NEE and the existence of a hierarchy of Hamiltonian structures are established.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 120, pp. 55–68, 1982.     

Effect of vibrational kinetics of He2 + ions on the afterglow of a discharge in helium

A decaying weakly ionized helium plasma [n_e=(0.2–1.1)·10¹¹ cm^–3, p=(40–70) mm Hg] was studied experimentally. It is shown that the experimental time dependences of the intensities of atomic lines and molecular bands in the afterglow phase can be explained if the vibrational kinetics of He₂ ⁺ ions is included in the analysis. Analysis of the measurements shows that for n_e 10¹¹ cm^–3 and N_a 10¹⁸ cm^–3 deexcitation of He₂ ⁺ ions occurs primarily as a result of inelastic collisions with helium atoms. Based on the experimental data, an approximate value was obtained for the rate constants of the vibrational relaxation of molecular helium ions 10^–16 cm³/sec. These results are used for making a qualitative analysis of the distribution of He₂ ⁺ ions over the vibrational states in the discharge phase.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 88–96, November, 1986.     

Determinants and characteristic polynomials

The supersymmetric model in one dimension is used to calculate the fermion and scalar determinants in constant fields and express them in terms of the characteristic polynomials appearing in anomalies and index theorems. The operator determinants are transformed into those of a matrix.     

Structure and properties of nonclassical polymers

Utilizing an extended Hubbard-type Hamiltonian which incorporates both nearest-neighbour Coulomb repulsion and exchange interactions, we have studied the energy dispersion of the lowest elementary excitation from the ferromagnetically aligned state of quasi one-dimensional alternant hydrocarbon networks. It was found that the main effect of the long range Coulomb interaction may be thought of as a renormalization (screening) of the on-site Hubbard integral. This implies an enhancement of the kinetic exchange term and impairs the stability of the ferromagnetic state towards single spin inversions. However, for physically relevant values of the parameters entering the model Hamiltonian, the collective spin excitation represents a magnon, whose energy band lies above the reference value pertaining to the magnetically saturated configuration.Dedicated to Prof. Dr. Adolf Neckel on the occasion of his 60th birthday     

Liquid chromatography of platinum metals and prospects of development

Summary A survey of the authors' work on liquid chromatography of platinum metals in the form of chelates with 1-(2-pyridylazo)-2-naphthol (PAN) is given. Extraction chromatography with PAN in isopentanol as a stationary phase was used to achieve a group concentration of these metals (Pd, Pt and Rh, concentration coefficient 100) from large volumes of aqueous solutions and a selective extraction of palladium from solutions containing other platinum, nonferrous and heavy metals on a 85–98° C thermostatted chromatographic column. The prospects for the use of liquid chromatography in the analysis of platinum metals are discussed.

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Flüssig-Chromatographie von Platinmetallen und zukünftige Entwicklungen

     

Ion-induced CO adsorption on polycrystalline nickel. Secondary ion mass spectrometry study

In the process of ion-induced CO adsorption (Ar⁺, 4 keV, 4 A/cm²) on polycrystalline Ni at room temperature and P=(1–40)×10^–6 Pa the emission of Ni⁺, NiCO⁺, CO⁺, NiO⁺ and C⁺ ions is observed. The emission of the last three ions is due to the ion-stimulated dissociation of weakly bound CO state and NiO formation. The weakly bound state is formed owing to surface defects produced by ion bombardment. The cross sections of the ion-induced desorption are 1.8 and 0.8×10^–14 cm², respectively, for weakly bound and strongly bound states.     

Proton Relaxometry of Long-Lived Spin Order

A study of long-lived spin order in chlorothiophene carboxylates at both high and low magnetic fields is presented. Careful sample preparation (removal of dissolved oxygen in solution, chelating of paramagnetic impurities, reduction of convection) allows one to obtain very long-lived singlet order of the two coupled protons in chlorothiophene derivatives, having lifetimes of about 130 s in D₂O and 240 s in deuterated methanol, which are much longer than the T₁-relaxation times (18 and 30 s, respectively, at a field =9.4 T). In protonated solvents the relaxation times become shorter, but the lifetime is still substantially longer than . In addition, long-lived coherences are shown to have lifetimes as long as 30 s. Thiophene derivatives can be used as molecular tags to study slow transport, slow dynamics and slow chemical processes, as has been shown in recent years.     

Asymptotics of many-electron wavefunctions and calculation of tunnel transitions

A new method for defining the wavefunction asymptotics for many-electron systems in the far-subbarrier region is suggested. The method is based on the Lippman-Schwinger formalism and can provide an accuracy in defining the asymptotics similar to that in the main region of the electron localization (MREL). The wavefunctions in MREL are the basis for obtaining the asymptotics. Molecular, cluster and surface systems are considered. A new approach to the calculation of tunneling transitions is formulated. A general expression for the tunneling current in scanning tunneling microscopy (STM) is obtained which strictly takes into account the penetration factor, the correlation between the tunneling current from individual atoms, and the angular dependence of asymptotics of basic atomic functions. This permits us to state and correctly solve the problem of defining the electron wavefunctions of the surface using the data of the tunneling current measurement at various biases and the positions of the tip.