Thermodynamics of the spin-S antiferromagnetic Heisenberg chain

The numerical solution of the Bethe ansatz equations of an integrableSU (2)-invariant generalization of the spin-S antiferromagnetic Heisenberg chain in zero magnetic field is presented. The thermodynamics is obtained numerically. The temperature dependence of the entropy, specific heat and susceptibility is presented forS5/2. The results are compared to those of then-channel Kondo problem with a spin-S impurity withn=2S.     

Solution of then-channel Kondo problem (scaling and integrability)

The exact solution of the Kondo model forn-flavours of electrons with the spin 1/2 scattered by theS-spin impurity is presented. Forn=2S=5 the model describes manganese impurities dissolved in a metal. It is shown that atn>2S the effective exchange coupling approaches a finite fixed point as the energy scale decreases. It means that atn>2S the Gell-Mann-Low function turns to zero in this point and the scaling behaviour of physical quantities is observed. The scaling behaviour, first obtained in the 1D quantum field theory, can be analyzed on the basis of the exact solution. In the casen≦2S the effective coupling becomes infinitely strong at low energies.     

A new approach to potential scattering

An approximate integral-representation of theS-matrix in partial-wave expansion is derived for a scalar Schrödinger particle in a central field. The method consists of linearizingCalogero's Riccati equation for the interpolatingS-matrix in such a way that the solution of the linearized equation deviates as little as possible from the exact one. TheS-matrix thus obtained exhibits exact crossing-symmetry and uniform convergence independent of the coupling constant of the scattering potential. In the weak coupling limit it is especially shown thatour method is more accurate than the second Born approximation. In the second part of the paper we specialize ourS-matrix to low and large energies. At low energies, a general integral for the scattering length is obtained and at large energies the summation over all angular momenta is carried out yielding an expression for the scattering amplitude.     

Kondo effect in spin glasses: Electrical resistivity

We investigate the influence of the Kondo effect on the electrical resistivity of spin glasses. Our approximation reduces in the limit of vanishing impurity concentrations to the Suhl-Nagaoka theory for the Kondo effect. The magnetic impurity interactions are taken into account in the form of time dependent two-spin correlation functions which can be measured by neutron scattering. The dynamics of the impurity spins leads to a partial destruction of the Kondo effect. For the resistivity this can be described by a temperature dependent effective spinS _eff ² (T) withS _eff ² 0 forT0 andS _eff ² S(S+1) forT, and by a reduction of the Kondo temperatureT _K. Sufficiently strong interactions lead toT _K=0. We obtain a resistivity maximum at a temperatureT _m due to the interplay of the Kondo effect and the spin dynamics;T _m depends onT _K and on the excitation spectrum, and therefore on parameters such as impurity concentration or pressure. The ratioT _m/T_f (T _f is the freezing temperature) is calculated for a single relaxation time and for a square density of relaxation modes and is compared with experimental data forAuCr,AuMn,AgMn, andCuMn. The influence of other possible modes on various spin glass properties is discussed.SFB 125 Aachen-Jülich-Köln     

Existence theorems for π/n vortex scattering

The analysis of 90° vortex-vortex scattering is extended to /n scattering in all head-on collisions ofn vortices in the Abelian Higgs model. A Cauchy problem with initial data that describe the scattering ofn vortices is formulated. It is shown that this Cauchy problem has a unique global finite-energy solution. The symmetry of the solution and the form of the local analytic solution then show that /n scattering is realized.     

Spectral-Luminescence Characteristics of Carbazole, Dibenzofuran, and Dinaphthofuran in the Gas Phase in Excitation by Electrons and Photons

The spectra of electron-energy loss, the excitation functions, and the fluorescence spectra in excitation of carbazole, dibenzofuran, and dinaphthofuran by monoenergetic beams of electrons of different energies are determined. The singlet-triplet transitions S ₀–T ₁ and the singlet-singlet transitions up to S ₀–S ₇ are recorded, which covers the region 2–11 eV. In the spectra of electron-energy loss, bands that refer to the n^ast and ^* transitions are identified. The replacement of the heteroatom of nitrogen by the atom of oxygen in the five-membered ring has no substantial effect on the spectra of electron-energy loss.     

Multichannel Kondo problem and some applications

We review analytical and numerical results derived from the Bethe ansatz solution of the n-channel Kondo model of arbitrary spin S as a function of temperature, external field, impurity spin S and the number of channels n. Three situations have to be distinguished: (i) If n = 2S the conduction electrons exactly compensate the impurity spin into a singlet at low temperatures, (ii) if n < 2S the impurity spin is only partially compensated (undercompensated), and (iii) if n > 2S the impurity spin is said to be overcompensated giving rise to critical behaviour. The results are discussed in the context of magnetic impurities, e.g. Fe, Cr and Tm in simple metals, the quadrupolar Kondo effect, an impurity spin embedded in the Takhtajan-Babujian Heisenberg model and electron assisted-tunnelling of an atom in a double-well potential.     

Magnetic impurity effects inAgMn,AuFe, andCuCr studied by tunneling in superconducting proximity layers

Magnetic interactions were studied by superconducting tunneling into diluteAgMn,AuFe, andCuCr alloys in which superconductivity had been induced by a proximity effect. A detailed investigation ofAgMn, for concentrations up to 0.4 at.% Mn and at temperatures down to 0.05 K, revealed a weak impurity band within the energy gap of the density of excited states at about 0.68 of the half energy gap . The amplitude of the band, however, was twenty times smaller than expected from the theory by Müller-Hartmann and Zittartz. This makes the interpretation of the effect as being due to bulkAgMn doubtful. The localisation of the band would imply a Kondo temperature,T _K , of about 1 mK for an impurity spinS=5/2. No effect of spin-glass ordering was seen in the temperature dependence of the tunneling density of states inAgMn which contradicts a report by Schuller et al. The zero bias conductance could instead be reproduced from low temperature measurements if the temperature variation in was taken into account. InCuCr, the shape of the impurity band was found to be temperature dependent. The location of an impurity band at about 0.68 inAuFe indicates. together with previous observations, the presence of two impurity bands in this alloy. The one found here, might be due to long-range Fe pairs.     

Magnon spectrum and curie temperature of doped ferromagnetic semiconductors

The influence of a partially filled conduction band on the magnetic properties of ferromagnetic semiconductors is studied within the framework of thes-f model. Allowing for magnon scattering to arbitrary order in the form of virtual electron- holecreation the magnon spectral density is derived, from which one gets magnon energies which are substantially renormalized by the presence of conduction electrons. In particular it is shown how the quasiparticle structure of the electronic excitation energies [4, 5] leads to scattering corrections in the magnon spectrum. These corrections are always negative and reduce the positive mean field part, which is proportional to the electron densityn. The calculated magnon spectrum is then used to determine the strikingn-dependence of the Curie-temperatureT _c of Gd-doped EuO and EuS.     

Manifestation of the vibronic analogue of the Fermi resonance in quasi-line spectra of porphyrins: Experiment and theoretical analysis

The quasi-line low-temperature (4.2 K) fluorescence excitation spectra of two porphyrins, meso-tetraazaporphin and meso-tetrapropylporphin introduced into an n-octane matrix are measured in the range of the S ₀ → S ₂ electronic transition. A characteristic feature of these spectra is that a conglomerate of quasi-lines—a structured complex band—is observed instead of one 0–0 quasi-line of the S ₀ → S ₂ transition. In this band, the intensity distributions for the two main types of impurity centers considerably differ from each other. The occurrence of such conglomerates is interpreted as a result of nonadiabatic electronic-vibrational interactions between vibronic S ₂ and S ₁ states (the complex vibronic analogue of the Fermi resonance). The frequencies and intensities of individual transitions determined from the deconvolution of complex conglomerates are used as the initial data for solving the inverse spectroscopic problem: the determination of the unperturbed electronic and vibrational levels of states involved in the resonance and the electronic-vibrational interaction matrix elements between them. This problem is solved with a method developed previously. The energy intervals between the S ₂ and S ₁ electronic levels of the two main types of impurity centers formed by molecules of a given porphyrin in the crystal matrix are found to significantly differ from each other (～100 cm^?1). At the same time, the energies of the unperturbed vibrational states of the S ₁ electronic level partcipating in the resonance are very close to each other for these two types of impurity centers.     

Effect of the Electron-Vibrational Interaction on the Second Electron Transition of Tetraazaporphin and Tetraazachlorin Molecules

We have traced the change in the complex structure of the intense 0–0 band of the electronic S ₂ S ₀ transition in the quasi-line absorption spectra (n-octane, 77 K) for individual types of impurity centers in the series of compounds tetraazaporphin–tetraazachlorin–di(tert-butylbenzo)barrelene-substituted tetraazachlorin. It has been concluded that the reason for the appearance of this structure is the interaction of the pure electronic S ₂ state with the vibronic S ₁ states rather than the Franck–Condon manifestation of low-frequency vibrations. Attempts to detect the short-wave S ₂ S ₀ fluorescence for all three compounds were unsuccessful. The reasons for the difference from the case of bacteriochlorin, in which such a fluorescence was observed earlier, are discussed.     

Transition temperature and gap anisotropy of pure and impure superconductors

The algebraic structure of linearized Eliashberg theory atT=T _c is exploited to derive expressions for the anisotropic gap(k, i _n ) and theT _c-enhancement. These formulas are exact to second order in the anisotropy, and require as input the isotropic gap(k, i _n ), the anisotropic spectral function ² F(k, ), and the impurity scattering rate 1/ _k . Approximate formulas based on a square well model are also given. The formulas for impurity effects are new and very simple.     

Features of current carrier scattering in epitaxial films

The properties of epitaxial cadmium selenide films obtained by condensation in a vacuum on mica substrates under almost equilibrium conditions are investigated. The temperature dependences of the conductivity and current carrier mobility and concentration are studied. The electron concentration in the films depended on the gas phase composition (coevaporation of CdSe + Se or CdSe + In) and varied between 5·10¹⁰cm^–3 and 3.5·10¹⁸. It is shown that the current carrier scattering mechanism depends on their concentration and production conditions. For n₁ 10¹⁶ cm^–2 (T_S520C),n₂ < 10¹⁵ (T_S=630C), scattering on intercrystallite barriers predominated. For n₁ and n₂ greater than the quantities mentioned, scattering by ionized defects becomes dominant. It is established that the magnitude of the intercrystallite barrier in films with 10¹⁵ < n < 10¹⁶ cm^–3 is comparatively small and does not exceed 4·10^–3 eV, whereupon scattering at the barriers is not explicitly manifest. Concentrations of the ionized centers, magnitudes of the intercrystallite barriers, and ionization energies of the donor levels are determined for films obtained under different conditions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 98–103, September, 1977.     

High-Energy Two-Electron Photoabsorption as a Three-Body Problem

We study the high-energy behaviour of double photoionization and of the ionization accompanied by excitation of the states n¹S and n³S of the H^– ion, helium atom, and light helium-like ions. We show that the high-energy nonrelativistic limit of the ionization+excitation to the single-ionization cross section ratio is still valid for the photon energies, corresponding to the relativistic energies of the outgoing electron. The same applies to the double photoionization of the triplet states. The situation for the double photoionization of singlet states differs due to the quasifree mechanism. All these ionization ratios are calculated by using the high-precision locally correct wave functions for the bound electrons. The importance of using locally correct functions is emphasized.     

Threshold anomaly in doubletn-d scattering

The behaviour of the doubletn-d scattering phase shift ₂(k) at energies close to the three-particle threshold is studied analytically and numerically. The scattering parameters possess an anomaly associated with the low energy of the singletN-N virtual state. The anomaly manifests itself both as a bend in the energy dependence of the functionk cot(Re ₂) in the range around 0.5 MeV and in the nonstandard behaviour of the break-up cross section near the threshold.     

Die charakteristische Thermokraft der Grenzflächenatome

For a single-band conductor where two or more scattering mechanisms are present, each giving rise to a characteristic thermoelectric powerS _n and a electrical resistivity? _n the resultant thermoelectric powerS is given, as a first approximation, by\(S = \sum\limits_n {\varrho _n S_n /\varrho } \). Denoting withS ₀ the characteristic thermoelectric power due to the scattering of the conduction electrons by the boundary atoms, and withS _i and? _i the resultant thermoelectric power and electrical resistivity arising from all other scattering mechanisms, one may writeS=S ₀+? _i(S _i?S ₀)/?. The thermoelectric powerS and the electrical resistivity? of thin layers of potassium, evaporated in a vacuum ～5·10^?9 Torr on a glass substrate at 90° K temperature, were measured at different thicknesses. The variation ofS as a function of 1/? verifies the above mentioned relation. Thus, the thermoelectric power, characteristic for the scattering by potassium boundary atoms can be determined.     

Muonic atom-nucleus collisions in the energy region of dtµ, resonant states

We calculated the (dµ) _n=1 +t scattering in the energy region of the (dtµ)^* resonant states below then=2 level of the tµ atom. From the cross sections, we estimated the resonant energies, widths and branching ratios. We found eleven resonant states with angular momentumJ=0, and some of their resonant energies relative to then=2 level of tµ are small enough to form the [(dtµ)^* dee] by the Vesman mechanism. These resonant states decay to (dµ)[inn=1 +t or (tµ) _n=1 + d scattering states. The total decay rates are about 10¹¹ s^–1 which is three orders of magnitude larger than the fusion rates of (dtµ)^*4 He + n+ 17.6 MeV + µ. The main part of the decaying channel from the shallow resonant states is the (dµ) _n=1 +t channel. The branching ratios of the (dµ) _n=1 +t decay channel are around 0.9. Most of the muons that reach to then=2 states of tµ can transfer to then=1 state of du through (tµ) _n=2 + D₂ [(dtµ)^*dee] and (dtµ)^* (dµ) _n=1 +t processes.     

Optoelectrical investigations on MOS-sandwiches at low temperatures

MOS-structures are irradiated with light of energy from 1.5 to 6 eV at different temperatures (300, 77, 12 K) while the resulting photocurrent is measured. At high photon energies (hv>4 eV) the threshold energy and the scattering mean free path for electrons at the Si — SiO₂-interface are determined. They are independent from temperature. At low photon energies (hv<3 ev)=" electrons=" are=" released=" from=" traps=" with=" energy=" levels=" 1.2=" and=" 1.9=" ev=" below=" the=" si-conduction=" band.=" the=" trap=" concentration=" is=" 4.8="> 10¹³ cm^–3. The capture cross section is measured in a rather direct way. The temperature and electrical field dependence of this cross section is explained by a trapping model.     

SimpleC*-algebra generated by isometries

We consider theC*-algebra generated byn2 isometriesS ₁,...,S _n on an infinite-dimensional Hilbert space, with the property thatS ₁ S*₁+...+S _n S* _n =1. It turns out that has the structure of a crossed product of a finite simpleC*-algebra by a single endomorphism scaling the trace of by 1/n. Thus, is a separableC*-algebra sharing many of the properties of a factor of typeIII with =1/n. As a consequence we show that is simple and that its isomorphism type does not depend on the choice ofS ₁,...,S _n .