We discuss new methods for non-compact sigma models with and without RR fluxes.The methods include reduction to one dimensional supermagnets,supercoset constructions and supertwistors.This work is a first step towards the solution of these models,which are important in several areas of physics. I dedicate it to the memory of Volodya Gribov.December 2005

Yrr. N. MOSKVICH et al.: NMR Study of Internal Motions in M,SbF, 615 phys. stat. sol. (b) 166, 615 (1989) Subject classification: 76.60; 66.30; 72.20; S9.16 L. V . Kirenskii Institute of Physics, Academy of Sciences of the USSR, Siberian Branch, Krasnoyarskl) ( a ) and Institute of Chemistry, Academy of Sciences of the USSR, Vladivostok (b) NMR Study of Internal Motions in a New Family of Ionic Conductors MzSbFs BY Yu. N. MOSKVICH (a), B. I. CHERKASOV (a), A. M. POLYAKOV (a), A. A. SUKHOVSKII (a), and R. L. DAVIDOVICH (b)lgF NMR spectra and relaxation times TI, T2, TI, and electric conductivity in isostructural polycrystalline pentafluoroantimonates (111) M,SbF, (M = Rb, K, Cs, Ti, NH,) are measured. It is found that the observed changes in the NMR spectra and relaxation times with temperature are determined by three types of motion : anisotropic and isotropic reorientations of [SbF,El2octahedra and diffusion motion of the fluorine ions. Parameters of these motions are found. All the compounds investigated show high conductivity a t high temperature, amounting in the case of thallium and ammonium salts the values of u = lo1 to loo Q-l m-l typical of superionic crystals.It is shown that the observed high conductivity is determined by fast diffusion motion of fluorine ions. On the basis of the data obtained a mechanism of fluorine ion diffusion is proposed. I n (NH,),SbF, at 398 K a phase transition is found. H3MepeHbI CIIeKTpbI HMP H BpeMeHa PeJIaHCaqHH I , , T,, TI, HHep "F H 3JIeRTpOIIpOBOn-HOCTb B H30CTpYKTYpHOM PRAY IIOJIMIiPMCTaJIJIH9eCEiHX lIeHTa@TOpOaHTMMOHaTOB (111) M,SbF,, M = K, Rb, CS, T1, NH,. yCTaHOBJIeH0, 9 T O ~a6~1mxam11piec~ H3MeHeHMH CneKTpOB RMP rUHPOKMX JIHHMg, BbICOKOrO pa3pelUeHHH I.I BpeMeH PeJIaKCaUHIi C TeM-IIepaTypOfi 06yCJIOB.i1eHb1 TpeMFl BHAaMH nBHweHHH: aHH30TPOIIHbIMH H H30TPOllHbIMH peopMeHTaqMRMM OKTa3ApOB [SbF,E]'-Ei aM@@Y3HOHHhIM HBMZeHHeM MOHOB @Topa. OIIpeHeJIeHbI IIapaMeTpbl 3THX ABHW€!HM@. B O BCeX HCCJIeAOBaHHblX COeHHHeHMRX I I P M BbICOKMX TeMllepaTypaX 06HapymeHa BblCOKaR IIpOBOAHMOCTb, nOCTHramll1aFl B CyIIepHOHHbIX HpHCTaJIJIOB. nOKa3aH0, 9 T O ~a 6~1 m~a e~a~ BblCOKaH IlPOBOALrMOCTb 06yCJIOBneHa 6bICTphIM AH@@Y3HOHHbIM aBM%eHMeM MOHOB @Topa. H a OCHORe lIOJIy-geHHbIX AaHHbIX npenJIomes MeXaHH3M aH@@Y3HH MOHOB #Topa. B (NH,),SbF, IIpM 398 K 06HapyHWH @a30BbIt nepexox. cnysae coneii T a m m H a M M o H m a~a s e~u B u = lo1 no i O o C..' m-l, xapaKTepHbrx HJIR

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The Green function formalism is applied to the problem of grazing-incidence small-angle X-ray scattering from statistically rough surfaces. Kirchhoff's integral equation is used to describe the X-ray wavefield propagation through a single rough surface separating vacuum and medium. Taking into account multiple diffuse X-ray scattering effects, the reflection R(coh)(θ) and transmission T(coh)(θ) coefficients of the specular wave are obtained using the Gaussian statistical model of rough surfaces in terms of the two-point height-height correlation function. In the limiting cases when the correlation length xi is equal to zero or infinity, analytical formulae for the reflection R(coh)(θ) and transmission T(coh)(θ) coefficients of the specular wave are obtained. It is important that in the case xi --> infinity they coincide with the corresponding reflection R(DW)(θ) and transmission T(DW)(θ) coefficients related to the conventional Debye-Waller approximation for describing the grazing X-ray scattering from a rough surface. In the case of finite values of correlation length \xi the reflection |R(coh)(θ)|(2) and transmission |T(coh)(θ)|(2) scans are numerically calculated.