Cyclotron instabilities of a two-component electron plasma

A study is made of instability at frequencies close to the electron cyclotron frequency _B and its multiples, subject to the presence of two different groups of electrons. It is shown that a mixture of hot and cold electrons ( _ph ² _pc ² ) in the region of frequencies s _B, s2 can be unstable with respect to waves of the flute type (k _z=0) with maximum increment _max ( _ph/_pc). _B, if there exists an interval of transversal velocities in whichF/ >0. When the curvature of the magnetic field is taken into account, even waves with _B can be unstable in such a plasma. The effect of spatial inhomogeneity of the hot component on flute-type instability and on two-beam cyclotron instability is also examined.The author extends his thanks to A. B. Mikhajlovskij for his valuable comments and discussions.     

The Gelfand-Levitan equation and its application to the scattering of neutrons on protons

The Gelfand-Levitan equation for the kernelP(r, r) (withrr) is formulated and then applied for determining the scattering potential in the scattering of slow neutrons on protons (for the case when the dependence of the nuclear forces on the spins can be neglected and onlys-scattering need be considered). The potentials obtained are the same as the Bargmann ones, found by a different method.

---

-

- P(r, r) ( rr). , ( s- ). , .

     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

A note on the Watanabe theory of weak interactions

It is shown that according to the Watanabe theory of weak interactions a resonant scattering of electrons by protons must take place. The resonant energy depends on the massm _B of the intermediate boson. Form _B=2300m _e this energy is about 213 MeV in the centre of the mass system (c. m. s.). The energy width at resonance is 1·4 MeV.

---

, . , , . _{m B}=2300_{m B} , 213 MeV -. 1,4 MeV.

---

---

The author would like to thank Professor V. Votruba for suggesting this note and for valuable advice and help during the work.     

Single crystal diffraction patterns of germanium. Part II

The rocking curves of Ge (111), (220), (333) for CuK ₁ radiation were measured by means of the triple-crystal diffractometer. Perfect silicon single crystals, cut parallel to the (111) plane were used in the monochromator part of the triple-crystal diffractometer. The results prove the suitability of such a monochromator for studying diffraction patterns.

---

. II

(rocking curves) (111), (220), (333) CuK ₁ . , (111). .

---

---

In conclusion the authors thank A. Haruý for preparing the germanium single crystals and they are indebted to V. Smutná and A. Irra for the care with which they carried out various tasks.     

Quantum Ergodicity of Boundary Values of Eigenfunctions

Suppose that ⁿ is a bounded, piecewise smooth domain. We prove that the boundary values (Cauchy data) of eigenfunctions of the Laplacian on with various boundary conditions are quantum ergodic if the classical billiard map on the ball bundle B^*() is ergodic. Our proof is based on the classical observation that the boundary values of an interior eigenfunction , =² is an eigenfunction of an operator F_h on the boundary of with h=^–1. In the case of the Neumann boundary condition, F_h is the boundary integral operator induced by the double layer potential. We show that F_h is a semiclassical Fourier integral operator quantizing the billiard map plus a small remainder; the quantum dynamics defined by F_h can be exploited on the boundary much as the quantum dynamics generated by the wave group were exploited in the interior of domains with corners and ergodic billiards in the work of Zelditch-Zworski (1996). Novelties include the facts that F_h is not unitary and (consequently) the boundary values are equidistributed by measures which are not invariant under and which depend on the boundary conditions. Ergodicity of boundary values of eigenfunctions on domains with ergodic billiards was conjectured by S. Ozawa (1993), and was almost simultaneously proved by Gerard-Leichtnam (1993) in the case of convex C^1,1 domains (with continuous tangent planes) and with Dirichlet boundary conditions. Our methods seem to be quite different. Motivation to study piecewise smooth domains comes from the fact that almost all known ergodic domains are of this form.The first author was partially supported by an Australian Research Council Fellowship.The second author was partially supported by NSF grant #DMS-0071358 and DMS-0302518.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Effect of hydrogen doping on the magnetic properties of Gd2CuO4

We report the results of ac-susceptibility and dc-magnetization measurements for H_yGd₂CuO₄ (0y0.54). It is shown thatH doping lowers the weak ferromagnetic component in the material. The distinct hysteresis loops observed atT=77 K for both non- and hydrogenated samples change its shape withy. The magnetic ordering temperatures T _N ^Cu and T _N ^Gd , as determined from the temperature dependencies of ac-susceptibility, remain unchanged with sample's hydrogenation. This result seems to indicate that extra electrons are not doped onto the Cu-O planes of Gd₂CuO₄. The frequency dependencies ofx(, T) andx(, T) for bothy=0 andy=0.15 samples are analysed., The maximums ofx andx found at about 200K are considered in terms of susceptibility dependence on the spin-lattice relaxation time (). The anomalies in ac-susceptibility found recently in Gd₂CuO₄ atT _a=8 K andT _b=9.5 K decrease significantly withy. Results are discussed in the context of available data on 214T-type compounds.     

Weak four-fermion interaction in terms of SU(3) invariants. II

A lepton octet is constructed by analogy with the baryon octet by the substitution p⁺N ₁e⁺,⁺₁ é⁺,^-₂^-, ^- N ₂^-, where ₁, ₂,N ₁,N ₂ are arbitrary constants. The neutral components are replaced by a linear sum of the electron and muon neutrinos with arbitrary coefficients. The constants are determined from the system of general conditions (normalization, absence of crossed terms of the type ( etc.). As a result, the lepton octet is determined to within a single constant, and this is shown to be identical with the Cabibbo angle. Calculations are also made of the weak decays of baryons of the octet in the case of both charged and neutral currents. In the case of charged currents, the results agree with Cabibbo's theory. Calculations are also made of the lepton-lepton weak interactions and the ratios of the corresponding constants are determined. The ratios are in qualitative agreement with the existing experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–56, January, 1976.     

Parametric excitation of spherical modes in ferromagnetic spheres by perpendicular and parallel pumping

The fine structures of the threshold of subsidiary absorption and parallel pumping, observed on highly polished YIG spheres in 1975 by W. Jantz et al., are discussed with a model which uses instead of plane spin-waves the true modes regarding the shape of the sphere. These spherical modes are magnetostatic modes taking additionally the exchange interaction into account. At the closely spaced resonances of the fine structure of parallel pumping single spherical modes with angular-momentum quantum numberm=0 are excited, whereas at the resonances of subsidiary absorption pairs of spherical modes with big angular-momentum quantum numbers (|m|1000) satisfying the selection rulem+m=1 are excited. The analysis of the fine structure of subsidiary absorption shows that in regimes where the plane wave approximation predicts the excitation of spin-waves with formalk0, modes withk1.5·10⁵ cm^–1 have the lowest threshold. This discrepancy is discussed with the effect of surface pit scattering, which increases the threshold of modes withk < 2/_pit, where _pit is a typical size of the surface pits. Consequently modes withk22/_pit instead ofk0 have the lowest threshold.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Total dynamic structure factor of icosahedral and As-quenched and relaxed glassy Pd58.8Si20.6U20.6 measured at 296 K

The total dynamic structure factorsS(Q, ) of icosahedral, glassy Pd_58.8Si_20.6U_20.6, and the crystallized sample have been determined at room temperature using inelastic scattering of cold neutrons (IN6 of ILL). In contrast to the static structure factorS(Q), where the long range bond orientational order (BOO) leads to pronounced diffraction peaks with finite half width, the dynamic structure factor shows little or no influence of the long range BOO on the atomic dynamics of icosahedral PdSiU in the range of frequencies (0.525 meV) and momentum transfers Q(5Q30 nm^–1 for inelastic scattering) investigated here. The wavelength-dependence of the atomic dynamics of icosahedral PdSiU is very similar to that of the metallic glass and is different from that of the crystallized sample. As for glassy PdSiU no well defined vibrational collective excitations are found as peaks in the inelastic part ofS(Q, ) of the icosahedral sample,-quite in contrast to theoretical expectations and to the dispersions of pronounced excitations determined under identical experimental conditions fromS(Q, ) of the crystallized sample. On structural relaxation of the metallic glass Pd_58.8Si_20.6U_20.6 the largest amount of low energy modes is annealed out at lowest energy.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Group duality and the Kubo-Martin Schwinger condition. II

Let be an invariant state of theC*-system { ,G, } on a locally compact noncommutative groupG. Assume further that is extremal -invariant for an action of an amenable groupH which is -asymptotically abelian and commutes with . Denoting byF _AB,G _AB the corresponding two point functions, we give criteria for the fulfillment of the KMS condition with respect to some one parameter subgroup of the center ofG based on the existence of a closable mapT such thatTF _AB=G _AB for allA,B . Closability is either inL (G),B(G) orC (G), according to clustering properties for . The basic mathematical technique is the duality theory for noncompact, noncommutative locally compact groups.This work is supported in part by the National Science Foundation, Grant MCS 79-03041     

A Note on Anisotropic Percolation

We consider an anisotropic independent bond percolation model on , i.e. we suppose that the vertical edges of are open with probability p and closed with probability 1–p, while the horizontal edges of are open with probability p and closed with probability 1– p, with 0 < p, < 1. Let , with x₁ < x₂, and . It is natural to ask how the two point connectivity function P_p,({0 x}) behaves, and whether anisotropy in percolation probabilities implies the strict inequality P_p,({0 x})> P_p,({0 x}). In this note we give affirmative answer at least for some regions of the parameters involved.Mathematics Subject Classifications (2000). 82B20, 82B41, 82B43.     

Adjoint solutions of the Brans-Dicke equations

It is shown that if the Brans-Dicke equations have the solution,g _ij generated by the trace free sourceT _n (T-O) then there exists an adjoint solution ^–1, ²g_ij of these equations generated by the source ^-2 T _u. An example is considered.     

Semimodularity and the logic of quantum mechanics

If (, ,P, ) is an event-state-operation structure, then the events form an orthomodular ortholattice (, , ) and the operations, mappings from the set of states into , form a Baer *-semigroup (S, , *, ). Additional axioms are adopted which yield the existence of a homomorphism from (S, , *, ) into the Baer *-semigroup (S(), , *, ) of residuated mappings of (, , ) such thatx S maps states while _x S () maps supports of states. If (, , ) is atomic and there exists a correspondence between atoms and pure states, then the existence of provides the result: (, , ) is semimodular if and only if every operationx S is a pure operation (maps pure states into pure states).Supported in part by the United States Atomic Energy Commission and in part by the Fonds National Suisse.     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

The translation-rotation paradox in the nucleation theory

The factor of 10¹⁷ proposed by Lothe and Pound in the theory of nucleation of droplets from the vapor phase is studied using classical statistical mechanics. The controversial factor is derived from partition functions for an isolatedn-mer and for ann-molecular cluster imbedded in the bulk liquid phase. The rotational degrees of freedom have no place in, in agreement with Reiss, Katz, and Cohen's treatment. It is proved that the surface free energy of a cluster is proportional to the surface area. The estimate of what Lothe and Pound called the replacement term is different from those of previous authors. It is concluded that is written as a ratio = _g/_l, where _g and _l , are the volumes per molecule in the gas phase and in the liquid phase, respectively. For water at 300K, is approximately equal to 10₄.     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.