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.     

К ВОПРОСУ ТЕОРИИ КОЭР ЦИТИВНОЙ СИЛЫ ТОНКИХ ЛИСТОВ

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Влияние сильного выс окочастотного поля на расслоение положи тельного столба постоянного тлеющег о разряда

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The influence of a strong high-frequency field on the stratification of the positive column of a D-C glow discharge

An experimental study is made of the damping of moving striations in a d-c glow discharge by a strong high-frequency field. The results of measurement are in agreement with existing conceptions on the production and mechanism of propagation of moving striations. Apart from the process of damping the paper also describes the standing stratification of the positive column of a d-c discharge as a result of a superposed high-frequency discharge.

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Surface tension,step free energy,and facets in the equilibrium crystal

Some aspects of the microscopic theory of interfaces in classical lattice systems are developed. The problem of the appearance of facets in the (Wulff) equilibrium crystal shape is discussed, together with its relation to the discontinuities of the derivatives of the surface tension (n) (with respect to the components of the surface normaln) and the role of the step free energy ^step(m) (associated with a step orthogonal tom on a rigid interface). Among the results are, in the case of the Ising model at low enough temperatures, the existence of ^step(m) in the thermodynamic limit, the expression of this quantity by means of a convergent cluster expansion, and the fact that 2^step(m) is equal to the value of the jump of the derivative / (when varies) at the point =0 [withn=(m ₁ sin ,m ₂ sin , cos )]. Finally, using this fact, it is shown that the facet shape is determined by the function ^step(m).     

On the Surface Pressure for the Edwards-Anderson Model

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic ^* boundary conditions (by symmetry ⁽⁾=^(*)), and prove the bounds We show moreover that at high temperatures ⁽⁾ is close to ^2/4 and ⁽⁾ is close to ^2/4 uniformly in the volume .     

The semi-conducting properties of CdSnAs2

The paper gives the results of measuring the temperature dependence of the electrical conductivity(T), the Hall coefficientR _H (T) and the magnetic susceptibility(T) forn-type CdSnAs₂. The effective mass of the electrons was determined by analysis of the measured dependences on the basis of the simple theory for an isotropic non-degenerate semi-conductor. It was found to bem _n /m ₀=2×10^–2 in the intrinsic region and does not depend on the temperature; the energy gap ise _g ⁰=0·26 eV and the molar susceptibility of the CdSnAs₂ lattice _G ^mol=–112× ×10^–6. The mobility of the electrons in the intrinsic region reaches a value of _n =25 000 cm²V^–1sec^–1 at 500°K and decreases exponentially _n T ^–1.67 with rising temperature. The density of CdSnAs₂ was determined pyknometrically,g9=5·35 g cm^–3. The measurements were made on ann-type polycrystalline sample consisting of crystals a few millimetres in diameter, which at a temperature of 100°K had a free electron concentration ofn _s =6×10¹⁶ cm^–3.

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CdSnAs₂

(T), R _H (T) (T) CdSnAs₂ . m _n /m ₀= =2.10^–2, ; E _G ⁰=0,26 eV, CdSnAs_{2 G} ^mol= =–112.10^–6. 500°K _n =25 000 cm²V^–1sec^–1 , _n T ^–1,67. CdSnAs₂ =5,35 g cm^–3. , , 100°K n _s =6.10¹⁶cm^–3.

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The authors would like to thank Mr. P. Jansa for help in measuring the temperature dependence of the magnetic susceptibility.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Приготовление оченъ чистого железа и опре деление его чистоты по некото рым физическим свойс твам

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Correlations and spectra of an intermittent chaos near its onset point

A one-parameter family of piecewise-linear discontinuous maps, which bifurcates from a periodic state of periodm, (m=2, 3,...) to an intermittent chaos, is studied as a new model for the onset of turbulence via intermittency. The onset of chaos of this model is due to the excitation of an infinite number of unstable periodic orbits and hence differs from Pomeau-Manneville's mechanism, which is a collapse of a pair of stable and unstable periodic orbits. The invariant density, the time-correlation function, and the power spectrum are analytically calculated for an infinite sequence of values of the bifurcation parameter which accumulate to the onset point _c from the chaos side - _c > 0. The power spectrum near=0 is found to consist of a large number of Lorentzian lines with two dominant peaks. The highest peak lies around frequency=2/m with the power-law envelope l/¦-(2/m)¦⁴. The second-highest peak lies around o = 0 with the envelope l/¦¦². The width of each line decreases as, and the separation between lines decreases as/lg3^–1. It is also shown that the Liapunov exponent takes the form-/m and the mean lifetime of the periodic state in the intermittent chaos is given bym ^–1(ln ^–1+1).     

Matrix field theory for disordered local pairing superconductors with two glass order parameters and spin-flip pairbreaking processes

We derive the exact matrix field theory for a replicated grassmannian representation of a local pairing superconducting disorder ensemble including three superconducting order parameters and the spin-flip pairbreaking mechanism. Disorder is assumed to be gaussian distributed. We find by exactly solving the saddle-point equation the criterion for a vanishing gap ^–1 + ^–1 , where denotes the averaged superconducting order parameter, ^–1 the spin-flip scattering rate, and ^–1 the scattering rate corresponding to correlations of Re(–). Taken at =0, our field theory, which is exact in all orders of ^–1 , contains new terms in addition to those of theO( ^–1 ) model derived by Efetov et al. Our formulation transfers correctly to all orders the invariances of the action into symmetries of the matrix field theory. The saddle point approximation is outlined and it is shown how singular corrections to the saddle point density of states arise atE _F in a gapless superconductor. Finally singular corrections in the two particle propagator, the density correlation function and the conductivity are calculated for =0 in one loop order. It turns out that these corrections can be entirely expressed by those of the single particle density of states.     

Effect of radiation on hydromagnetic vertical channel flow

The effect of radiation on the combined free and forced convection flow of an electrical conducting viscous fluid through an open-ended vertical channel in slip flow regime and permeated by a constant magnetic field in transverse direction has been considered. The temperature on the walls has been supposed to vary linearly with distance. On the assumption of optically thin limit, the expressions for velocity, induced magnetic field, temperature, flow rate and the heat transfer coefficient due to thermal conduction are obtained and the influence of radiation on these solutions are shown either graphically or in tabulated forms.Notation x, y, z cartesian coordinates - v velocity - 2L distance between the channel walls - B ₀ applied magnetic field - B induced magnetic field - T temperature - p pressure - density - magnetic permeability - v kinematic coefficient of viscosity - conductivity of the fluid - g acceleration due to gravity - coefficient of volume expansion - thermal diffusivity of the fluid - c _p specific heat at constant pressure - q_R radiative heat flux - k absorption coefficient - e _b Plank function - T 0 reference temperature - N vertical temperature gradient - M= B₀L[/(v)]^1/2 Hartmann number - R _a=gNL⁴/(v) Rayleigh number - P_m = magnetic Prandtl number - 2d₁, 2d₂ thickness of the walls - ₁, ₂ conductivities of the walls     

On the indistinguishability of classical particles

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature become small. Thus, microscopic particles like electrons must remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2)³ are reduced to points in the phase space, the partition functionTr{exp(–) for N identical bosons (fermions) approaches (2)^–3N(N!) ... d³r₁ d³p₁ ... d³r_N d³p_N exp(–H). The two factors, (2)^–3N and (N!)^–1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles.     

Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR     

The physical nature of the production of moving striations in a d-c discharge plasma

The physical nature of the stratification of the d-c discharge plasma is found and physically interpreted. The interpretation is based on the mathematical expression of the production of periodic structure in plasma after an aperiodic disturbance, derived from an extremely simplified system of equations. Only three basic phenomena occurring in the plasma of each d-c discharge are included: a) the dependence of the rate of ionization on the electron temperature and hence on the electric field, b) the production of space charges due to the different rates of diffusion of the electrons and ions, c) the creation of additional electric fields due to the creation of space charges. The interactions of these phenomena gives rise to a chain, expanded in time and space, which leads to the production of moving striations. In agreement with experiment this structure is developed only on the side towards the anode from the place where the equilibrium state is disturbed.

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. (9, 10) (4, ), . , , : ) , , ; ) , ; ) , . , , — — . , .

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In conclusion the authors thank J. Fousek, J. Kaczér and M. Novák for carefully reading this paper and for valuable remarks, and J. Holub for carrying out the numerical and graphical work.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Bosons in thermal contact: AC*-algebraic model

A gas of two Boson systems coexisting inR ³, and interacting only mutually, is analyzed. The interaction is quadratic, so that the dynamical problem may be solved completely and exactly.The initial state is taken to be the mutually uncorrelated Gibbs states: ^{(1) (2)} = . We find the time evolved state, and its projections onto the separate species and the subvolumes.The principle consequences of this model are discussed. In particular we examine the possible occurrence of harmonic oscillations between the species.On Study Leave at the Department of Physics and Astronomy, The University of Rochester.This research was partially supported by the National Science Foundation under Contract No. 5-28501.     

New interpretation of experiments on the intermediate meson

A new theory of weak interactions is proposed in which the coupling between theV-A currents j(X) and j(X) is achieved not by vector mesons [by a propagator D ^c (X-X)], but by a scalar functionR(X – X), a fermion-antifermion loop which plays the role of a unique film joining two different pointsX andX of completely uncoupled space-times (as a result of which the space becomes a continuum). The existence of the actual currents j results from correlations between the two different spinor layers of Dirac layer formation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 25–40, February, 1996.     

Локалъная чувствите лъностъ фотокатодов фотоумножителей

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The local sensitivity of photo-multiplier photo-cathodes

The influence of the non-uniform distribution of the sensitivity of a photo-multiplier photo-cathode on the spectrum shape of the output pulses from a scintillation detector is studied. Methods of scanning the local sensitivity and determining its distribution function are described. The theory was compared qualitatively with measurement on a slow-neutron detector from a mixture of zinc sulphate and boric acid.

     

Spectral properties of random Schrödinger operators with unbounded potentials

We investigate spectral properties of random Schrödinger operators H = - + _n()(1 + |n|) acting onl ²(Z ^d), where _n are independent random variables uniformly distributed on [0, 1].Research partially supported by a Sloan Doctoral Dissertation Fellowship and NSERC under grant OGP-0007901Research partially supported by NSF grant DMS-9101716