Kinetics and mechanism of copper fracture due to deformation in surface-active paths

The general kinetic characteristics of copper fracture in the presence of surface-active bismuth-lead baths during creep and elongation under tension are explained. It is shown that the subcritical stage of crack development controls the process, whereupon the effects of stresses , temperature, strain rate , surface energy at the copper-bath interface _SL, and surface energy at the grain boundaries _b on the rate of crack development l/ are analyzed. The basic conclusions are that: a)l/=(–) ( and being constants here); b) the crack development activating energy ) the reduction of energy _b, achieved by intergranular internal adsorption of 0.5% antimony, lowers the value of about 50 times; d) a 30% increase in surface energy _SL reduces the cracking rate 30 times, according to the relation (where A=6 · 10^–15 cm²); and e) .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–15, May, 1976.     

On the theory of amplification of meso-ultrasound in anisotropic monopolar semiconductors

The electronic absorption coefficient (_e) of meso-ultrasound (_p ^–1 _en, _t, _ee; ql 1, where _p, _en, _t are the times of pulse relaxation, energy, and current carrier traps; _ee ^–1 is the frequency of intraelectron collisions; , q are the frequency and wave vector of sound; l is the carrier mean free path) in the presence of a permanent external field E₀ e ₀ ^–1 q₀T is calculated for anisotropic single-valley semiconductors with piezoelectrical and potential-deformation acoustoelectronic interaction. Considered arbitrary are: 1) the anisotropy of the tensors * and _p (and other crystal parameters); 2) the degree of Fermi degeneration of the carriers; 3) the dependence of _p on the carrier energy . The acoustoheat nonlinearity is neglected. The possibility of meso-ultrasound amplification by the transverse field (E₀ - q) is predicted. By changing the orientation of the vector q relative to the crystal axes, the transverse threshold field (E ^thr ) can be controlled smoothly and within broad limits, This permits the production of a mechanical sound-amplification regulator or a modulator of its intensity. The ratio between E ^thr and E ^thr yields a measure of the relative anisotropy of the mobility.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 87–92, February, 1977.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Multiple coherent scattering of γ-radiation

Conclusions Multiplying (5) by 2d and integrating over angle, we get the relationship between the total flux and depth in the form , where .A similar result is obtained from integration of (11) over the angles and integration of (12) over the plane z = const. It thus follows that if we are interested in the angular distribution for in the first two cases and in the radial distribution for z in the third case, we can make an approximate estimate of the coherent scattering by eliminating the appropriate term from. This approach has been used in [15 etc.] but no indications were given of the conditions under which this is permissible.For problems in which small angles or small distances from the axis of a collimated source are important, allowance for the coherent scattering can change the result by an order of magnitude or more. For angles and it is possible to consider only the coherent scattering and to use (5), (11), and (12). For angles >gh and scattering >z, the contribution from coherent and incoherent scattering can be comparable. The kinetic equation must then be solved with allowance for both effects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 129–132, May, 1973.     

Simultaneous geometrization of classical and quantum mechanics of spinless particles

It is shown that classical and quantum equations of motion of a relativistic spinless particle (the Lorentz and Klein-Gordon equations) allow for a geometrization on the same manifold ₄. A classical particle on ₄ is described as a free particle ( p=0), while the quantum particle, as a free wave ( s=0).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1990.     

Interaction of a neutrino with a circularly polarized plane wave accompanied by (n¯n) pair production

We consider the processes (n )and n , induced by the interaction of the anomalous magnetic moment of the neutron with the field of a circularly polarized plane wave. Using the invariant solution of the modified Dirac equation, we obtain expressions for the total probabilities of these processes, which consist of several different contributions. The asymptotic behavior of the results at high energy is analyzed and the possibility of observing the effects is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 1990.The authors thank V. G. Bagrov for useful discussions.     

Isospectral hamiltonian flows in finite and infinite dimensions

A moment map is constructed from the Poisson manifold _A of rank-r perturbations of a fixedN×N matrixA to the dual of the positive part of the formal loop algebra =gl(r)[[, ^–1]]. The Adler-Kostant-Symes theorem is used to give hamiltonians which generate commutative isospectral flows on . The pull-back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in _A. The latter may be identified with flows on finite dimensional coadjoint orbits in and linearized on the Jacobi variety of an invariant spectral curveX _r which, generically, is anr-sheeted Riemann surface. Reductions of _A are derived, corresponding to subalgebras ofgl(r, ) andsl(r, ), determined as the fixed point set of automorphism groupes generated by involutions (i.e., all the classical algebras), as well as reductions to twisted subalgebras of . The theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of PDE's.This research was partially supported by NSF grants MCS-8108814 (A03), DMS-8604189, and DMS-8601995     

Green's functions of spinor field in conformally plane space—time

A complete set of solutions of the Dirac equation is found in space-time with the metric ds² = ²(d ²- dx²- dy²- dz²). For the Green's functions in$$ " align="middle" border="0"> and in$$ " align="middle" border="0"> , representations are found in the form of contour integrals from the Schwinger-De Witt nucleus over various contours.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 35–40, April, 1985.It remains to thank Yu. Yu. Vol'fengaut for discussions in the course of the present work.     

Spectral distribution and kinetics of the high-voltage photoelectromotive force of PbS layers

The spectral dependences of the short-circuit current Iph and the photoconductivity _ph of photovoltaic PbS layers are similar in shape and in the position of the long-wavelength threshold. As the temperature is reduced, the spectral curves shift toward longer wavelengths. Several samples show a photoemf of different sign in different parts of the spectrum. The relaxation of the photoemf V_ph, the current I_ph, and the photoconductivity _ph is characterized by times , respectively, where > \tau \sigma > > \tau I$$ " align="middle" border="0"> . The temperature dependences of these times and of the layer resistance have been studied. The results are interpreted on the basis of a barrier model for the high-voltage photoemf in PbS layers.     

A spectral characterization of KMS states

Let be a state on aC*-dynamical system . For each of the following properties of : (1) is -K MS with respect to for some given , 0<+, (2) is either a KMS state or a ground state, necessary and sufficient conditions are given involving only the spectral subspaces of associated with . The results provide a new insight in the concept of passivity, introduced by W. Pusz and S. L. Woronowicz.Aangesteld navorser N.F.W.O., Belgium, on leave from Katholieke Universiteit Leuven. Research partially supported by N.A.T.O.     

Proof of a retroactive influence

Quantum theory predicts that, e.g., in a Stern-Gerlach experiment with electrons the measured spin component does not come about by an adjustment at the last moment, a forced flipping or tilting of the spin (vector), which would imply z-angular momentum exchange between particle and instrument, but will afterward appear to have had the value already before the measurement. Because an electron spin cannot have components in all directions at the same time, the measuring direction has a privileged status before the measurement, however we choose that direction, which implies a retroactive effect. A second proof of retroactivity is derived from a special case of the paradox of Einstein, Podolsky, and Rosen. It is strongly suggested by our result that, in essential respects, both Bohr and Einstein were right in their famous controversy about determinism and considering microprocesses as a whole.     

Complex Hyperspherical Equations, Nodal-Partitioning, and First-Excited-State Theorems in ℝ n

Three problems related to the spherical quantum billiard in are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in . The second topic addresses the first-excited-state theorem for the spherical quantum billiard in . Wavefunctions for this system are given by the product form, ( )Z _q+()Y ⁽ⁿ⁾ , where is dimensionless displacement, is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written . It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in . In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in by enumerating independent degenerate product eigenstates of the Laplacian.     

Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

Leptonic charge and weak neutrino-lepton interactions

A scheme is discussed according to which the system of leptons is characterized by a single leptonic charge with different values for muonic leptons and electronic leptons. The weak neutrino-lepton interaction is investigated within the framework of this scheme. Charged (V + A)-currents are introduced to describe the and transitions.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 30–34, December, 1971.     

Spinorial analysis and physical properties of fermions

We study the formalism of covariant differentiation of a spinor field in a space of affine connection with an invariant metric. We find the most general formula for the coefficients of spinorial connection consistent with the fundamental relationship between the space and spin ( + = 2g), and which is a generalization of the formula for the Fock-Ivanenko coefficients. The obtained formula contains additional terms describing the interaction between the spinor field and the scalar field, the vector field A, and the pseudovector field (presumably, the pseudotrace of the spacetime torsion). The existence of these interaction terms also follows from the analysis of spinor fields from the gauge-theoretical point of view. We show that the interaction between the spinor and pseudovector fields found in this paper substantially modifies the electrodynamics of spinor fields. As a result, the combined system of equations describing the dynamics of the vector (electromagnetic) and pseudovector fields is, unlike the Maxwell equations, symmetric with respect to the right-hand sides (sources). The source for the field strength tensor of the field comples A and is the vector current of the spinor field ¯gy, while the source for the dual field strength tensor is the pseudovector current of the spinor field ¯5. It is suggested that the obtained interaction between the spinor and the scalar and pseudovector fields plays a role on a deeper level of matter structure —in quark and preon (subquark) systems.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 20–25, October, 1986.In conclusion, the author finds it a pleasure to thank the participants of the theoretical seminars led by D. Ivanenko, Yu. S. Vladimirov, and N. V. Mitskevich, for the discussion of the results of this paper and for valuable comments.     

Yet another formulation of the Dirac equation

The 2-by-2 Pauli matrix algebra is used to write the 1-by-4 Dirac field in anequivalent 2-by-2 matrix . The current 4-vectors and *_µ are then compared and the latter is shown to not be easily interpretable as a probability density, and also tocontain .     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

Geometro-stochastic quantization of a theory for extended elementary objects

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of is a resolution kernel Hilbert space constructed in terms of generalized coherent states related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter . The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from .Supported in part by NSERC Research Grant No. A5206.     

Decay π → + ν in the field of a plane electromagnetic wave with allowance for the polarizability of the pion

The process + in the field of a plane electromagnetic wave is investigated with allowance for the complex structure of the pion. Exact values are obtained for the probability of pion decay in circularly and elliptically polarized fields. Pion structure effects become observable for 5, where .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 65–68, December, 1991.     

Anomalous fall to the center in a one-dimensional singular field

The fall to the center in a singular, one-dimensional, even field is investigated. It is shown that the fall of the ground level in a field with a weak singularity , 0 < 2) is caused by a -well arising from the nonphysical choice of a self-adjoint broadening of the Hamiltonian, unconnected with the increased symmetry of the Hamiltonian and easily eliminated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 75–79, October, 1989.