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 .     

A dynamical phase transition in a caricature of a spin glass

This paper studies the rate of convergence to equilibrium of Glauber dynamics (Gibbs Sampler) for a system ofN Ising spins with random energy (at inverse temperature >0). For each of the 2 ^N spin configurations the energy is drawn independently from the values 0 and-logN with probabilities 1-N ^–7, resp.N ^– (>0), and is kept fixed during the evolution. The main result is an estimate of the coupling time of two Glauber dynamics starting from different configurations and coupled via the same updating noise. AsN the system exhibits two dynamical phase transitions: (1) at =1 the coupling time changes from polynomial (>1) to stretched exponential (<1) inN; (2) if <1, then at = the almost coupling time [i.e., the first time that the two dynamics are within distanceo(N)] changes from polynomial (<) to stretched exponential (>) inN. The techniques used to control the randomness in the coupling are static and dynamic large-deviation estimates and stochastic domination arguments.     

The van der Waals limit for classical systems. I. A variational principle

We consider the thermodynamic pressurep(, ) of a classical system of particles with the two-body interaction potentialq(r)+ ^v K(r), where is the number of space dimensions, is a positive parameter, and is the chemical potential. The temperature is not shown in the notation. We prove rigorously, for hard-core potentialsq(r) and for a very general class of functionsK(s), that the limit 0 of the pressurep(, ) exists and is given by where the limit and the supremum can be interchanged. Here is a certain class of nonnegative, Riemann integrable functions,D is a cube of volume |D|, anda ⁰() is the free energy density of a system withK=0 and density . A similar result is proved for the free energy.     

Deposition kinetics of the γ′ phase in N36T2YU2 steel

Electron microscopy is reported for the deposition in this steel; quantitative results are given on the particle size of the phase deposited during a continuous and uninterrupted decomposition. The deposition of the phase occurs in one stage, while the two stages in the variation in the mechanical properties arise from features of the interaction of dislocations with the phase particles. There appears to be only a small energy barrier to the generation of phase particles. Spherulites are formed in regions of interrupted decomposition. The effects of quenching temperature on the deposition mechanism are discussed.Translated from Izvestiya VUZ, Fizika, No. 3, pp. 41–45, March, 1973.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Width and shift of coherent spontaneous radiation line of system of identical emitters

A study is made of the influence of the retarded electromagnetic interaction of a system of identical oscillators arranged in a cubic lattice on the form of the line of spontaneous radiation. All the cases of the mutual relation of the wave-length, the lattice constanta and the length of the crystalL = Na are solved in a unified manner. In the long-wave case (a) it is shown that the line is greatly broadened and shifted (Fig. 3). Especially in the micro-wave case (a< ) the broadening is of the order ofN ³ _e and the shift of the orderN ²(/a) _e , where _e is the natural line width of an isolated emitter. In the optical case (a) the broadening is of the order ofN(/a) ² _e and the shift of the order (/a)³ _e . In the directions satisfying Bragg's condition the line loses its Lorentz form and further broadening and also shifting of the line may occur. It is shown that the vibrations of the crystal lattice influence the coherent effects studied in the same way as they influence the Mössbauer effect.     

Computational study of propagating fronts in a Lattice-gas model

Velocities and other features of propagating fronts in the lattice-gas model analyzed by Bramsonet al. are computed by Monte Carlo simulation. The propagation velocity() is found to converge slowly to its asymptotic dependence on the exchange-rate parameter. The number density of occupied sites in the interaction zone (extending from the forwardmost occupied to the rearmost unoccupied site) appears to converge to 2/3 for large. Spatial profiles of site occupancy and interface number density for finite are compared to the profiles originally computed by Fisher using the differential equation obeyed in the large- limit. Several significant features inferred from the computations have not yet been explained analytically.     

The form factors of the decays π− → e−¯veγ and K− → e−¯veγ

In the special type of the quark model we obtain the ratio=h _A/h_V of the axial (h_A) and vector (h_V) form factors for the decays ^– e^– ¯v_e and K^– e^–¯v_e different from unity. The low-energy theorem, relating the electric polarizability of the charged pion with the ratio, is analyzed. It is shown that < 1 corresponds to , calculated by accounting the contribution of the scalar meson(700) into the amplitude of the Compton effect on the pion. In the absence of the(700) contribution we have=1.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

A “hydrodynamic” theory of surface reaction rates

The Brownian motion of adsorbed particles is described in terms of the first four velocity moments of the distribution function (number density, momentum density, energy density and energy current density). The resulting hydrodynamic equations turn out to be sufficient for a simple derivation and extension of Kramers' results for chemical reaction rates in terms of the friction constant of an underlying Fokker-Planck equation. An interpolation formula is obtained for() containing Kramers' results for small and large as limiting cases. For temperaturesT small compared to the well depthV ₀ one finds a large regionT/V ₀/v ₀V ₀/T in which Eyring's absolute rate theory is approximately valid.On leave of absence from Physikdepartment der TUM, München-Garching     

Statistical properties of secondary γ-transitions in the175,176Lu(nres, γ)176,177Lu reactions

The^175,176Lu(n,)^176,177Lu reactions have been studied at the JINR Fast Pulsed Reactor IBR-30. Using a time-of-flight technique,-ray spectra on isolated resonances have been measured. From analysis of secondary-transition intensities resonance spins have been deduced for both reactions studied. Statistical treatment of the secondary-ray intensities has shown, that population of low-lying levels in the product nuclei^176,177Lu fluctuate from resonance to resonance stronger than is expected on the basis of the statistical model. A hypothesis is advanced, that the increased fluctuation is a consequence of a statistical correlation between partial radiation widths for the transitions of intermediate energies and the reduced neutron widths.     

Short distance scale invariance and high-energy processes in field theory

The dynamics of short distance interaction is considered from viewpoint of the quark field theory. If the effective coupling of quarks (the invariant charge(p ²)) decreases with distance (with increasingp ²) the field picture unifies different phenomenological models: reggeology in the region of smallp and partonology in the region of highp but(p ² ) lnp ² 1 and predict deviations with a subsequent increase ofp . A character of the deviations depends on the behaviour of whenp ². The variants of the asymptotic freedom (0) and scale invariance (g ₂ ⁰ ) are discussed. The strong suppression of—3 decay is considered as a support for the latter.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.     

On the significance of Killing tensors

Killing vectors give the linear first integrals of the geodesic equations on Riemannian manifolds and spacetimes, while Killing tensors give the quadratic, cubic, and higher-order first integrals. Here it is shown that the Lie algebra of Killing vectors,, is extended by Killing tensors into a graded algebra,. This sheds some light on the comment by Xanthopoulos [1] on the apparent scarcity of irreducible Killing tensors. Examples are presented of the graded algebras when is abelian and when is nonabelian.     

Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids

We construct a family of probability spaces,P ), <0 associated with the Euler equation for a two dimensional inviscid incompressible fluid which carries a pointwise flow _t (time evolution) leavingP globally invariant. _t is obtained as the limit of Galerkin approximations associated with Euler equations.P is also in invariant measure for a stochastic process associated with a Navier-Stokes equation with viscosity, , stochastically perturbed by a white noise force. Dedication. After completion of this work the terrible news of the sudden death of Raphael Høgh-Krohn reached us. In deep sorrow we mourn his departure. The present work has its roots in previous inspiring work by him and we dedicate it to him as a small sign of our gratitude.     

The Duffing oscillator in the low-friction limit: Theory and analog simulation

By a joint use of theory and analog simulation the low-friction regime of the Duffing oscillator is explored. In the weak-temperature case it is shown that the low-friction regime, in turn, must be divided in two well-distinct subregimes. In the former one, characterized by the friction ranging from 2 ₀ ( ₀ is the harmonic frequency) up to a lower bound _T, the method of statistical linearization applies and a continued fraction procedure (CFP) generated by the Zwanzig-Mori projection techniques is shown to provide correct information for both the renormalized frequency of the oscillator and the corresponding line shape. The latter subregime, characterized by the friction ranging from = 0 to = _T , is fraught with the complete breakdown of the statistical linearization method. The CFP is shown to provide an incorrect picture of the line shape while suggesting a novel mean field approximation which is then proven analytically via an alternative method of calculation. This method consists of expressing the system in a form reminiscent of the model of Kubo's stochastic oscillator. By using this alternative approach we are in a position to account for the residual linewidth which is shown by the analog experiment to survive for 0.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

Microscopic selection principle for a diffusion-reaction equation

We consider a model of stochastically interacting particles on , where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this particle V() then satisfies ^–1/2V() as. This limit corresponds to that of the macroscopic density obtained by rescaling lengths by a factor ^1/2 and letting. This density solves the reaction-diffusion equation , and under Heaviside initial data converges to a traveling wave moving at the same rate .     

Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; (x) are the covariant-fixed Dirac matrices; ^,=(1/4)[, ]: a(^b)=(1/2) (a b +ab ); [A, B]=A·B – B·A; A,B=A·B+B·A; g(x)=det(g (x));R = –...; the speed of light c=1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 1990.The author wishes the thank Yu. G. Ignat'ev and members of the seminar in General Relativistic Statistics and Cosmology of the Kazan' Pedagogical Institute for useful discussions.     

Measurement of the reaction γp → K0Σat photon energies up to 2.6 GeV⋆

The reaction p K⁰⁺ was measured in the photon energy range from threshold up to 2.6 GeV with the SAPHIR detector at the electron stretcher facility, ELSA, in Bonn. Results are presented on the reaction cross-section and the polarization of the ⁺ as a function of the kaon production angle in the centre-of-mass system, cos^c.m._K, and the photon energy. The cross-section is lower and varies less with photon energy and kaon production angle than that of p K⁺⁰. The ⁺ is polarized predominantly at cos^c.m._K 0. The data presented here are more precise than previous ones obtained with SAPHIR and extend the photon energy range to higher values. They are compared to isobar model calculations.