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     

Corrections to the critical temperature in 2D Ising systems with Kac potentials

We consider ad=2 Ising system with a Kac potential whose mean-field critical temperature is 1. Calling >0 the Kac parameter, we prove that there existsc ^*>0 so that the true inverse critical temperature _cr() > 1 +by ² log ^-1, for anyb<c ^* and correspondingly small. We also show that if 0 andbc ^*, suitably, then the correlation functions (normalized and rescaled) converge to those of a non-Gaussian Euclidean field theory.     

Scaling in the mean of the p+p→π0+X inclusive reaction data and the energy dependence of Feynman variable

We have studied the p+p⁰+X inclusive reaction data of Carey et al. in the framework of the scaling in the mean hypothesis first proposed by Dao et al. These data have been used to obtain the gamma ray spectrum in terms of the average value of the Feynman variablex, written as x.A comparison with the observed gamma ray spectrum at Mt. Chacaltaya by the Japanese and Brazilian Group gives the energy dependence of x at very high energy.     

Stability and structure of Newtonian gravitars

The solution r² for a scalar field (gravitational constant), which is asymptotically exact for supercompact configurations and which Saakyan and Mnatsakanyan obtained from the numerical solution of the hydrostatics equations in the Newtonian approximation of the Jordan-Brans-Dicke theory, is used to study the gravitational stability of such configurations. We have found the stability condition 2/3 for polytropic configurations ( is the polytropic exponent) instead of 4/3, which is known for configurations of low compactness. Analytic solutions of the equations of internal structure are found for configurations which are intermediate with respect to stability (=2/3) and for some other important series of configurations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 98–102, July, 1982.In conclusion, the present author expresses his indebtedness and gratitude to V. N. Ponomarev, for assistance in executing the work.     

Self-Similar Decay in the Kraichnan Model of a Passive Scalar

We study the two-point correlation function of a freely decaying scalar in Kraichnan's model of advection by a Gaussian random velocity field that is stationary and white noise in time, but fractional Brownian in space with roughness exponent 0<<2, appropriate to the inertial-convective range of the scalar. We find all self-similar solutions by transforming the scaling equation to Kummer's equation. It is shown that only those scaling solutions with scalar energy decay exponent a(d/)+1 are statistically realizable, where d is space dimension and =2–. An infinite sequence of invariants J _p, p=0, 1, 2,..., is pointed out, where J ₀ is Corrsin's integral invariant but the higher invariants appear to be new. We show that at least one of the invariants J ₀ or J ₁ must be nonzero (possibly infinite) for realizable initial data. Initial datum with a finite, nonzero invariant—the first being J _p—converges at long times to a scaling solution _p with a=(d/)+p, p=0, 1. The latter belongs to an exceptional series of self-similar solutions with stretched-exponential decay in space. However, the domain of attraction includes many initial data with power-law decay. When the initial datum has all invariants zero or infinite and also it exhibits power-law decay, then the solution converges at long times to a nonexceptional scaling solution with the same power-law decay. These results support a picture of a two-scale decay with breakdown of self-similarity for a range of exponents (d+)/<a<(d+2)/, analogous to what has recently been found in the decay of Burgers turbulence.     

56,57,60CoFe NMR/ON,hyperfine anomalies and γ-factors of cobalt isotopes

The results of NMR/ON measurements on^56'57'60Co isotopes in iron are presented. To avoid the uncertainties caused by local demagnetizing field inhomogenities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factor ratios ⁵⁷/ ⁶⁰ = 1.805 (20), ⁶⁰/ ⁵⁶ = 0.761 (20), ⁵⁶/ ⁵⁷ = 0.726 (20) and hyperfine anomalies⁵⁶⁶⁰ = -0.036 (10),^{60 57} = 0.017 (10) and⁵⁷⁵⁶ = 0.018 (10) have been calculated from the experimental results.     

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.     

Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

Hydrodynamic Limit of Brownian Particles Interacting with Short- and Long-Range Forces

We investigate the time evolution of a model system of interacting particles moving in a d-dimensional torus. The microscopic dynamics is first order in time with velocities set equal to the negative gradient of a potential energy term plus independent Brownian motions: is the sum of pair potentials, V(r)+ ^d J(r); the second term has the form of a Kac potential with inverse range . Using diffusive hydrodynamic scaling (spatial scale ^–1, temporal scale ^–2) we obtain, in the limit 0, a diffusive-type integrodifferential equation describing the time evolution of the macroscopic density profile.     

Model for γγ→VV reactions near threshold

We propose a Veneziano-like model for VV reactions near threshold involving exchanges of 0^– trajectories int- andu-channels. The model is applied to , , , and processes. The model in its simplest form cannot account for the disparities in the cross sections for andK ^*+ K ^*– and for ⁰⁰ and ^+–. Further refinements of the model are suggested.     

A dynamical system with integer information dimension and fractal correlation exponent

In this paper we construct a family {T }, 0<<1/2, of exact endomorphisms of [0, 1] such that the invariant measurem ofT is equivalent to Lebesgue measure but has fractal correlation exponent =2. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems.Research supported by the Natural Sciences and Engineering Research Council of Canada     

The critical point indices of ferroelectric and ferromagnetic phase transitions

Magnetic transitions are described by the critical indices0,1/3,4/3 while some ferroelectric transitions appear to give0,R~1/2,1. It is pointed out that these two sets of values for the critical indices are allowed by the scaling laws and stability conditions near the phase transitions.The authors thank Prof. R. S. Krishnan for his encouragement and Mr. B. Viswanathan for some discussions. The financial assistance from DAE and CSIR is also acknowledged.     

Investigation of Rust Formed on Steel Surfaces and Related Oxyhydroxides

In order to indentity the corrosion products formed on steel surfaces from ⁵⁷Fe Mössbauer spectroscopy, detailed Mössbauer parameters have been determined for various kinds of iron-oxyhydroxides: -FeOOH, -FeOOH, -FeOOH and -FeOOH. ⁵⁷Fe Mössbauer measurements of the iron oxyhydroxides indicate the following results. Fe occupies a single site in -FeOOH, but below the Néel temperature as at e.g., 300 K the Mössbauer spectrum is always broad, showing a distribution of the strength of the magnetic exchange interactions. Its shape depends on the grain-size and synthetic methods of the specimen. Fe occupies 3 sites in -FeOOH. High-purity reagents of -FeOOH always contain small amounts of -FeOOH and their Néel temperatures depend on the synthetic methods of the specimen. Mössbauer spectroscopy of the synthetic -FeOOH shows very broad distribution of the hyperfine magnetic fields.     

Amplitude-distortion factors for the inelastic scattering of an electron at a neon atom in an electric field

Inelastic electron scattering at a neon atom in the presence of an external electric field is considered. The distortion factors of the cross section _M (F) are calculated for a series of 4d and 5d levels. It is shown that the distortion factor in strong fields is a nonlinear and nonmonotonic function of the field. The distortion factors and transition probabilitiesA , are compared. The correlation between the behavior ofA , and _M (F) is explained by the dependence of the mean dipole moment of the Stark state on the field strength.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–110, January, 1996.     

To the problem of KL→π0γγ decay

It is shown that the contribution of diagrams with intermediate state vector mesons to the K_L ⁰ amplitude, intensively discussed in literature in recent years, is close to zero provided that theSU(3) group breaking is taken into account. At the same time, the contribution of scalar mesons in the intermediate state is essential. The obtained estimates for Br(K_L ⁰) conform with the recent experimental data Br(K_L ⁰ )=(2·1 ± 0·6)×10^–6.Dedicated to the memory of our friend Prof. M. Gmitro.We wish to thank S. B. Gerasimov and A. B. Govorkov for useful discussions.     

Production of neutral mesons in the reaction12C+12C at 2 GeV/u

A systematic study of neutral meson production in heavy-ion reactions at 2 GeV/u was started with a¹²C+¹²C experiment using the photon spectrometer TAPS. Special emphasis is put on the possible observation of the-meson in a heavy-ion reaction exploiting the decay channel ⁰.Presented at the International School-Workshop Relativistic Heavy-Ion Physics, Prague (Czech Republic), 19–23 September 1994.     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Asymptotics for Bosonic atoms

It was proved by Benguria and Lieb that for an atom where the electrons do not satisfy the exclusion principle, the critical electron number N _c, i.e., the maximal number of electrons the atom can bind, satisfies lim inf_zN_c/Z 1 + , where Z is the nuclear charge. Here is a positive constant derived from the Hartree model. We complete this result by proving that the correct asymptotics for N _c(Z) is indeed _zN_c/Z = 1 + .This work was done while the author was a graduate student at Princeton University supported by a Danish Research Academy fellowship and U.S. National Science Foundation grant PHY-85-15288-A03.     

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.     

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.