Strict inequalities for some critical exponents in two-dimensional percolation

For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponent for the percolation probability isstrictly less than 1. The same argument is applied to prove that ifL():={(x, y):x=r cos, y=r sin for some r0, or} and():=limpp _c [log(p–p _c )]^–1 log P_cr {itO is connected to by an occupied path inL()}, then() is strictly decreasing in on [0, 2]. Similarly, lim_n [–logn]^–1 logP _cr {itO is connected by an occupied path inL()() to the exterior of [–n, n]×[–n, n] is strictly decreasing in on [0, 2].     

A study of the ϱ0 meson polarization in π− p reaction at 5 GeV/c

Experimental data on ⁰ meson polarization in ^– p reaction at 5 GeV/c are presented. Change in ⁰ meson polarization for mesons produced at smallP ² and atP ² 0·3 or produced in backward direction in CMS is demonstrated. Natural explanation of these phenomena is one pion exchange mechanism and mechanism of quark-antiquark annihilation as observed for ⁰ meson production in¯pp reactions.The authors are indebted to Ján Piút, Richard Lednický, V. S. Rumiancev and N. K. Koutsidi for discussions and critical comments.     

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).     

Solar wind protons,alpha particles and electrons in the shock wave and the potential barrier (The intershock project)

The paper discusses the dynamics of solar wind proton,-particle and electron fluxes near the Earth's bow shock front. In subsequently developed events, deceleration and deflection of ion components and electron heating are observed. The velocity distributions of protons and-particles behind the shock front have a strongly inhomogeneous structure that is gradually smoothing out in the magnetosheath. Unlike protons,-particles behind the front do not generate beams with energy exceeding that of the solar wind.Presented at the Colloquium on Plasma physics Topics Common to the Laboratory and the Space Plasma Research, September 21–25, 1987, Skalsky Dvr, Czechoslovakia.     

Analysis of intermediate structures of spectral emission in pre-equilibrium nuclear reactions in the microscopic approach

The quasi-particle-phonon model of pre-equilibrium decay (QP Ph M PED) is proposed. Within this model, intermediate states are specified by the number of quasi-particles, quasi-holes and phonons. In describing nuclear relaxation we consider two types of internuclear transitions with the change in exciton number byN _ex=0, ±2 and number of phononN _ph=±1. The mixed densities of intermediate states(N _ex,N _ph,E) have been determined. An analysis has been made of the structure of the hard part of the emission spectrum in the⁶⁰Ni(p,p) and¹²⁰Sn(p,p) reaction at _p=62 MeV. This analysis suggests the importance of taking into account the transitions withN _ph=+1, along with the transitions withN _ex= +2.     

Unitarity equations and structure of theS-matrix at them-particle threshold in a theory with purem→m interaction

The structure of theS-matrix at them-partical thresholds=(m)² of amm process (m2) inv-dimensional space-time is determined in a theory with a simplified unitarity equation corresponding to a puremm interaction. If (m–1)(v–1) is odd, a two-sheeted, square-root type structure is obtained as in the usual case of two-particle thresholds in dimension 4. The nature of the singularity is more complicated if (m–1)(v–1) is even (e.g.m=3 in dimension 4). Results obtained in this case include an orthogonal decomposition of the scattering functionT with nonholomic eigenvalues of the form [1/2iln+b _i ()]^–1 [where =(m)²–s andb _i is uniform around =0] and a related infinite expansion ofT in powers of ln involving an on-shell irreducible kernelU which is the analogue for (m–1)(v–1) even of Zimmerman'sK-matrix.     

Stability of uniformly driven domain walls

An infinite ferromagnetic medium with orthorombic crystal field anisotropy and with a constantdc field applied along the easy axis is considered in the framework of micromagnetics. It is shown that in the presence of Gilbert damping the uniformly driven plane domain wall (Walker wall) with positive Döring mass is linearly stable for any strengthH of the applied field below a critical valueH ₀, where it connects to an unstable wall configuration with negative Döring mass. The critical fieldH ₀ is lower than the existence limitH _W (Walker limit) of the solitary travelling-wave type domain wall solutions, and represents the threshold of the field regionH _{0 W} where negative wall mobilities occur. The instability atH=H ₀ is associated with a nonuniform localized relaxation mode (corrugating mode) of the plane domain wall. If coupling to the external circuit is taken into account, negative-mobility walls also become unstable against uniform perturbations for sufficiently small circuit resistance.Work supported by the Swiss National Science Foundation     

Conserved moments in nonequilibrium field dynamics

We demonstrate with the example of Cahn-Hilliard dynamics that the macroscopic kinetics of first-order phase transitions exhibits an infinite number of constants of motion. Moreover, this result holds in any space dimension for a broad class of nonequilibrium processes whose macroscopic behavior is governed by equations of the form /t = W(), where is an order parameter,W is an arbitrary function of , and is a linear Hermitian operator. We speculate on the implications of this result.     

Long-wave optical absorption in electron-bombarded GaAs

The absorption spectra of n- and p-type GaAs bombarded with 2-MeV electrons at T=300K were studied in the spectral range from 0.2 eV to Eg. It was found that shallow radiation-defect levels E_c – 0.01 eV and E_c + (0.06–0.1) eV were formed. The structureless character of the absorption in the region h < Eg in electron-bombarded gallium arsenide specimens was shown to be due to the distinctive features of photoionization of deep levels and the strong electron-phonon interaction in this material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 93–97, July, 1981.     

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.     

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.     

Some results for the exponential interaction in two or more dimensions

We show that for the regularized exponential interaction :e : ind space-time dimensions the Schwinger functions converge to the Schwinger functions for the free field ifd>2 for all or ifd=2 for all such that ||>₀.Partially sponsored by the I.H.E.S. through the Stiftung Volkswagenwerk     

Dispersion of Singularities of Solutions for Schrödinger Equations

We consider the singularities of solutions for the Schrödinger evolution equation associated with where Q is a d×d real symmetric matrix with the eigenvalues ₁,,_d, and WC(R^d,R) satisfies W(x)=o(|x|²) as |x|. Under additional conditions, we show the dispersion of microlocal singularities of solutions due to the principal symbol in all directions at time and in the nondegenerate directions at t. We also show the weaker dispersion of microlocal singularities of solutions due to the subprincipal symbol W in the degenerate directions at t if W satisfies W(x)=O(|x|¹⁺) as |x| for some 0<<1 and additional conditions. In particular, we prove the dispersion of microlocal singularities of solutions at resonant times when H is a perturbed harmonic oscillator.Partly supported by Grand-in-Aid for Young Scientists (B) 14740110, Japan Society of the Promotion of Science; and Mathematical Sciences Research Institute in BerkeleyDedicated to Professor Mitsuru Ikawa on his sixtieth birthday     

Logically independent von Neumann lattices

Three definitions of logical independence of two von Neumann latticesP₁,P₂ of two sub-von Neumann algebras ₁, ₂ of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P₁, 0 B P₂. Propositions relating logical independence ofP₁,P₂ toC ^*-independence,W ^* independence, and strict locality of ₁, ₂ are presented.     

Baryon decays and gamma-spectroscopy of hypernuclei

The applicability of (K ^–,^–) - and (K ^–,^– N)-reactions on^13,14C and^14,15N nuclei to the study of -transitions in primary and daughter -hypernuclei is discussed. The intensity of -deexcitation of ¹³C state |S ¹²C(15·11 MeV; 1⁺1): 1/2⁺ has been shown to be comparable with the intensity of baryon decay. Isospin selection rules are used to distinguish excitation energy ranges of primary hypernuclei, where the identification of the secondary -lines is probable.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

One criterion of semigroup product convergence

Let exp(-tA) and exp(-tB) be C ₀ contraction semigroups on both K and , where K is a Hilbert space and is a reflexive Banach space such that the linear space K is dense both in K and . Let ^* be a dual pair of Banach spaces. In this paper we study some properties of infinitesimal operators of these semigroups. We show that under suitable assumptions there is some connection between the form-sum A+B and a closure of A ₁+B₁, where -A ₁ is an infinitesimal operator of C ₀ contraction semigroup exp(-tA ₁) which is the extension by continuity on of C ₀ contraction semigroup exp(-tA) Kin . In particular we give some criterion of an m-accretive closability A ₁+B ₁ which may be applied for example to the Schrödinger operators acting in suitable L ^p-spaces. Also this criterion together with properties of semigroups under consideration results in the establishment of the Lie-Trotter formulae.     

Asymptotic Behaviour for Critical Slowing-Down Random Walks

The jump processes W(t) on [0, [ with transitions ww at rate bw (0<1, b>0, >0) are considered. Their moments are shown to decay not faster than algebraically for t, and an equilibrium probability density is found for a rescaled process U=(t+)^– W. A corresponding birth process is discussed.     

Anomalies and curvature ofW manifolds

We study the holomorphic structure of certain complex manifolds associated withW algebras, namely, the flag manifoldsW /T andW ₁₊/T ₁₊, and the spacesW /SL(),R) andW ₁₊/GL(,R), whereT andT ₁₊ are the maximal tori inW andW ₁₊. We compute their Ricci curvature and show how the results are related to the anomaly-freedom conditions forW andW ₁₊. We discuss the relation of these manifolds with extensions of universal Teichmüller space.Supported in part by the U.S. Department of Energy, under grant DE-AS05-81ER40039Supported in part by the U.S. Department of Energy, under grant DE-FG03-84ER40168     

On the Large-Distance Behavior of Correlations for a Hierarchical N-Component Classical Vector Model in Three Dimensions

We consider the correlation functions for a hierarchical N-component classical vector model in three dimensions. For N = , we find explicitly the eigenvalues and global eigenfunctions of the linearized renormalization group transformation. In a very direct way, this yields the correlation functions for the N = model. In particular, we check that the two-point function has canonical decay.     

The equation curl 73-173-173-1(x)=0 in quantum field theory

In one time and arbitrarily many space dimensions we obtain necessary and sufficient conditions for the existence of a local operator solution of the equation _v =W _v . Here the given local fieldsW _v satisfy _µ W _v - _v W _µ=0 and the spectrum of the two point function (,W _µ(x)W _v (y)) is assumed to have a mass gap.Research supported in part by Stiftung Volkswagenwerk and the Alfred P. Sloan Foundation.On leave from II. Institut für Theoretische Physik der Universität Hamburg, Germany.