The influence of a surface on Ising and conjugate model spin correlations atT=T c

We calculate rigorously the two-point correlation function in the 2-d Ising model on a quasi-cylindrical lattice at the critical temperatureT _c .The scaling predictions for the surface critical exponents = 5/8, = 1 are confirmed and the change from surface to bulk behavior is studied. By a correspondence relation the results are mapped to the conjugate model, a subcase of the 8-vertex model. We find in this model = 5/4, = 2.     

Kinetics of small perturbations in an isotropic world

Long-wavelength gravitational perturbations are studied in an isotropic expanding universe filled with an ultrarelativistic gas. A kinetic study in the collisionless approximation shows that scalar and vector perturbations which appear at a time ₀ 1/n, where N is the wave vector and is the time coordinate x⁴, grow if the perturbation of the macroscopic momentum density of the gas at time ₀ is nonvanishing. The growth continues until the time ₁=27₀, at which the perturbation of the macroscopic momentum density of the gas vanishes. A solution is also derived for tensor perturbations in the limit n 1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 37–45, April, 1978.     

The role of weak resonances in ac-driven Brownian motion and rate processes

In recent paper a theory of the effect of ac drive on the distribution function and escape rate of a multidimensional underdamped nonlinear oscillator subject to thermal damping and noise was suggested. The approach was based on describing the dynamics in terms of isolated nonlinear resonances and supposing that the noise intensity is asymptotically small,0. In the present work, the case of finite is considered, when weak resonances cannot be described asymptotically. It is shown that forp _r/1(p _r, is the resonance width) the asymptotic results are valid. Forp _r/1, a semiphenomenological theory is developed.     

Metastates in Disordered Mean-Field Models II: The Superstates

We continue to investigate the size dependence of disordered mean-field models with finite local spin space in more detail, illustrating the concept of superstates as recently proposed by Bovier and Gayrard. We discuss various notions of convergence for the behavior of the paths (t_[tN]()) _{t(0, 1]} in the thermodynamic limit N. Here _n () is the Gibbs measure in the finite volume {1,..., n} and is the disorder variable. In particular we prove refined convergence statements in our concrete examples, the Hopfield model with finitely many patterns (having continuous paths) and the Curie–Weiss random-field Ising model (having singular paths).     

The special status ofη 1 in QCD

On the basis of the approximate vanishing of the singlet axial charge of the nucleon, it is argued that ₁ should decouple from all hadrons constructed out of the constituentu, d ors quarks in theU(3) _L ×U(3) _R chiral limit for largeN _c . Furthermore ₁ should dominate the processesJ/, . A phenomenological analysis of the and couplings to many hadronic states is consistent with these results.     

The mixing of elementary particles and the mass formula for bosons

The paper deals with the possibility of the existence of — ₂ mixing and the question of the Gell-Mann-Okubo formula (GOF) for bosons.     

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 .     

The η N interaction cross section near the S11N*(1535) resonance

Calculations are presented for the integral cross-sections ofN N, N N incorporating the one-particle intermediate state, theS₁₁N * resonance; cross-sections are given for kinetic energies of the meson from 0 to 200 MeV for various values of the width of the resonance. The calculated cross-sections agree with experiment for r 160 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 119–122, July, 1973.We are indebted to our colleagueat the Institute G. N. Radutskom forvaluable advice and discussion on this paper.     

On the directional dependence of composite field operators

The Wilson expansion of the field operator productA ₁(x ₁)A ₂(x ₂) may be used to define composite operators which are local with respect to 1/2(x ₁+x ₂) and depend in addition on a vector proportional to the distancex ₁–x ₂. It is proved that the composite operators are polynomials in , for fixed ² 0, and that their dependence on ² only involves powers of ² and lg².This work was supported in part by the National Science Foundation Grant No. GP-25609.     

Levinson's Theorem for the Schrödinger Equation in One Dimension

Levinson's theorem for the one-dimensional Schrödinger equation with asymmetric potential which decays at infinity faster thanx ^–2 is established by theSturm-Liouville theorem. The critical case where the Schrödinger equation hasa finite zero-energy solution is also analyzed. It is demonstrated that the numberof bound states with even (odd) parityn ₊(n _–) is related to the phase shift ₊ (0)[_– (0)] of the scattering states with the same parity at zero momentum as ₊ (0)+ /2 =n ₊ and _– (0) =n _– for the noncritical case, and ₊ (0) =n ₊ and_– (0) – /2 =n _– for the critical case.     

Nuclear quadrupole interaction of199mHg-ferrocenethiol complexes

We determined the^199mHg nuclear quadrupole interaction (NQI) by time differential perturbed angular correlation in the following ferrocenethiol complexes with mercury: ferrocenethiol (v _Q =1253(4) MHz, =0); 1,1-ferrocenedithiol (47%v _Q =1555(8) MHz, =0.13(2); 25%v _Q =726(19) MHz, =0.81(2); rest unspecific); 2-ferrocenyl-ethanethiol (v _Q =1306(6) MHz, =0.17(1)); and a 1, 1-bis (2-mercapto-propylthio)ferrocene oligomer (v _Q =1411(5), =0). All NQIs are rather large with small asymmetry parameters, indicating essentially linear S-Hg-S bonds. The only exception is the minority fraction in 1,2-ferrocenedithiol which suggests the formation of a 1,3-dithia-2-mercura[3]ferrocenophane.     

Analysis of the Photoproduction of η-Mesons on Protons in a Resonance Energy Range

A model of the photoproduction of -mesons on protons with energies from the reaction threshold to 2.5 GeV takes into account contributions to the amplitude of eleven nucleon resonances: S ₁₁(1535), S ₁₁(1650), P ₁₁(1440), P ₁₃(1720), D ₁₃(1520), D ₁₅(1675), F ₁₅(1680), F ₁₇(1990), G ₁₇(2190), G ₁₉(2250), and H ₁₉(2220) and of the background component comprising the nucleon pole and the exchange by vector mesons in the t-channel. Recent experimental data on cross sections and -asymmetry of the pp process measured from the reaction threshold to 1.1 GeV are used as a criterion of correctness of the model. Starting from photon energies of 1.7 GeV and higher, the cross section of the process depends strongly on the contribution of the -meson, that is, on the mechanism of action of vector mesons on the photoproduction amplitude and constants of vector meson coupling with -mesons and nucleons. The calculated cross sections and -asymmetry of the pp process at energies exceeding 1.4 GeV do not contradict the available experimental data.     

The ηHe scattering length revisited

The possible existence of -mesic nuclei poses an interesting and still open issue of research. Since the occurence of such -nucleus bound states is reflected in the corresponding -nucleus scattering length, we critically review the present knowledge for the ³He system. Specifically, we scrutinize the available experimental information for the reaction p + d + ³He which is commonly used to extract the ³He scattering length. We point out several striking discrepancies between the various measurements. Subject to those inconsistencies, we deduce a value a = | 4.3±0.3| + i(0.5±0.5) fm.     

The S-matrix for abstract scattering systems

Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()- _HS ² d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation.     

Integrability conditions for Killing spinors

The conditions for the existence of solutions ofD _µ=±c_µ are discussed. In general, it is not sufficient to consider only the first integrability condition [D _µ,D _v ]=–2c ²_{µv}; in particular, the second integrability condition is needed to explain why, in certain cases, only for one choice of sign does a solution exist. The Killing spinor-tensors, as defined by Walker and Penrose, are shown to be the spinorial equivalent of conformal Killing tensors. Their relationship to the Killing spinors and spinor-vectors used in supergravity, is given.On leave from the Institute for Theoretical Physics of the State University of New York at Stony BrookWork supported in part by the U.S. Department of Energy under Contract No. DEAC-03-81-ER 40050 and Weingart Fellowship     

Melnikov's criterion for nondifferentiable weak-noise potentials

The stationary probability density of Fokker-Planck models with weak noise is asymptotically of the form exp[–1 /(q)]. If is smooth, it satisfies a Hamilton-Jacobi equation at zero energy and can be interpreted as the action of an associated Hamiltonian system. Under this assumption, has the properties of a Liapounov function, and can be used, e.g., as a thermodynamic potential in nonequilibrium steady states. We consider systems having several attractors and show, by applying Melnikov's method to the associated Hamiltonian, that in general is not differentiable. A small perturbation of a model with differentiable leads to a nondifferentiable . The method is illustrated on a model used in the treatment of the unstable mode in a laser.     

Positive similarity solutions for a discrete velocity boltzman coagulation-fragmentation model

We consider the coagulation-fragmentation model of Slemrod and coworkers which is essentially the two-dimensional Broadwell model including inelastic collisions. We construct two classes of similarity solutions (variable =x -t), positive for (- , ): the Rankine-Hugoniot solutions and the scalar Riccati similarity solutions. Previous solutions were built up with positivity along half of thex-axis. For the two classes, we determine in the parameter space, building up the solutions, domains corresponding to positive solutions.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Induced geometry and confinement

A classical, Poincaré invariant dynamical system is developed which contains, besides the natural metric _v , an induced metricg _v that is generated by a real scalar dynamical field. It is shown that scalar fields whose dynamics are governed by the induced metric can be consistently introduced. Also, point particles which follow timelike quasi-geodesic trajectories can be introduced. The reaction forces acting ong _v due to the presence of these fields and particles are computed. A discussion of causality and geometrical confinement is given.     

Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities

The restricted eight-vertex solid-on-solid (SOS) model is an exactly solvable class of two-dimensional lattice models. To each sitei of the lattice there is associated an integer heightl _i restricted to the range 1l _i r–1. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2K, and involve a parameter. In an earlier paper we considered the case=K/r. Here we generalize those considerations to the case=sK/r, s an integer relatively prime tor. We are again led to generalizations of the Rogers-Ramanujan identities.