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.     

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.     

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.     

Generalized Stefan-Boltzmann law

Thermodynamics arguments have been employed to derive how the energy density depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = ( –1), where is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expression = T/( –1), where is a constant. This result also appears naturally in the framework of general relativity for spacetimes with constant spatial curvature. Some particular cases are vacuum (p = –), cosmic strings (p= –1/3), radiation (p = 1/3), and stiff matter (p = ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions.     

Heavy-mesons exchange and the backward deuteron electrodisintegration

Backward electrodisintegration of the deuteron is calculated using an exchange-current operator containing , , , , , , andA ₁ exchanges. The deuteron and¹S₀ np wave functions are derived from the Bonn OBEPs. For completeness, we introduced theA ₁-meson exchange into the OBEP's as well. As a consequence, the value ofD-state probabilityP _D is increased by 0.2%–0.8%. The computed cross sections are compared with new data.Partially supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

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.     

Quantum Pushdown Automata

Quantum automata are mathematical models for quantum computing. We analyze the existing quantum pushdown automata, propose a q quantum pushdown automata (qQPDA), and partially clarify their connections. We emphasize some advantages of our qQPDA over others. We demonstrate the equivalence between qQPDA and another QPDA. We indicate that qQPDA are at least as powerful as the QPDA of Moore and Crutchfield with accepting words by empty stack. We introduce the quantum languages accepted by qQPDA and prove that every -q quantum context-free language is also an -q quantum context-free language for any (0, 1) and (0, 1).     

The theory of melting in heteropolymers. I. Random chains

A method is developed for the calculation of the ground-state melting curves ( _o vs.T) for random, infinite heteropolymers. Here _o is the ground-state value of the fraction of melted links ( _o in the strong cooperativity approximation). It is shown that the differential melting curves (d /d T vs.T) can have a fine structure in the form of several peaks on the bell-shaped main curve. Positions, magnitudes, and widths of these peaks are estimated. The accidental fine structure of melting curves, which is caused by a finite length of the polymer, is briefly discussed.Work supported in part by NSF Material Research Laboratory at Case Western Reserve University.Part of this work was submitted to the faculty of the Graduate School at SUNY Buffalo in partial fulfillment of the requirements for the Ph.D. degree.     

Distribution of nuclear quadrupole splittings in amorphous materials and the topology of the (Vzz, η)-parameter space

In structural investigations of amorphous materials by determination of nuclear quadrupole splittings, the connectivity of the region of non-zero probability density in the space of the splitting parameters V_zz and is important. The conventional presentation of the parameter plane conceals the continuous connection between regions of positive and negative V_zz via the common boundary defined by =1. A new conceptual view of the (V_zz, )-plane is proposed which clearly expresses its topological structure.     

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).     

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.     

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.     

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.     

Intramolecular energy transfer in compounds with two 1-pyrenoate groups separated by methylene spacers

Steady-state fluorescence anisotropy (r) and fluorescence lifetime () measurements have been used to study the efficiency of nonradiative singlet energy transfer as a function of alkane size in 1-pyrenecarboxylic acid alkanediyl esters (as a function ofm in Py-COO-(CH₂) _m -OOC-Py, where Py denotes pyrene substituted in the 1-position, andm=2–6). Experiments were performed in media of different viscosity, , obtained by changing the temperature (from –20 to 40°C) of dilute solutions in ethylene glycol and by examination of the compounds in a solid matrix of poly(methyl methacrylate) (PMMA) at ambient temperature. The Py-COO-(CH₂)_m-OOC-Py exhibit intramolecular excimer emission in ethylene glycol at these temperatures, but the intensity of this emission is much lower than when these compounds are placed in common solvents of lower . The values of indicate that excitation hopping or intramolecular energy transfer takes place between the chromophores attached to the ends of the alkane bridges. Values ofr obtained by the extrapolationsT/0 orT/0 in ethylene glycol, as well as the values obtained in the rigid matrix of PMMA, show very little dependence onm. A theoretical conformational analysis, using the rotational isomeric state (RIS) model, was also performed. The combination of the experimental results forr in the media of high with the theoretical (RIS) analysis produces an estimated value of 21 ±2 Å for the Förster radius in Py-COO-(CH₂)_m-OOC-Py.     

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.     

Sensitivity of spinI=5/2 perturbed-angular-correlation measurements to combined magnetic-dipole and electric-quadrupole hyperfine interactions

To design, analyze, and interpret perturbed-angular-correlation (PAC) experiments, the theory of the combined nuclear-magnetic-dipole and nuclear-electric-quadrupole interaction is applied. The applications involve polycrystalline sources that contain spinI=5/2 intermediate-quantum-level PAC probes. Frequenciesw _kk , amplitudesa _kk , and perturbation functionsG ₂₂ (t) are calculated for various values of the combined-interaction parameters, , and, wheny=w _L /W _Q is fixed at 30. For relatively large values ofy, the weak shift in them-state energies caused by the electric-quadrupole interaction generally produces a large change in the resulting perturbation function, and the effect is sensitive to the specific values of the parameters, , and. This sensitivity arises because the weak shift inm-state energies produces heterodyning. Moreover, this analysis indicates that PAC measurements of combined interactions in highly-distorted crystals (W _Q 0 and0) can provide potentially more information than previously thought. This analysis strongly suggests that more experimental investigations should be performed on highly-distorted crystals.     

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.     

Collision term of the Fokker Planck equation in strong external magnetic field

The collision term of the Fokker-Planck-type magnetized kinetic equation is approximated for an electron-ion plasma in a strong external uniform magnetic field. The collision term is evaluated explicitly in the case of unmagnetized Maxwellian ions for 1<= _e / _pi 2<. It is shown that the dominant effects are determined by the parameter ln (/) which replaces the Coulomb logarithm ln in the components of the diffusion coeficientD.     

Interpretation of the a0(980) meson as a four-quark system

Quantum chromodynamics methods are used to calculate the section of the reaction a₀ ⁰ with formation as an intermediate state of the meson a₀(980), which is interpreted as a bound state of two quark-antiquark pairs, formed upon dissociation of two virtual photons, with which an electron and positron are exchanged in incident e^–- and e⁺-beams. It is shown that the a₀ 2⁰ decay is significantly more suppressed than the a₀ ⁰ decay.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 19–23, July, 1991.