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 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.     

Group velocity difference effect on incoherent sum-frequency generation spectrum

The spectral distribution of optical sum-frequency generation (SFG) by incoherent non-linear mixing of two chaotic beams with identical spectral width is calculated theoretically in the first approximation of the iterative method including dispersion of the non-linear medium and the difference between the group velocity of the input beams. It is shown that for the same group velocities (=0) of the input beams in non-linear medium the resultant field has a spectral width narrower than , and if a phase mismatch is present the spectral maximum of the resultant field is shifted towards lower or higher frequencies according to the sign of the phase mismatch. If the input beams have different group velocities (0) in the non-linear medium, then the spectral distribution of SFG is strongly dependent on . For small the spectral distribution of SFG is the same irrespective of . For large the difference in group velocities broadens the spectrum of SFG and for very large differences in group velocity the SFG has a spectral width identical to that of the input beams.     

From where do quantum groups come?

The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other () expressing the quantum groups as deformation of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the -deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.Dedicated to Asim Barut with all our friendship.     

Basic Properties of Quantum Automata

This paper develops a theory of quantum automata and their slightly more general versions, q-automata. Quantum languages and -quantum languages, 0<1, are studied. Functions that can be realized as probability maps for q-automata are characterized. Quantum grammars are discussed and it is shown that quantum languages are precisely those languages that are induced by a quantum grammar. A quantum pumping lemma is employed to show that there are regular languages that are not -quantum, 0<1.     

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.     

Quantum Automata: An Overview

Quantum state machines are introduced.Amplitudes of computational paths, computational bases,superposition states, and evolution operators arediscussed. The main part of the paper develops a theoryof quantum automata and their slightly moregeneral versions, q-automata. Quantum languages and-quantum languages, 0 < 1, arestudied. A method is given for reducing the size of thestate space. Functions that can be realized as probabilitymaps for q-automata are characterized. Quantum gates arediscussed. A quantum pumping lemma is employed to showthat there are regular languages that are not -quantum, 0 < 1. The papercloses with a list of open problems.     

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 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 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.     

The analytic structure of the anomalous dimension of the four-gluon operator in deep inelastic scattering

The phenomenology of the pseudoscalar (1440) meson (also known as l) is discussed in a simplified , l mixing scheme in which the is assumed to have no glueball component. The parameters of the model are quite well constrained from the and two-photon decays. First it is shown that the scheme is in rather good general agreement with (almost) all the available data. Then a number of testable predictions concerning decays involving the iota are made. The iota turns out to be largely a glueball in this model.     

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 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.     

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.     

Theoretical Study for Wavelength Conversion of Cascaded Second-Order Nonlinearity in Silica Fiber

In this paper, A novel wavelength divison multiplexing (WDM) nets is proposed by use of cascaded second-order nonlinearities (⁽²⁾:⁽²⁾) in the D-fiber grating after periodically thermal/electric-field poling, and is theoretically analyzed for the first time. The coupled mode equations of the ⁽²⁾:⁽²⁾ nonlinearities are derived, and the analytic expressions for the electric-field amplitude of converted light wave and the conversion efficiency are obtained under the small signal approximation, which are well consistent with numerical calculations. Both analytic expressions and numerical results show that, under the phase matching, is proportional to the logarithm of the square of pump light power, and the 4th power of the grating length L and the second-order nonlinearity d. The calculated results also show that and of this fiber grating can be reached over -17dB and 120nm, respectively. With the increase of L, increases rapidly while decreases quickly. The results of simulated calculations and theoretical analysis show that the cascaded ⁽²⁾:⁽²⁾ process is different from quasi-phases-matched difference-frequency generation.     

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.     

Phonon assisted quantum diffusion in a periodic potential

We study the diffusion of a quantum heavy particle moving in a one dimensional strongly corrugated periodic potential, and interacting with a phonon bath.By integrating out the phonons degrees of freedom we derive an effective action functional for the particle, which includes a non-local self-interacting term whose strength is proved to be the classical friction coefficient .Using an instanton approach we express the velocity-velocity correlation function, and thus the mobility, of the brownian particle in terms of the charge density-density correlation function of a classical Coulomb gas, which in the strong corrugation limit has a very low fugacity.By making a virial expansion in the gas fugacity we evaluate the static mobility of the brownian particle as a function of the temperature, and we find two different behaviours: a diffusive behaviour at low friction, where decreases withT, and a localised behaviour at high friction, where increases withT.The cross-over between the two régimes takes place at a critical friction ₀, corresponding to the Kosterlitz-Thouless transition for the Coulomb gas.     

Invariance principle for a solid-on-solid interface model

A stochastic process describing the behavior of the solid-on-solid interface in a strip of widthL is studied. The invariant and reversible measure for the process is the Gibbs state with HamiltonianH|(x)–(x+1)|. Under free boundary conditions, we show that the height of the moving interface at any site converges, when suitable renormalized, to Brownian motion with a diffusion coefficient proportional toL ^–1.     

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 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.