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.     

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.     

On the Gibbsian Nature of the Random Field Kac Model Under Block-Averaging

We consider the Kac–Ising model in an arbitrary configuration of local magnetic fields = , in any dimension d, at any inverse temperature. We investigate the Gibbs properties of the 'renormalized' infinite volume measures obtained by block averaging any of the Gibbs-measures corresponding to fixed , with block-length small enough compared to the range of the Kac-interaction. We show that these measures are Gibbs measures for the same renormalized interaction potential. This potential depends locally on the field configuration and decays exponentially, uniformly in , for which we give explicit bounds. The construction of the potential is based on a high temperature-type cluster expansion.     

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.     

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.     

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.     

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.     

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.     

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 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.     

Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities

The eight-vertex model is equivalent to a solid-on-solid (SOS) model, in which an integer heightl _i is associated with each sitei of the square lattice. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2K, and involve a variable parameter . Here we begin by showing that the hard hexagon model is a special case of this eight-vertex SOS model, in which =K/5 and the heights are restricted to the range 1l _i4. We remark that the calculation of the sublattice densities of the hard hexagon model involves the Rogers-Ramanujan and related identities. We then go on to consider a more general eight-vertex SOS model, with =K/r (r an integer) and 1l _ir–1. We evaluate the local height probabilities (which are the analogs of the sublattice densities) of this model, and are automatically led to generalizations of the Rogers-Ramanujan and similar identities. The results are put into a form suitable for examining critical behavior, and exponents, , are obtained.Supported by the Guggenheim Foundation and in part by the National Science Foundation, grant MCS 8201733.     

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     

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.     

The C1 Σ +-B1-Σ + amplified spontaneous emission in CO

The first observation of the amplified spontaneous emission (ASE) from the RydbergC ^{1 +}( = 0) state of CO is reported. When theC ^{1 +}( = 0) state was populated through the two-photon excitation, infrared radiation near 2.0 m was ejected in forward as well as backward directions along the laser propagation. The assignment as theC ^{1 +}( = 0) B ^{1 +}( = 0) transition was confirmed. Several characteristics of ASE from theC ^{1 +}( = 0) state are presented.This work was supported by the Morino Foundation, a Grant-in-Aid (No. 07640697) and that on Priority-Area-Research Photoreaction Dynamics (No. 07228268) from the Ministry of Education, Science, Sports and Culture, Japan.     

Spectral characteristics for a fiber grating external cavity laser

A numerical investigation has been carried out on the influence of the antireflection (AR) coating of laser, the coupling efficiency of laser and fiber (), and the reflectivity of fiber grating (R _g) on the side-mode suppression ratio (SMSR) of the fiber grating external cavity laser (FGECL). The FGECL was fabricated by the assembly of the multimode Fabry–Perot (FP) laser chip and fiber grating. The results showed that the FGECL with a lower AR coating, higher and R _g exhibited a better SMSR. A comparison of the SMSR dependence on the and R _g showed that SMSR increased more rapidly with increasing than SMSR for R _g. These spectral characteristic studies of the SMSR dependence on the device parameters of the AR coating, , and R _g may provide useful device designs for the practical fabrication of a FGECL for use in dense wavelength division multiplexing (DWDM) applications.     

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).