Finite-temperature perturbation theory for the random directed polymer problem

We study the random directed polymer problem—the short-scale behavior of an elastic string (or polymer) in one transverse dimension subject to a disorder potential and finite temperature fluctuations. We are interested in the polymer short-scale wandering expressed through the displacement correlator 〈[δu(X)]²〉, with δu(X) being the difference in the displacements at two points separated by a distance X. While this object can be calculated at short scales using the perturbation theory in higher dimensions d > 2, this approach becomes ill-defined and the problem turns out to be nonperturbative in the lower dimensions and for an infinite-length polymer. In order to make progress, we redefine the task and analyze the wandering of a string of a finite length L. At zero temperature, we find that the displacement fluctuations 〈[δu(X)]²〉 ∝ LX ² depend on L and scale with the square of the segment length X, which differs from a straightforward Larkin-type scaling. The result is best understood in terms of a typical squared angle 〈α²〉 ∝ L, where α = ? _x u, from which the displacement scaling for the segment X follows naturally, 〈[δu(X)]²〉 ∝ 〈α²〉 X ². At high temperatures, thermal fluctuations smear the disorder potential and the lowest-order results for disorder-induced fluctuations in both the displacement field and the angle vanish in the thermodynamic limit L → ∞. The calculation up to the second order allows us to identify the regime of validity of the perturbative approach and provides a finite expression for the displacement correlator, albeit depending on the boundary conditions and the location relative to the boundaries.     

Flat connections on a punctured sphere and geodesic polygons in a Lie group

Let G be a compact connected Lie group and X denote the complement of n distinct points of the sphere S². The space of isomorphism classes of flat G connections on X with fixed conjugacy class of holonomy around each of n punctures has a natural symplectic structure. This space is related to the space of geodesic n-gons in G. The space of geodesic polygons in G has a natural 2-form. It is shown that this 2-form coincides with symplectic form on the space of isomorphism classes of flat G-connections on X satisfying holonomy condition at the punctures.     

Metal-insulator transition in the mercury-xenon system

A gradual conductivity transition as the atomic composition (X) of Hg/Xe samples is varied at 6 K has been observed. The temperature coefficient of the conductivity (TCC) follows the power law TCC α (X₀ ? X)^{2.4 ± 0.4} with X₀ = 0.790 ± 0.005, the conductivity at X₀ being 400 ± 50 (Ω-cm)^-1. The gradual conductivity transition is interpreted in terms of a Mott-Anderson metal-nonmetal transition smeared out by thermally activated hopping.     

The missing mass squared dependence of the average charged particle multiplicity in the reaction K+p → KoX++ from 5–16 GeV/c

The average charged particle multiplicity, 〈n_ch(M_X²)〉, in the reaction K⁺p→K^oX⁺⁺ is studied as a function of the mass squared, M_X², of the recoil system X and also as a function of the K^o transverse momentum, p_T, at incident momenta of 5.0, 8.2 and 16.0 GeV/c. The complete data samples yield distributions which are not independent of c.m. energy squared, s, They exhibit a linear dependence on log (M_X²_X/M_o²)[M_o²=1 GeV²] with a change in slope occurring for M_X²≈s/2, and do not agree with the corresponding distributions of 〈n_ch〉 as a function of s for K⁺ p inelastic scattering. Sub-samples of the data for which K^o production via beam fragmentation, central production and target fragmentation are expected to be the dominant mechanisms show that, within error, the distribution of 〈n_ch(M_X²)〉 versus M_X² is independent of incident momentum for each sub-sample separately. In particular in the beam fragmentation region the 〈n_ch(M_X²)〉 versus M_X² distribution agrees rather well with that of 〈n_ch〉 versus s for inelastic K⁺p interactions. The latter result agrees with recent results on the reactions pp → pX and π^?p → pX in the NAL energy range. Evidence is presented for the presence of different production mechanisms in these separate regions.     

Selective effects of homogeneous and heterogeneous reactions in the system N21-CO

In the system N₂¹-CO, effects arising only from the reactions in the homogeneous phase have been isolated in a reactor with inert walls. After an induction period of 0.13 s, they involve a stationary rate of enhancement of N₂(B³Π_g) and N(⁴S) concentrations according to the reactions N₂(X¹Σ_g⁺)_v¹+CO→ CO(X¹Σ⁺)_v1 + N₂(X¹Σ_g⁺ and CO(X¹Σ⁺)_v1 + N₂(A³Σ_u⁺) → N (⁴S) + N(⁴S) + CO(X¹Σ⁺).In a reactor with active walls, both the above reactions in the homogeneous phase and heterogeneous reactions due to CO adsorbed on the walls are involved according to CO_ads + N₂(X¹Σ_g⁺)_{v1 ads or not} → CO(X¹Σ⁺)_v1 + N₂(X¹Σ_g⁺ and N(⁴S) + N(⁴S) + CO_ads → N₂(X¹Σ_g⁺) + CO(X¹Σ⁺)N(⁴S) + CO_ads → N₂(X¹Σ_g⁺) + CO(X¹Σ⁺). In this case, the rate of enhancement is not stationary. Furthermore, for cylindrical reactors with large diameters, the two types of reaction do not interact and their effects are additive.     

Franck-Condon factors and r-centroids for the RKRV potential (A2IIr → X2Σ+ transition of BeCl)

Turning points of the vibrating BeCl molecule in the A²II_r and X²Σ⁺ electronic states are evaluated using the RKRV potential. The Franck-Condon factors and r-centroids have been computed for the A²II_r → X²Σ⁺ transition using wave functions appropriate to the RKRV potential curve. The results are consistent with the intensity distribution in the vibrational bands for the specified transition. The sequence difference Δ$\text{r}$ remains approximately constant for the r-centroids.     

Unitary and singular value decompositions of parametric processes in fibers

Parametric (four-wave mixing) processes in fibers, driven by one or two strong pumps, couple the evolution of two weak sidebands. These processes are governed by the (spatial) evolution equations d_zX=AX+BX^†t and their associated input-output relations X(z)=M(z)X(0)+N(z)X^†t(0), where X is the (sideband) amplitude vector, A and B are coefficient matrices, and M and N are transfer matrices. In principle, one can use unitary decompositions (UDs) to facilitate the mathematical analyses of evolution equations, or singular value decompositions (SVDs) to facilitate the physical interpretations of input-output relations (by diagonalizing them). In these notes, the SVD method is reviewed, and applied to studies of modulation interaction (MI), phase conjugation (PC) and Bragg scattering (BS). The UD method is also reviewed. It works for BS driven by continuous-wave (CW) or pulsed pumps. Although it works for MI and PC driven by CW pumps, it does not work for MI and PC driven by pulsed pumps (because the coefficient matrices are not simultaneously diagonalizable). Another decomposition method, based on eigenvectors of an extended coefficient matrix, and their adjoints, works for CW and pulsed pumps. Further work is required, to clarify the relation between the SVD and adjoint methods, and apply the latter method to processes of current interest.     

Algebraic determination of the metric from the curvature in general relativity

The general solution for a symmetric second-order tensorX of the equationX _e(a R ^e _b cd=0 whereR is the Riemann tensor of a space-time manifold, andX is obtained in terms of the curvature 2-form structure ofR by a straightforward geometrical technique, and agrees with that given by McIntosh and Halford using a different procedure. Two results of earlier authors are derived as simple corollaries of the general theorem.     

Reexamination of the vacuum ultraviolet emission spectrum of CO in the 950–1200 Å region

New spectrograms of CO below 1200 Å reveal that emission bands terminating on the high energy $\text{E}{}_0{}^1\text{Σ}{}^{\mathrm{+}}$ and ¹Π states plus most of the previously reported unidentified emission bands of CO actually originate from molecular nitrogen. Four new emission band systems in CO, tentatively identified as V¹Π-X¹Σ⁺, W¹Π-X¹Σ⁺, Y¹Σ⁺-X¹Σ⁺, and Z¹Σ⁺-X¹Σ⁺, have been observed. The corresponding T_v0′s are 98917, 102804, 99963, and 105724 cm^?1, respectively.     

The length and the relative length of tangent vectors of finsler spaces

We consider the length of a vector in a Finsler space with the fundamental function L(x,y). The length of a vector X is usually defined as the value L(x,X) of L. On the other hand, we have an essential tensor g_ij(x,y), called the fundamental tensor, and the concept of relative length |X_y| of X may be introduced by |X|_y^y = g_ij(x,y)XⁱX^j with re spect to a supporting element y. The question arises whether is L(x,X) the minimum of |X|_y or not? If there exists a supporting element y satisfying |X|_y < L(x,X), then a curve x(t) in the Finsler space will be measured shorter than the usual length, by integrating |dx/dt|_y with the field of such supporting element y(t) along the curve.     

Rotational Analysis of the A2Π → X2Σ+ visible band system of boron monoxide,BO

Seventeen bands of the A²Π → X²Σ⁺ system of ¹¹BO with v′ ≤ 8 and v″ ≤ 5, and 13 bands of the same system of ¹⁰BO with v′ ≤ 6 and v″ ≤ 4 have been photographed at high resolution and rotationally analyzed. No local perturbations, except for the already known perturbation of A²Π, v = 4 with X²Σ⁺, v = 17 in ¹¹BO have been found for either isotope. The constants obtained from least-squares fits of the line positions of individual bands have been merged for each isotope to obtain single-valued estimates. RKR turning points for the two electronic states are reported.     

The B3Π(0+) → X1Σ+ emission spectrum of 79BrF and 81BrF in the range 6250–8700 Å: Rotational analysis of bands in the v′ = 0, 1, 2, 3, 4 progressions,and merged molecular constants for the X1Σ+ and B3Π(0+) states

Sixteen emission bands of the B³Π(0⁺) → X¹Σ⁺ systems of ⁷⁹BrF and ⁸¹BrF have been analyzed rotationally. Measured line frequencies are fitted by least-squares to determine the rotational constants and origin for each band. The least-squares results for 0 ≤ v′ ≤ 4 and 4 ≤ v″ ≤ 12 are merged with constants from previously reported B ← X absorption and X-state microwave data. RKR potentials for the two states and Franck-Condon factors and r-centroids for the BrF (B-X) system are reported.     

Solid solution formation in the systems CuMIIIX2-AgMIIIX2 where MIII=Al,Ga, In and X2=S,Se

A study of solid solution formation in the systems CuAlX₂-AgAlX₂, CuGaX₂-AgGaX₂ and CuInX₂-AgInX₂, where X=S, Se, has shown that when M^III=Al and Ga, CuM^IIIX₂ and AgM^IIIX₂ were not completely miscible. The CuInX₂-AgInX₂ system, however, showed complete solid solubility. The limits of solid solubility are explained in terms of the c/a ratio, and the internal atomic coordinate u. The lattice constant a is a linear function of composition, while c bows upwards. This behavior is also discussed in terms of trends in 2-c/a.     

Radiative recombination in the helium sequence

Recombination coefficients for the reaction X^+m+1(1²S+e → X^+m(1¹S) + hv for the helium] sequence are calculated using recently obtained optical differential oscillator strengths for electron temperatures in the range 10 to 5 x 10⁴ K. The coefficients for the entire sequence are represented by a simple formula, which requires only the ionization potential of the members of the sequence.     

Investigating highly excited states of the 8Li isotope

Highly excited states of the ⁸Li isotope are sought in absorption reactions of π^? mesons stopped by ^10,11B isotopes. The ground and three excited states of the ⁸Li isotope are observed in inclusive measurements of reactions ¹⁰B(π^?, d)X and ¹¹B(π^?, t)X. The states with excitation energies E _x ≈ 8.7 and 10.1 MeV are observed for the first time in correlation measurements of reactions ¹⁰B(π^?, dt)X and ¹¹B(π^?, tt)X.     

Short-Range Characterization of the MeAr (Me=Zn, Cd) Ground-State Potentials from Fluorescence Spectra

First-time observed D1(¹Π)_v′=10→X0⁺(¹Σ) fluorescence in ZnAr, and A0⁺(³Π)_v′=4→X0⁺ and D1(¹Π)_v′=7,8→X0⁺ fluorescence in CdAr van der Waals (vdW) molecules were produced in a continuous supersonic molecular beam crossed with a pulsed dye-laser beam, following excitation of single vibronic levels. The dispersed fluorescence spectra displayed characteristic Condon internal diffraction (CID) patterns consisting of bound-free, reflection type, continuous spectra, and, in certain cases, bound-bound discrete features. An analysis of the A0⁺→X0⁺ and D1→X0⁺ bound-bound spectra indicates that Morse functions are adequate representations of the X0⁺ potential energy (PE) curves below their dissociation limits. In simulation of the A0⁺→X0⁺ and D1→X0⁺ bound-free spectra, the Morse, Lennard-Jones L-J(n−6), and Maitland-Smith M-S(n₀,n₁) functions were tested, and the respective M-S(11.3, 9.0) and M-S(10.6, 7.0) potentials were found to be good representations for the repulsive walls of the X0⁺ PE curves of ZnAr and CdAr, respectively, over the short range, R=2.45-4.38 Å (ZnAr) and R=2.85-4.31 Å (CdAr), of internuclear separations.     

A measurement of the electromagnetic form factor of the eta meson and of the branching ratio for the eta Dalitz decay

In an optical spark chamber experiment we have obtained a sample of 80 eta Dalitz decays (η → e⁺e^?γ) and have measured the eta electromagnetic form factor to be F(X) = 1.0?(0.22 ±0.45)X, where X=M_ee²/M_η², and the branching ratio (η→e⁺e^?γ/(η→π⁺π^?π⁰)= (0.0082 ± 0.0020).     

Intensity perturbation in the B2Σ-X2Σ band system of SrF

The intensity anomaly of the B²Σ-X²Σ system of SrF was analyzed based on the interaction between the A²Π and B²Σ states. The theoretical relative intensity was calculated from overlap integrals and spectroscopic constants previously obtained. Comparison between theoretical and observed intensities showed that the electronic transition moment of the B-X system is the same order of magnitude as that of the A-X system.     

Goldstino and sgoldstino in microscopic models and the constrained superfields formalism

We examine the exact relation between the superconformal symmetry breaking chiral superfield (X) and the goldstino superfield in microscopic models of an arbitrary Kahler potential (K) and in the presence of matter fields. We investigate the decoupling of the massive sgoldstino and scalar matter fields and the offshell/onshell-SUSY expressions of their superfields in terms of the fermions composites. For general K of two superfields, we study the properties of the superfield X after integrating out these scalar fields, to show that in the infrared it satisfies (offshell) the condition X³=0 and X²≠0. We then compare our results to those of the well-known method of constrained superfields discussed in the literature, based on the conjecture X²=0. Our results can be used in applications, to couple offshell the (s)goldstino fields to realistic models such as the MSSM.     

Ground-state energy and stability of three-particle coulomb systems versus the masses of the particles involved

The ground-state energy of three-particle Coulomb systems (trions) is investigated versus the masses of the particles involved. Variational calculations are performed for 34 asymmetric trions X^±Y^±Z^? consisting of electrons, muons, pions, kaons, nuclei of hydrogen isotopes and their antiparticles, as well as for more than 100 auxiliary three-particle systems involving particles of masses chosen arbitrarily. Wide bases of Laguerre exponential-polynomial functions depending on perimetric particle coordinates are used. Approximate analytic formulas for the ground-state energies of all trions X^±Y^±Z^? with arbitrary particle masses are constructed on the basis of the values found here for the energies of asymmetric trions and the values calculated previously for the energies of symmetric trions X^±X^±Z^?. Particle-mass regions are determined where trions are stable with respect to dissociation. In addition to symmetric trions X^±X^±Z^?, which are stable at any particle masses, asymmetric trions X^±X^±Z^? possess the stability property if the masses of the particles X and Y exceed the mass of the particle Z, where, by Z, we mean, for example, an electron, a muon, a pion, or a kaon. The t⁺d⁺p^? and t⁺d⁺d^? combinations of hydrogen nuclei and antinuclei are also stable with respect to dissociation. The general properties of the ground-state trion energy as a function of the particle masses are discussed.