Universality classes of self-avoiding fixed-connectivity membranes

We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. We simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we find the membrane to be flat for all temperatures: the size exponent in three dimensions is ν = 0.95(5) (Hausdorff dimension d _H = 2.1(1)). The single flat phase appears, furthermore, to be equivalent to the large bending rigidity phase of non-self-avoiding fixed-connectivity membranes --the roughness exponent in three dimensions is ξ = 0.63(4). This suggests that there is a unique universality class for flat fixed-connectivity membranes without attractive interactions. Finally, we address some theoretical and experimental implications of our work. Received 23 June 2000 and Received in final form 25 October 2000     

The Lie-Poisson structure of integrable classical non-linear sigma models

The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into ther-s-matrix formalism for non-ultralocal integrable models first discussed by Maillet. The matricesr ands are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrixc. It is proposed that all these Poisson brackets taken together are, representation conditions for a new kind of algebra which, for this class of models, replaces the classical Yang-Baxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed.Suported by the Deutsche Forschungsgemeinschaft, Contract No. Ro 864/1-1Supported by the Studienstiftung des Deutschen Volkes     

Über die Gleichstromleitfähigkeit flüssiger Kohlenwasserstoffe

The steady-state current-voltage characteristic of the d.c. conductivity was measured for several liquid hydrocarbons, as well as its dependence on electrode spacing and — material. A hopping model is proposed in order to interpret the results. The temperature dependence of the conductivity of every hydrocarbon obeys the law

$$\sigma = \sigma _1 + \sigma _2 = \sigma _{01} \exp ( - E_1 /kT) + \sigma _{02} \exp ( - E_2 /kT)$$     

从热释光曲线同时确定电子复合与俘获之比及陷阱深度

复合发光的本质是两种载流子的复合,但其衰减规律则视具体情况可以从一个极限(指数)变到另一个极限(抛物线),即复合发光是一个连续变化的过程。这主要取决于导带电子的行为,导带电子的行为可以用电子与离化发光中心复合与被陷阱俘获之比来表示。加热发光是在变化温度下的发光弛豫,它既与复合与俘获之比有关,还是陷阱深度的函数,因此在利用加热发光曲线测定陷阱深度时,要同时确定这两个参数。利用热释光动力学模型及其原理,对其发光过程进行了分析,解释了热释光过程既不是一个单分子过程也不是一个双分子过程,这两个过程实际是两个极端情形,都是近似。文章同时利用一些工具软件具体计算了ZnS:Cu, Co的陷阱深度及电子复合与俘获概率之比,精确的计算了这些参数,得n₀ =2.6, ε=0.86eV。     

Simultaneous measurement of the ratio R=B(t --> Wb)/B(t --> Wq) and the top-quark pair production cross section with the D0 detector at sqrt(s) = 1.96 TeV

We present the first simultaneous measurement of the ratio of branching fractions, R=B(t --> Wb)/B(t --> Wq), with q being a d, s, or b quark, and the top-quark pair production cross section sigma(tt[over]) in the lepton plus jets channel using 0.9 fb(-1) of pp[over] collision data at sqrt(s)=1.96 TeV collected with the D0 detector. We extract R and sigma(tt[over]) by analyzing samples of events with 0, 1, and > or =2 identified b jets. We measure R=0.97(+0.09)/(-0.08)(stat+syst) and sigma(tt[over])=8.18(+0.09)(-0.84)(stat+syst) +/- 0.50(lumi) pb, in agreement with the standard model prediction.     

Highly accurate H2 Lyman and Werner band laboratory measurements and an improved constraint on a cosmological variation of the proton-to-electron mass ratio

Transition wavelengths on a large set of H2 Lyman and Werner band spectral lines have been obtained at an accuracy of 5 x 10(-8), using a narrow band tunable extreme ultraviolet laser. The data are used to determine a constraint on a possible cosmological variation of the proton-to-electron mass ratio (mu=Mp/me) from a comparison with highly redshifted spectral data of quasistellar objects, yielding a fractional change in the mass ratio of Deltamu/mu=-0.5+/-3.6 x 10(-5) (2sigma), which would correspond to a temporal change of d/dt(Deltamu/mu)=-0.4+/-3.0 x 10(-15) per year (2sigma) if a linear cosmological expansion model is assumed.     

Indication of a cosmological variation of the proton-electron mass ratio based on laboratory measurement and reanalysis of H2 spectra

Based on highly accurate laboratory measurements of Lyman bands of H2 and an updated representation of the structure of the ground X 1sigma(g)+ and excited B 1sigma(u)+ and C 1pi(u) states, a new set of sensitivity coefficients K(i) is derived for all lines in the H2 spectrum, representing the dependence of their transition wavelengths on a possible variation of the proton-electron mass ratio mu = m(p)/m(e). Included are local perturbation effects between B and C levels and adiabatic corrections. The new wavelengths and K(i) factors are used to compare with a recent set of highly accurate H2 spectral lines observed in the Q 0347-383 and Q 0405-443 quasars, yielding a fractional change in the mass ratio of deltamu/mu = (2.4 +/- 0.6) x 10(-5) for a weighted fit and deltamu/mu = (2.0 +/- 0.6) x 10(-5) for an unweighted fit. This result indicates, at a 3.5sigma confidence level, that mu could have decreased in the past 12 Gyr.     

Weak and electromagnetic corrections to sin2 θ w in deep inelastic neutrino-nucleon scattering

The weak and electromagnetic corrections to deep inelastic neutrino scattering experiments are calculated. The results are used to determineθ _w from the ratios $$R_v = \frac{{\sigma _{nc} }}{{\sigma _{cc} }} and D_ - = \frac{{\sigma _{nc} - \bar \sigma _{nc} }}{{\sigma _{cc} - \bar \sigma _{nc} }}$$ It is found that the effect of the weak corrections is less than 1% and that electromagnetic corrections decrease the angle by about 3%.     

Coisotropic Submanifolds and Dual Pairs

The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma model are related to coisotropic submanifolds (a result announced in [math.QA/0309180]) and that the corresponding reduced phase space is a (possibly singular) dual pair between the reduced spaces of the given two coisotropic submanifolds. In addition the generalization to a more general tensor field is considered and it is shown that the theory produces Lagrangian evolution relations if and only if the tensor field is Poisson.     

Poisson Sigma Model on the Sphere

We evaluate the path integral of the Poisson sigma model on the sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kähler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.     

Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork that are such that the meshwork's energy is a function F(el)[A(xi)] not of the real microscopic membrane area A, but of a smoothed membrane's area A(xi), which corresponds to the area of the membrane coarse grained at the mesh size xi. We show that the meshwork modifies the membrane tension sigma both below and above the scale xi, inducing a steep crossover of amplitude deltasigma=dF(el)/dA(xi). The predictions of our model account for the fluctuation spectrum of red blood cell membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane areas. We also predict an observable tension jump for membranes decorated with polymer "brushes."     

Heuristic Relative Entropy Principles with Complex Measures: Large-Degree Asymptotics of a Family of Multi-variate Normal Random Polynomials

Let \(z\in \mathbb {C}\), let \(\sigma ^2>0\) be a variance, and for \(N\in \mathbb {N}\) define the integrals

$$\begin{aligned} E_N^{}(z;\sigma ) := \left\{ \begin{array}{ll} {\frac{1}{\sigma }} \!\!\!\displaystyle \int _{\mathbb {R}}\! (x^2+z^2) \frac{e^{-\frac{1}{2\sigma ^2} x^2}}{\sqrt{2\pi }}dx&{}\quad \text{ if }\, N=1,\\ {\frac{1}{\sigma }} \!\!\!\displaystyle \int _{\mathbb {R}^N}\! \prod \prod \limits _{1\le k<l\le N}\!\! e^{-\frac{1}{2N}(1-\sigma ^{-2}) (x_k-x_l)^2} \prod _{1\le n\le N}\!\!\!\!(x_n^2+z^2) \frac{e^{-\frac{1}{2\sigma ^2} x_n^2}}{\sqrt{2\pi }}dx_n &{}\quad \text{ if }\, N>1. \end{array}\right. \!\!\! \end{aligned}$$

These are expected values of the polynomials \(P_N^{}(z)=\prod _{1\le n\le N}(X_n^2+z^2)\) whose 2N zeros \(\{\pm i X_k\}^{}_{k=1,\ldots ,N}\) are generated by N identically distributed multi-variate mean-zero normal random variables \(\{X_k\}^{N}_{k=1}\) with co-variance \(\mathrm{{Cov}}_N^{}(X_k,X_l)=(1+\frac{\sigma ^2-1}{N})\delta _{k,l}+\frac{\sigma ^2-1}{N}(1-\delta _{k,l})\). The \(E_N^{}(z;\sigma )\) are polynomials in \(z^2\), explicitly computable for arbitrary N, yet a list of the first three \(E_N^{}(z;\sigma )\) shows that the expressions become unwieldy already for moderate N—unless \(\sigma = 1\), in which case \(E_N^{}(z;1) = (1+z^2)^N\) for all \(z\in \mathbb {C}\) and \(N\in \mathbb {N}\). (Incidentally, commonly available computer algebra evaluates the integrals \(E_N^{}(z;\sigma )\) only for N up to a dozen, due to memory constraints). Asymptotic evaluations are needed for the large-N regime. For general complex z these have traditionally been limited to analytic expansion techniques; several rigorous results are proved for complex z near 0. Yet if \(z\in \mathbb {R}\) one can also compute this “infinite-degree” limit with the help of the familiar relative entropy principle for probability measures; a rigorous proof of this fact is supplied. Computer algebra-generated evidence is presented in support of a conjecture that a generalization of the relative entropy principle to signed or complex measures governs the \(N\rightarrow \infty \) asymptotics of the regime \(iz\in \mathbb {R}\). Potential generalizations, in particular to point vortex ensembles and the prescribed Gauss curvature problem, and to random matrix ensembles, are emphasized.

     

Total cross sections of charged-current neutrino and antineutrino interactions on isoscalar nuclei

New measurements of the total crosssections of charged-current interactions of muonneutrinos and antineutrinos on isoscalar nuclei have been performed. Data were recorded in an exposure of the CHARM detector in an 160 GeV narrow-band beam. The antineutrino flux was determined from the measurements of the pion and kaon flux, and independently from the muon flux measured in the shield; the two methods are found to agree. The neutrino flux was determined from the muon flux ratio forv _μ and \(\bar v_\mu \) runs which was normalized to the antineutrino flux. The cross-section slopes thus determined are $$\begin{gathered} \sigma _T^{\bar v} /E = (0.335 \pm 0.004(stat) \hfill \\ \pm 0.010(syst)).10^{ - 38} cm^2 /(GeV \cdot nucleon) \hfill \\ \sigma _T^v /E = (0.686 \pm 0.002(stat) \hfill \\ \pm 0.020(syst)).10^{ - 38} cm^2 /(GeV \cdot nucleon) \hfill \\ \end{gathered} $$ The momentum sum of the quarks in the nucleon and the ratio of sea quark to total quark momentum are derived from the measurements.     

An improvement of the Griffiths-Hurst-Sherman inequality for the Ising ferromagnet

We prove the following inequality for the truncated correlation in the Ising model in zero external field: $$\begin{gathered} \langle \sigma _i \sigma _j \sigma _k \sigma _l \rangle - \langle \sigma _i \sigma _j \rangle \langle \sigma _k \sigma _l \rangle - \langle \sigma _i \sigma _k \rangle \langle \sigma _j \sigma _l \rangle - \langle \sigma _i \sigma _l \rangle \langle \sigma _j \sigma _k \rangle \hfill \\ \leqslant - 2\langle \sigma _i \sigma _m \rangle \langle \sigma _j \sigma _m \rangle \langle \sigma _k \sigma _m \rangle \langle \sigma _l \sigma _m \rangle \hfill \\ - 2 \left( {\langle \sigma _i \sigma _k \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right) \left( {\langle \sigma _j \sigma _k \rangle - \langle \sigma _j \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right)\langle \sigma _k \sigma _l \rangle \hfill \\ - 2 \langle \sigma _i \sigma _m \rangle \langle \sigma _j \sigma _m \rangle \left( {\langle \sigma _i \sigma _k \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right)\left( {\langle \sigma _i \sigma _l \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _l \rangle } \right) \hfill \\ \end{gathered} $$ This inequality is a strengthening of the Lebowitz inequality for the four-point function and implies the following improvement of the GHS inequality: $$\langle \sigma _i ;\sigma ;_j \sigma _k \rangle ^T \leqslant - 2\langle \sigma _i ;\sigma _k \rangle ^T \langle \sigma _j ;\sigma _k \rangle ^T \langle \sigma _k \rangle $$ This in turn implies the critical exponent inequality $$\Delta '_3 \geqslant \gamma ' - \beta $$      

Low-temperature relaxation in spin glasses

We analyze the mechanism governing the long-time, low-temperature relaxation of the thermoremanent magnetization (σ_TRM) in metallic spin glasses. Ideas of quantum tunneling and “screening” of the local magnetic moments are employed to explain the existence of a hierarchy of relaxation times. This results in a time decay which is described by anenhanced power law: $$\sigma _{TRM} = \sigma _0 \exp - A[\ln (\omega t)]^y = \sigma _0 (\omega t)^{ - A[\ln (\omega t)]y - 1} $$ withy≧1. A crossover is predicted below which most parameters become temperature-independent.     

Production of chi(c1) and chi(c2) in pp collisions at sqrt[S] = 1.8 TeV

We have measured the ratio of prompt production rates of the charmonium states chi(c1) and chi(c2) in 110 pb(-1) of pp collisions at sqrt[s] = 1.8 TeV. The photon from their decay into J/psi(gamma) is reconstructed through conversion into e+e- pairs. The energy resolution this technique provides makes the resolution of the two states possible. We find the ratio of production cross sections sigma(chi(c2))/sigma(chi(c1)) = 0.96+/-0.27(stat)+/-0.11(syst) for events with pT(J/psi) > 4.0 GeV/c, /eta(J/psi)/ < 0.6, and pT(gamma) > 1.0 GeV/c.     

First measurement of the ratio of central-electron to forward-electron W partial cross sections in pp[over] collisions at (square root)s =1.96 TeV

We present a measurement of sigma(pp[over] --> W) x B(W --> e nu) at (square root)s = 1.96 TeV, using electrons identified in the forward region (1.2 < |eta| < 2.8) of the CDF II detector, in 223 pb(-1) of data. We measure sigma x B = 2796 +/- 13(stat)(-90)(+95)(syst) +/- 162(lum) pb. Combining this result with a previous CDF measurement obtained using electrons in the central region (|eta| approximately < 1), we present the first measurement of the ratio of central-electron to forward-electron W partial cross sections R(exp) = 0.925 +/- 0.006(stat) +/- 0.032(syst), consistent with theoretical predictions using Coordinated Theoretical-Experimental Project on QCD (CTEQ) and Martin-Roberts-Stirling-Thorne (MRST) parton distribution functions.     

Coexistence and criticality in size-asymmetric hard-core electrolytes

Liquid-vapor coexistence curves and critical parameters for hard-core 1:1 electrolyte models with diameter ratios lambda = sigma(-)/sigma(+) = 1 to 5.7 have been studied by fine-discretization Monte Carlo methods. Normalizing via the length scale sigma(+/-) = 1 / 2(sigma(+)+sigma(-)), relevant for the low densities in question, both T(*)(c) ( = k(B)T(c)sigma(+/-)/q(2)) and rho(*)(c) ( = rho(c)sigma(3)(+/-)) decrease rapidly (from approximately 0.05 to 0.03 and 0.08 to 0.04, respectively) as lambda increases. These trends, which unequivocally contradict current theories, are closely mirrored by results for tightly tethered dipolar dimers (with T(*)(c) lower by approximately 0%-11% and rho(*)(c) greater by 37%-12%).     

Conjugation-length dependence of spin-dependent exciton formation rates in pi-conjugated oligomers and polymers

We have measured the ratio, r = sigma(S)/sigma(T) of the formation cross section, sigma of singlet and triplet excitons from polarons in pi-conjugated oligomer and polymer films, using a spectroscopic technique we developed recently. We discovered a universal relation between r and the conjugation length (CL): r(-1) depends linearly on CL-1, irrespective of the chain structure. Since r is directly related to the maximum possible electroluminescence quantum efficiency in organic light emitting diodes (OLED), our results indicate that polymers have an advantage over small molecules in OLED applications.