New hierarchies of knot polynomials from topological Chern-Simons gauge theory

In this Letter, we report on a study of the expectation values of Wilson loops in D=3 topological Chern-Simons theory associated with the fundamental representation of the simple Lie algebras SO(n) and Sp(n). The skein relations satisfied by these expectation values are derived by conformal field-theory techniques. New hierarchies of invariant polynomials for knots in S ³ can be derived from these relations (at least) up to ten crossings. The N=3 Akutsu-Wadati polynomials are a special case with G=SO(3). The expectation value of the Wilson loops for a couple of simple unknotted circles is identified to the Weyl character.Work supported in part by U.S. National Science Foundation Grant PHY8706501.Work supported in party by Chinese National Science Foundation through Nankai University.     

Quantum geometry of loops and the exact solubility of non-abelian gauge Chern-Simons theory-II

We quantize non-abelian Chern-Simons gauge theory in three dimensions in the presence of Wilson lines. We determine the theory dynamically in terms of the geometry of loops and show that it is exactly soluble. Remarkably the quantum loop equations are linear for S³ and they possess a class of solutions, among which is a non-critical Fermi string theory. Using these solutions we determine various important identities relevant to knot theory discovered recently by E. Witten, in particular, we show that the loop equation yields precisely the full exact skein relation of knot theory. As a byproduct we show that the partition function of an unknotted Wilson loop onS ³ is nothing but the character ofSU(2) in which the rotations areSU(N)-valued fractional angles. Furthermore, we generalize our solutions to the case where the manifoldM ₃ is oriented, closed, and non-simply connected withH ₁(M ₃)=0 (a homology 3-sphere).Address after 1^st October 1989: Physics Department, University of Florida, Gainsville, FL 32611, USA     

打结高分子链穿孔行为的研究

以三叶草型结(即3₁结)为例,采用分子动力学(MD)方法,研究打结高分子链在外场力作用下穿越微孔的动力学过程.模拟发现,在拉动打结高分子链的过程中,结的大小呈涨落变化,直至最后散结.定性讨论了结的存在对高分子链穿孔速率的影响.在外场力作用下,打结高分子链平均穿孔时间(τ)与链长(N)满足标度关系τ～N ^α,其中标度系数α随外场力f增大而增大.对于短链,外场力越大,平均穿孔时间越短     

Tropical Weyl Group Action via Point Configurations and τ-Functions of the q-Painlevé Equations

Starting from certain point sets in the projective plane, we construct a tropical (or subtraction-free birational) representation of Weyl groups over the field of τ-functions. In particular, our construction includes E ₈ ⁽¹⁾ , E ₇ ⁽¹⁾ , E ₆ ⁽¹⁾ and D ₅ ⁽¹⁾ as affine cases; each of them gives rise to the q-difference Painlevé equation.     

Effect of anomalous tbW vertex on decay-lepton distributions in e + e − → tt and CP-violating asymmetries

We obtain analytic expressions for the energy and polar-angle double differential distributions of a secondary lepton l ⁺ (l ⁻) arising from the decay of t(t) in e ⁺ e ⁻ → tt with an anomalous tbW decay vertex. We also obtain analytic expressions for the various differential cross-sections with the lepton energy integrated over. In this case, we find that the angular distributions of the secondary lepton do not depend on the anomalous coupling in the decay, regardless of possible anomalous couplings occurring in the production amplitude for e ⁺ e ⁻ → tt. Our study includes the effect of longitudinal e ⁻ and e ⁺ beam polarization. We also study the lepton energy and beam polarization dependence of certain CP-violating lepton angular asymmetries arising from an anomalous tbW decay vertex and compare them with the asymmetries arising due to CP-violation in the production process due to the top electric or weak dipole moment.     

强激光与高密度气体相互作用中电子和离子加速的数值模拟

在现有的一维粒子模拟程序的基础上发展了带光电离和碰撞电离及蒙特卡罗两体碰撞的模拟程序(1D PIC-MCC). 用此程序模拟研究了短脉冲激光与He气靶相互作用时电子和离子的加速过程. 研究表明当强激光与过临界密度的微米厚度的平面靶相互作用时，靶前表面物质将被激光脉冲前沿迅速离化；新生的电子被激光场有质动力加速成为高能电子，这些电子穿入到靶内，通过电子碰撞电离离化靶内物质；一部分高能电子穿透靶后，会在靶的后表面形成强的电荷分离场，该场迅速离化靶后表面物质，同时使得后表面离子得到加速. 部分穿透靶的超热电子将被电荷分离场重新拉回靶内，在靶的前后表面振荡. 一些振荡电子在此过程中得到电荷分离场加速，离开前表面，在前表面也形成电荷分离场，使前表面离子得到加速. 关键词： 激光等离子体 光电离和碰撞电离 电子加速 离子加速     

In-beam study of the doubly-odd nucleus 61 140 Pm79

A detailed -γ-ray study of¹⁵²Dy has been performed using the¹²⁴Sn(³²S,4n) reaction at low bombarding energy. Several γ rays deexciting non-Yrast states have been identified, among them transitions previously observed in coincidence with the superdeformed band. However we have no evidence for the lowest members of this band.     

Very high-frequency gravitational waves from magnetars and gamma-ray bursts

Extremely powerful astrophysical electromagnetic(EM) systems could be possible sources of highfrequency gravitational waves(HFGWs). Here, based on properties of magnetars and gamma-ray bursts(GRBs), we address "Gamma-HFGWs"(with very high-frequency around 10~(20) Hz) caused by ultra-strong EM radiation(in the radiation-dominated phase of GRB fireballs) interacting with super-high magnetar surface magnetic fields(～10~(11) T).By certain parameters of distance and power, the Gamma-HFGWs would have far field energy density ?gw around10~(-6), and they would cause perturbed signal EM waves of～10~(-20) W/m~2 in a proposed HFGW detection system based on the EM response to GWs. Specially, Gamma-HFGWs would possess distinctive envelopes with characteristic shapes depending on the particular structures of surface magnetic fields of magnetars, which could be exclusive features helpful to distinguish them from background noise. Results obtained suggest that magnetars could be involved in possible astrophysical EM sources of GWs in the very high-frequency band, and Gamma-HFGWs could be potential targets for observations in the future.     

带强迫振动项的三分子模型的倍周期分叉序列

本文对带强迫振动项的三分子模型,在强迫振动的幅度C=0.05和频率D一些取值下,进行了数值计算。通过数据分析,给出了2ⁿ周期分叉序列,并与Feigenbaum常数δ进行了比较。 关键词：     

Equivalence of deformations and associated *-products

In this letter we study the non-trivial formal differentiable deformations of the Lie algebraN=C (W, IR) whereW is a symplectic manifold. Under some assumptions (satisfied in particular forW=IR²ⁿ ) we show that these deformations are all equivalent, up to a monomial change of the parameter, to one of them (Moyal for IR²ⁿ ). Furthermore, if there exists a differentiable *-product corresponding to one of them, each of them is induced by a *-product which is essentially unique.Aspirant du Fonds National belge de la Recherche Scientifique.     

Pion bound states in nuclei

Bound π-nuclear states can appear under certain realistic conditions in finite nuclei. The best prospects are certain medium-weight nuclei with dense central regions and large neutron excess. Numerical illustrations are given for ¹⁶O, ²⁸Si, ³²Na and ²⁰⁸Pb with realistic parameters for the interaction. Further, we show that the usual low-energy π nuclear potential develops pathological features like an infinity of bound states beyond a certain critical strength. The natural remedies are indicated.     

A novel family of space-filling curves in their relation to chromosome conformation in eukaryotes

Spatial conformation of DNA chains during interphase in eukaryotic cell nucleus is relatively dense, yet unknotted and exhibits self-similar fractal properties. In this respect it resembles the space-filling curves of Hilbert, but differs in the experimentally accessible contact probability of distant loci. Here we construct space-filling curves with fractal domain boundaries of dimension close to that of the embedding space and show how these match the statistical properties and the contact probability of the DNA conformation. The present mathematical model should shed light on the statistical ensemble of unknotted dense polymers and ease the modeling of genome folding and related biological processes.     

Chern–Simons theory,Stokes’ theorem,and the Duflo map

We consider a novel derivation of the expectation values of holonomies in Chern–Simons theory, based on Stokes’ Theorem and the functional properties of the Chern–Simons action. It involves replacing the connection by certain functional derivatives under the path integral. It turns out that ordering choices have to be made in the process, and we demonstrate that, quite surprisingly, the Duflo isomorphism gives the right ordering, at least in the simple cases that we consider. In this way, we determine the expectation values of unknotted, but possibly linked, holonomy loops for SU(2) and SU(3), and sketch how the method may be applied to more complicated cases. Our manipulations of the path integral are formal but well motivated by a rigorous calculus of integration on spaces of generalized connections which has been developed in the context of loop quantum gravity.     

Spectral Gap for Multi-species Exclusion Processes

We consider a multi-species generalization of the symmetric simple exclusion process in homogeneous and non-homogeneous hypercubes of Z ^d . In this model, the hyperplanes of configurations with given numbers of particles of each species are not necessarily irreducible. We give a sufficient condition of the dynamics to make them irreducible. In addition, assuming the irreducibility of them, we show some estimates of the spectral gap (the absolute value of the second largest eigenvalue of the generator), which plays an important role in the study of hydrodynamic limit.     

Crossed Products of C*-Algebras and Spectral Analysis of Quantum Hamiltonians

We study spectral properties of a hamiltonian by analyzing the structure of certain C ^*-algebras to which it is affiliated. The main tool we use for the construction of these algebras is the crossed product of abelian C ^*-algebras (generated by the classical potentials) by actions of groups. We show how to compute the quotient of such a crossed product with respect to the ideal of compact operators and how to use the resulting information in order to get spectral properties of the hamiltonians. This scheme provides a unified approach to the study of hamiltonians of anisotropic and many-body systems (including quantum fields). Received: 5 November 2001 / Accepted: 10 March 2002     

Nahm Transform and Spectral Curves¶for Doubly-Periodic Instantons

We present the Nahm transform of the doubly-periodic instantons (i.e. instantons on T ²×ℝ²), converting them into certain meromorphic solutions of Hitchin's equations over an elliptic curve. We then show how to construct a triple consisting of an algebraic curve plus a line bundle with connection over it from a doubly-periodic instanton, and that such data coincides with the Hitchin spectral data associated with the Nahm transformed Higgs bundle. Received: 15 October 1999 / Accepted: 16 October 2001     

Lepton number violation in D meson decay

The lepton number violation(LNV) process can be induced by introducing a fourth generation heavy Majorana neutrino,which is coupled to the charged leptons of the Standard Model(SM). There have been many previous studies on the leptonic number violating decay processes with this mechanism. We follow the trend to study the process: D→Kllπ with the same-sign dilepton final states. We restrict ourselves to certain neutrino mass regions,in which the heavy neutrino could be on-shell and the dominant contribution to the branching fraction comes from the resonance enhanced effect. Applying the narrow width approximation(NWA),we found that the upper limit for the branching fractions for D0→ K-l+l+π-are generally at the order of 10-12 to 10-9,if we take the most stringent upper limit bound currently available in the literature for the mixing matrix elements. We also provide the constraints,which is competitive compared to the LNV B decays,on the mixing matrix element |VeN|2 based on the upper limit of D0→ K-e+e+π-estimated from the Monte-Carlo(MC) study at BESⅢ. Although the constraints are worse than the ones from(0νββ) decay in the literature,the future experiment at the charm factory may yield more stringent constraints.     

Unified field theories of bags and strings

Within our models of temporary quark confinement in field theoretical bags, we exhibit, in the tree approximation, string-like solutions. We argue that the bag-like and dual string-like pictures complement each other with the former describing the low-lying hadronic states and the latter the excited states of large angular momentum. When certain quantum fluctuation effects are included, we find Regge trajectories, in a certain dynamical regime, to always approach straight lines in a (J, E²) plane.     

Versal Deformations of a Dirac Type Differential Operator

Abstract

If we are given a smooth differential operator in the variable x ∈ R/2πZ, its normal form, as is well known, is the simplest form obtainable by means of the Diff(S ¹)-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced Diff(S ¹)-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced Diff(S ¹)-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters.