Kauffman knot polynomials in classical abelian Chern-Simons field theory

Kauffman knot polynomial invariants are discovered in classical abelian Chern-Simons field theory. A topological invariant t^I(L) is constructed for a link L, where I is the abelian Chern-Simons action and t a formal constant. For oriented knotted vortex lines, t^I satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, t^I satisfies the skein relations of the Kauffman bracket polynomial. As an example the bracket polynomials of trefoil knots are computed, and the Jones polynomial is constructed from the bracket polynomial.     

Phase behaviour of polyethylene knotted ring chains

The phase behaviour of polyethylene knotted ring chains is investigated by using molecular dynamics simulations. In this paper, we focus on the collapse of the polyethylene knotted ring chain, and also present the results of linear and ring chains for comparison. At high temperatures, a fully extensive knot structure is observed. The mean-square radius of gyration per bond ² / (Nb²) and the shape factor <δ^*> depend on not only the chain length but also the knot type. With temperature decreasing, chain collapse is observed, and the collapse temperature decreases with the chain length increasing. The actual collapse transition can be determined by the specific heat capacity C_v, and the knotted ring chain undergoes gas-liquid-solid-like transition directly. The phase transition of a knotted ring chain is only one-stage collapse, which is different from the polyethylene linear and ring chains. This investigation can provide some insights into the statistical properties of knotted polymer chains.     

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     

Secondary vacuum trajectories and scalar meson exchange

A new second vacuum trajectory passing throughf*(1515) and σ(548), α(t)=? 0.3+t, is proposed, which, together with α_p″(t=0)=? 0.5, overcomes the failure of Igi's original superconvergent πN sum rule and avoids the ghost-state of the conventionalP′-trajectory. The negative residue att=0 confirms the repulsive contribution of a vacuum pole component withJ=0 to the generalizeds-reaction potential, as postulated by Chew (1965). TheP- andP′-poles can build the non resonating background. The Gell-Mann nonsense mechanism at the negative integers with wrong signature explains the dips in the elastic π^± p-scattering att=?0.7, ?2.7 and ?4.5 (GeV/c)². σ(∞) for πN reactions turns out to be 24.3 mb, if α _p (t=0)=1, but the best fits to the total πN cross sections for pion momenta between 2 and 29 GeV/c yield α _p (t=0)=0.93.     

Continuum limit of finite temperature λφ3 from lattice Monte Carlo

The φ₃⁴ model at finite temperature is simulated on the lattice. For fixed N_t we compute the transition line for N_s → ∞ by means of finite size scaling techniques. The crossings of a renormalization group trajectory with the transition lines of increasing N_t give a well-defined limit for the critical temperature in the continuum. By considering different RG trajectories, we compute T^c/g as a function of the renormalized parameters.     

Topological recursion for chord diagrams,RNA complexes,and cells in moduli spaces

We introduce and study the Hermitian matrix model with potential _Vs,t(x)=x²/2−stx/(1−tx)$V_{s,t}(x)=x^2/2-stx/(1-tx)$, which enumerates the number of linear chord diagrams with no isolated vertices of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are convergent for small t and all s   as a perturbation of the Gaussian potential, which arises for st=0$st=0$. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given topology as well as the number of cells in Riemann?s moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly in genus less than four.     

The decay of93g Ru,93m Ru,91g Mo,91m Mo,91g Tc and91m Tc

Decay studies on a number of short-lived odd nuclei in theN=50 region are described. The 59.6-s ⁹³Ru ground state decay was studied in detail for the first time; in these experiments the 10.8-s activity^93m Ru was discovered. The⁹¹Tc activities were also observed for the first time. The ground state and an isomeric state of this nucleus decay with nearby equal half-lives (3.14 and 3.3-min). The activities^91g Mo (16.6-min) and^95m Mo (65.1-s) have been reinvestigated. A number ofγ-rays, previously erroneously assigned to the⁹¹Mo activities, could be eliminated. A strong similarity is noted for the decay schemes of theN=49 isotones^91m Mo and^93m Ru. The energy of the 1/2^? isomeric state in⁹³Ru and theB(M4)-value of the isomeric transition fit well into the systematics of the previously knownN=49 isotones.     

Entanglement dynamics in Coriolis coupled rovibrational states of formaldehyde

The entanglement dynamics of two vibrational modes of a polyatomic molecule coupled by Coriolis interaction to overall molecular rotation is studied in terms of two negativities, N(t) and N_s(t), respectively, defined by the minimum of the eigenvalues and by the sum of the negative eigenvalues of the partial transpose of a density matrix. Various initial states are the products of Dicke states and the products of coherent states of vibrations and rotations. Formaldehyde is taken as an example, and the von Neumann entropy s(t) is simulated for the comparison with both negativities. It is shown that negativity N_s(t) is positively correlated with entropy s(t), and the correlated behavior between negativity N(t) and entropy s(t) strongly depends on initial states. However, these three indicators of entanglement display a dominantly positive correlation for the coherent states with small or large parameters. In addition, for the latter state two quantities N(t) and s(t) are nearly unchanged for a long time. This time can be further increased by the increasing of vibrational quantum number so that molecular information processing and quantum computing is allowed. These results are useful in quantum information theory.     

Crossed-second-order specific-mass isotope shift in the Nickel atom

The crossed-second-order corrections to the specific mass shifts of the lowest terms of the two lowest configurations of the Nickel atom are evaluated ab initio in the Multiconfigurational Hartree-Fock scheme. The excitations towards the nf(l=3) empty subshells play the major role. If the contributions obtained are added to the Hartree-Fock values, the discrepancy between experiment and theory for the 3d ⁸ 4s ²?3d ⁹ 4s (virtual) transition is only reduced by one third. As concerns the differences between the specific shifts of the five Russell-Saunders terms of 3d ⁸ 4s ², the crossed-second-order contributions are predicted to be practically as large as the Hartree-Fock values, which makes the total definitely measurable.     

Theoretical lifetimes,transition energies,fluorescence yields,and nonradiative branching ratios for highly excited states of lithium-like argon

We have calculated theoretical transition rates and transition energies for the states of the excited electron configurations, 1s 2s nl and 1s 2p nl, of lithium-like argon. The values of n considered range from n=2 to n=4 with all allowed values of l included, l=0 to l=n-1. We present numerical results for the theoretical lifetimes, transition energies, fluorescence yields, and nonradiative branching ratios. These quantities are related to the dielectronic recombination rates and cross sections of helium-like argon.     

A multilevel Cartesian non-uniform grid time domain algorithm

A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at N_s observation locations from N_s collocated sources for N_t discrete time instances scales as O(N_tN_slogN_s) and O(N_tN_slog²N_s) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.     

Supermembranes and the signature of spacetime

We consider extended objects with s space and t time world-volume dimensions moving in a spacetime with S⩾ s space and T⩾t time dimensions. The requirements of spacetime supersymmetry and world-volume fermionic gauge invariance severely restrict the possible values of S and T. If we furthermore insist that the transverse group SO(S − s, T−t) be compact to avoid ghosts, then t=T. The results may be interpreted as a set of superconformal field theories with s+t⩽6 and N⩽8 whose superconformal groups are in one-to-one correspondence with those in Nahm's classification. Although the choice t = T = 1 is not uniquely singled out, it does seem to play a preferred role.     

Evaluation of ππ → NN d-waves for −25μu2 ⩽ t ⩽ 4μ2

A Froissart-Gribov projection of πN phase shifts and Regge amplitudes is used to evaluate the $\text{ππ→}\text{N}\text{N}$ scattering length at t=4μ², and partial waves for ?25μ² ? t < 4μ². The new value of the scattering length is 15% higher than a previous estimate made in the narrow width resonance approximation. The values for the partial waves are confronted with previous estimates, and lower bounds. As a result, the latter become saturated near t=0, but less restrictive near t=4μ².     

A buoyant flow structure in a magnetic field: Quasi-steady states and linear-nonlinear transitions

The confined evolution of a buoyant blob of fluid subject to a vertical magnetic field is investigated in the limit of low magnetic Reynolds number. When the applied magnetic field is strong, the rise velocity of the blob is small. As the vorticity diffuses along the magnetic field lines, a quasi-steady state characterised by a balance between the work done by buoyancy and Ohmic dissipation is eventually reached at time tqs∼(L²/δ²)τ, where L is the axial dimension of the fluid domain, δ is the radius of the buoyant blob and τ is the magnetic damping time. However, when the applied magnetic field is weak or the axial length is sufficiently large compared to the blob size, the growth of axial velocity eventually makes the advection of vorticity significant. The typical time for the attainment of this nonlinear phase is , where N₀ is the magnetic interaction parameter at time t=τ. The order-of-magnitude estimates for the timescales tqs and tnl are verified by computational experiments that capture both the linear and nonlinear phases.     

QCD thermodynamics with dynamical overlap fermions

We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on _Nt=6$N_t=6$ and 8 lattices. All our runs are performed with fixed global topology. Our results are compared with staggered ones and a nice agreement is found.     

Morphogenesis of sliced N-soliton solutions

Consider an instantaneous severing interaction which at t = t_s transforms is given N-soliton solution q⁰ into two new solutions, q^L and q^R, with discontinuous anitial conditions at t = t_s such that q^L(q^R) is equal to q⁰ to the left (right) of the severing point x_s and vanishes to the right (left) of x_s. The soliton content of q^L and q^R is studied in the context of the cubic Schrödinger equation and the sine-Gordon equation by solving the direct scattering problem. It is shown that the motion constants C_n, n = 1, 2 …, are related by , Furthermore, if q⁰ contains N solitons and no contribution from the continuous spectrum, then q^L(q^R) contains N^L(N^R) solitons with 0 ? N^L, N^R ? N and N^L + N^R = N. The slicing puts a soliton into q^L or q^R, respectively as the slicing point x_s is taken to the right or left of the soliton's “center” at t = t_s.     

Efficient photo-ionization for barium ion trapping using a dipole-allowed resonant two-photon transition

Two efficient and isotope-selective resonant two-photon ionization techniques for loading barium ions into radio-frequency (RF)-traps are demonstrated. The scheme of using the strong dipole-allowed transition 6s ²? ¹S₀→6s6p? ¹P₁ at λ=553 nm as a first step towards ionization is compared to the established technique of using a weak inter-combination line (6s ²? ¹S₀→5d6p? ³D₁,λ=413 nm). An increase of two orders of magnitude in the ionization efficiency is found favoring the transition at 553 nm. This technique can be implemented using commercial all-solid-state laser systems and is expected to be advantageous compared to other narrowband photo-ionization schemes of barium in cases where highest efficiency and isotope-selectivity are required.     

Dynamical spin system: Exact solution and mean recurrence time

A model involving a chain of N ≥ 2 spins s_i = ±1, i = 1,…,N, evolvi ng syncronously in discrete time t via a nonlinear, autonomous transformation s_i(t+1) = s_i(t)s_i+1(t), i = 1,…,N−1; s_N(t+1) = s_N(t), is presented. The transformation equations are solved explicitly and the detailed decomposition of state space into ergodic sets is found. On the assumption of equally likely initial states, the mean recurrence time is calculated and its variance is discussed. The model displays a strikingly sensitive dependence on the number of spins, and this is reflected in the “staircase” behavior of the mean recurrence time. Remarks are made regarding the connection between the behavior of the model and the ground states of a related two-dimensional Ising model.     

The effects of deformation on isovector electromagnetic and weak transition strengths

The summed strength for transitions from the ground state of ¹²C via the operators st, ℓt, rY¹t, r[Y¹s]^λt and r[Y¹ℓ]^λt are calculated using the ΔN = 0 rotational model. If we choose the z-component of the isospin operator t_z, the above operators are relevant to electromagnetic transitions; if we choose t₊, they are relevant to weak transitions such as neutrino capture. In going from the spherical limit to the asymptotic (oblate) limit the strength for the operator st decreases steadily to zero; the strength for the operator ℓt (scissors mode) increases by a factor of three. For the last three operators, isovector dipole, spin dipole and orbital dipole (including the twist mode), it is shown that the summed strength is independent of deformation. The main difference in the behavior is that for the first two operators we have in-shell transitions whereas for the last three operators the transitions are out of shell.