Thermodynamics and topology of disordered systems: Statistics of the random knot diagrams on finite lattices

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants, was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro-and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q→∞. It is shown that the highest power of the Kauffman invariant correlates with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The results obtained are compared to the probability distribution of the minimum energy of a Potts system with random ferro-and antiferromagnetic bonds.     

Landau-Zener tunneling of Bose-Fermi mixture in double-well

The nonlinear Landau-Zener tunneling of a Bose-Fermi mixture in a double-well potential is studied in the present paper. The effect of interaction parameters on bosonic and fermionic tunneling probability is studied for the mixture of ⁴⁰K-⁸⁷Rb. The tunneling phenomena of the system can be controled by adjusting sweeping rate, intraspecies interaction, interspecies interaction and the numbers of bosons and fermions. It is noted that there are three different regions in phase diagram: self-trapping (ST), complete tunneling (CT) and incomplete tunneling (ICT).     

Light-cone structure of vertex functions for composite fields

Vertex functions for composite fields are defined in a model field theory both on and off mass shell. Light-cone dominance at large momentum transfer is shown to hold, by the compositeness assumption, for the off-shell vertex function. On the other hand, it is in general untrue that the elastic form factor probes light-like distances between the constituents inside the nucleon. The relevant light-cone singularity (in the relative space-time separation x) is less important in this case than the large x₀ behaviour of the wave function at fixed x². It is found however that, under some conditions, the light-cone singularity determines the large x₀ behaviour of the wave function, and therefore the large q² behaviour of the form factor. For composite particles described by a Bethe-Salpeter equation, this result is equivalent to the known fact that at large q² the form factor depends on the binding interaction at small distances. A relation similar to that of Drell-Yan-West is finally established between the asymptotic behaviour of the elastic form factor and the threshold behaviour of the absorptive part of the vertex scaling function.     

Electron correlation in two-dimensional systems: CHNC approach to finite-temperature and spin-polarization effects

Applying the classical-map hypernetted-chain method (CHNC) developed recently by Dharma-wardana and Perrot, we have studied the temperature and spin-polarization effects on electron correlation in the uniform quantum two-dimensional gas (2DEG) over a wide range of temperature T and spin-polarization ζ. The quantum fluid at the temperature T is mapped to a classical fluid at the temperature T_cf given by T_cf²=T²+T_q², where the quantum temperature T_q is determined by comparing the calculated correlation energy to that of Monte Carlo results for the fully spin-polarized quantum system at zero temperature. By the iterative solution of the modified HNC equation and the Ornstein-Zernike equation, we have obtained the pair distribution function (PDF) and correlation energy for the two-component classical 2DEG with a classical fluid temperature T_cf. The anti-parallel bridge function B₁₂(r) appearing in the modified HNC equation is determined by using the Monte Carlo correlation energy at T=0 or STLS (Singwi-Tosi-Land-Sjölander) result at T>0 and the numerical solution to the Percus-Yevick (PY) equation for the system of hard disks. By calculating the Pauli potential, the bridge function, PDFs, structure factors and correlation energy, we have shown that in some cases, the properties of the uniform quantum 2DEG depend remarkably on the temperature and spin-polarization.     

An application of a new harmonic-oscillator basis to the calculation of trinucleon ground-state observables

A new harmonic-oscillator basis for trinucleon ground-state calculations is introduced, featuring different oscillator radii for the two intrinsic variables. This basis allows charge-dependent interactions to be handled and seems to yield a better convergence with respect to the previously used oscillator bases. A test calculation with the Reid soft-core interaction is presented. The resulting (extrapolated) triton binding energy is 7.3 ± 0.2 MeV, and the first minimum in the ³He charge form factor occurs at q² = 13.1 fm^?2.     

On the semiclassical green's function in the energy-representation

We present a detailed discussion of the semiclassical approximation for the Green's function in the energy representation, G(qⁱ,q^j; E). In particular, we describe the way in which classical catastrophes influence the semiclassical approximation, and present a practical scheme to determine the phases with which the contributions due to the various classical trajectories enter the semiclassical result.     

Form factors,threshold relations,and large angle elastic scattering of pions

The form factor F(q²) of the pion in a simple core model is investigated, together with the deep inelastic electroproduction structure function, F₂(ω). A relation between these two, analagous to the Drell-Yan-West relation for nucleons, is derived and it is found that F₂ is related to either the form factor or the square of the form factor depending on how rapidly F(q²) ultimately falls with momentum transfer. The unitarity equation and its implications for this kind of threshold relation are discussed. The simple core model is also applied to elastic large angle ππ scattering.     

Deuteron structure and diffractive deuteron-nucleus interaction

A nonrelativistic deuteron wave function involving the D-wave state and having a correct asymptotic behavior is constructed on the basis of the experimentally measured deuteron charge form factor G _C(q) and deuteron structure function A(q). The differential cross section for elastic deuteron-nucleus scattering is calculated by using this wave function and is found to agree with experimental data at an energy of 110 MeV. Integrated cross sections for various processes involving deuteron-nucleus interactions are also calculated. The distribution in the emission angle of the center of mass of the neutron-proton system produced in the diffractive dissociation of 110-MeV deuterons in the field of ²⁰⁸Pb nuclei is obtained.     

Thickness dependence of the surface plasmon dispersion in ultrathin aluminum films on silicon

The collective excitation in Al films deposited on Si(1 1 1)-7 × 7 surface was investigated by high-resolution electron-energy-loss spectroscopy (HREELS), X-ray photoelectron spectroscopy (XPS) and scanning tunneling microscopy (STM). At the Al film thickness d < 10 ML, the surface plasmon of Al film has only a small contribution to the observed energy-loss peaks in the long wavelength limit (q_∥≈0), while its contribution becomes significant for q_∥>d^-1. More interestingly, for thin Al films, the initial slope of the surface plasmon dispersion curve is positive at q_∥∼0, in a sharp contrast to bulk Al surface where the energy dispersion is negative. These observations may be explained based on the screening interaction of the space charge region at the Al-Si interface.     

A quantum mechanical mechanism for the dissociative chemisorption of N2 on metal surfaces

The time dependent Schrödinger equation was numerically solved for the transition dynamics from the N₂-metal to the N-metal to the N-metal potential energy surfaces. The resulting rapid increase of the dissociation probability (S₀) with incident kinetic energy, its saturation at high energies and vibrational enhancement are in good agreement with recent experiments. A novel explanation for the small value of S₀ is based on the high energy value of the crossing region between the two potentials, predicting that the dissociation occurs via a tunneling mechanism. Recombinative desorption experiments of ¹⁴N₂ and ¹⁵N₂ from Re(0001) are in excellent agreement with the tunneling model.     

Quenching of the triplet state of Pd-porphyrins by Cu-etioporphyrin in dimethyl formamide

Quenching of phosphorescence of Pd-tetrabenzoporphyrin (Pd-TBP) and Pd-etioporphyrin I (Pd-EP) by the Cu-EP molecules was studied using pulsed photoexcitation. The rate constant of quenching (K _q) by the Cu-EP molecules was found to be 2.3×10⁹ 1/(mol s) for the low lying triplet state (TS) of Pd-Ep and 5.8×10⁸ 1/(mol s) for the TS of Pd-TBP. It is concluded that the quenching was caused by the intermolecular energy transfer, and the low value of K _q for Pd-TBP can be explained by the fact that the level of Cu-EP (X), to which the energy is transferred, lies above the TS of Pd-TBP (E _T=12 900 cm^?1). Based on the results obtained and the published data, it is assumed that the energy transfer proceeds via the formation of long-lived excited complexes of interacting molecules. With the K _q value for Pd-TBP and the results of kinetic analysis of the adopted quenching mechanism, the difference between the energy of states, involved in energy transfer, and the X state energy are determined (E _X=13 520 cm^?1 and E _T=14 500 cm^?1 for Cu-EP). Some specific features of photophysical and luminescence properties of Cu-porphyrins are explained by the presence of such a state related to the excitation of the copper ion.     

Simple formulae for heavy ion subcoulomb transfer probabilities. Application to one and two-proton transfers in bismuth

A simple analytical formula is given to express the transition probability in a quasi-elastic transfer reaction. This formula is derived from the DWBA amplitude, using assumptions based on the fact that the main contribution to the DWBA integral comes from a narrow domain of distances of approach. Recoil effects are taken into account. This method is applied to calculate the excitation functions for one and two-proton transfer reactions induced in²⁰⁹Bi by heavy ions, below and near the barrier. The curves obtained are compared to the excitation functions measured for the production of residual²¹⁰Po and²¹¹At. The corresponding transfer reactions involve excitation energiesE ^* of the residue lying in the range 0–8 MeV. This excitation energy is taken as a free parameter in the calculation, and the valuesE _opt ^* which lead to the best agreement between the calculated and experimental curves are consistent with the classical values for the optimum reactionQ-values. Nuclear Reactions. Simplified transition probability for quasi-elastic transfer. Calculatedσ(E) ²⁰⁹Bi(X, Y)²¹⁰Po,²¹¹At,X=¹⁴N,¹⁶O,¹⁹F,⁴⁰Ar,⁴⁰Ca,⁵⁶Fe,⁶³Cu near threshold. Compared experimental data. Deduced optimum excitation energy.     

B → πlΝ form factors calculated on the light-front

A consistent treatment of B → πlν decay is given on the light-front. The B to π transition form factors are calculated in the entire physical range of momentum transfer for the first time. The valence-quark contribution is obtained using relativistic light-front wave functions. Higher quark-antiquark Fock-state of the B-meson bound state is represented effectively by the ¦B*π〉 configuration, and its effect is calculated in the chiral perturbation theory. Wave function renormalization is taken into account consistently. The ¦B*π〉 contribution dominates near the zero-recoil point (q ² ? 25 GeV²), and decreases rapidly as the recoil momentum increases. The calculated form factor ?+(q ²) follows approximately a dipole q ²-dependence in the entire range of momentum transfer. We estimate that ¦V _ub¦=0.003.     

Nucleon transfer in highly mass-asymmetric reaction systems between197au and relatively light projectiles in the energy region below 10 MeV/u

Mechanisms of heavy-ion induced nuclear reactions in mass-asymmetric systems were studied by focusing on the nucleon transfer reaction. Excitation functions and projected mean recoil ranges for the target-like products in³⁷-,¹⁶O-,¹⁴N-, and¹²C-induced reactions on¹⁹⁷Au were measured by means ofγ-ray spectrometry. The energy range studied was near the Coulomb barrier of the systems with incident energies below 10 MeV/u. Nucleon transfer reactions were discussed by distinguishing the products from quasi-elastic transfer (QET) and those from deep inelastic transfer (DIT). The tendency towards equilibration of theN/Z value and the energy damping, which are the characteristic features of DIT, were found in the production of Au isotopes. Observations are consistent with the generally accepted concept that QET takes place along a trajectory near the Coulomb trajectory. QET was made to be connected with the interaction radius and most of the cross section ratios were reproduced well by an extended tunneling model.     

The effect of nonextensivity on the time development of quantum systems

In this study, the classical evolution operator has been generalized within Tsallis thermostatistics. By using the generalized evolution operator, the q-dependent transition probability of a quantal system, namely Fermi Golden rule, has been introduced as w (n → m) = ‖[U _q(t, t ₀)]_mn‖². In order to make the situation concrete, a simple example from quantum mechanics has been solved in the frame of this formalism and the effect of q-index has been clearly illustrated in the figures.     

Untersuchung der beiden ersten angeregten Zustände des Li6-Kernes durch Elektronenstreuung

Inelastic electron cross sections for Li⁶ were measured using the facilities at the 300 MeV linear accelerator of the Institut für Kernphysik in Mainz. The form factor for theC 2 transition to the 2.184 MeV level is given in the region of momentum transfer 0.4 fm^?1<q<1.9 fm^?1. It was possible to determine the form factor for the 3.562 MeVM 1 transition up toq=1.2 fm^?1.     

Enhancement of two-proton transfer in N = 82 nuclei: A study of 1p, 2p and (2p+2n) transfer reactions induced by 16O on 140Ce, 142Nd and 144Sm near the Coulomb barrier

One-proton, two-proton, and α-particle transfer have been studied on nuclei with closed neutron shell N = 82 using ¹⁶O beams of 63 to 66.5 MeV incident energy. Transfer probabilities defined in a semiclassical model are derived for the different reaction channels. For this purpose the Q-value and angular dependence of the cross section are discussed. The two-proton transfer to the ground states shows an enhancement by a factor 20–25 compared to other nuclei, showing the effect of the proton pairing in these nuclei (they correspond to equivalent neutron configurations in ^{108, 110, 112}Sn). The total transfer probability follows a common trend for all three target nuclei as a function of energy above the Coulomb barrier for the proton and two-proton transfer, respectively, but not for the four-nucleon transfer.