Siebenmann-type cobordisms with borders and topology changes by quantum tunneling

Siebenmann-type cobordisms are constructed to describe topology changes with the Seifert fibered homology spheres in in- and out-states. We study the problem of determining of topology-changing amplitudes for these quantum tunneling processes. The calculations are performed in the stationary phase approximation for Kodama wave functions. In this approximation the amplitudes are expressed in terms of Chern-Simons invariants of flatSU(2)-connections over the cobordism boundary components. The topology-change amplitudes found are factorized into the Kodama wave functions for the lens spaces. The results are compared with those for Fintushel-Stern-type cobordisms which have been previously investigated.     

Factorization of topology changing amplitudes in the Regge calculus approach to quantum cosmology

We study the form of topology changing amplitudes within the Regge calculus approach to four-dimensional gravity. The four-dimensional simplicial complex is chosen to be a cone over the disjoint union of a number of topologically distinct lens spaces. By restricting attention to a simplicial minisuperspace, the analytic properties of the Regge action can be identified explicitly. The classical extrema and convergent steepest descent contours defining these amplitudes are determined, and a factorization property is established. In the cases studied, we find ground state wave functions which predict Lorentzian oscillatory behaviour in the late universe.     

Chern-Simons Theory,Matrix Integrals,and Perturbative Three-Manifold Invariants

The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some previous results of Lawrence and Rozansky, the Chern-Simons partition function with arbitrary simply-laced group for these spaces is written in terms of matrix integrals. The analysis of the perturbative expansion amounts to the evaluation of averages in a Gaussian ensemble of random matrices. As a result, explicit expressions for the universal perturbative invariants of Seifert homology spheres up to order five are presented.     

Witten's invariants of rational homology spheres at prime values ofK and trivial connection contribution

We establish a relation between the coefficients of asymptotic expansion of the trivial connection contribution to Witten's invariant of rational homology spheres and the invariants that T. Ohtsuki extracted from Witten's invariant at prime values ofK. We also rederive the properties of primeK invariants discovered by H. Murakami and T. Ohtsuki. We do this by using the bounds on Taylor series expansion of the Jones polynomial of algebraically split links, studied in our previous paper. These bounds are enough to prove that Ohtsuki's invariants are of finite type. The relation between Ohtsuki's invariants and trivial connection contribution is verified explicitly for lens spaces and Seifert manifolds.Work supported by the National Science Foundation under Grant No. PHY-92 009978.     

Hadronic quark distribution amplitudes from QCD sum-rule moments

We discuss the reliability of hadronic wave functions (quark distribution amplitudes) determined by a finite number of QCD sum-rule moments. Although the expansion coefficients for polynomial models of the wave function are uniquely determined by the moments, the inherent uncertainty in such moments leads to a considerable indeterminacy in the wave functions because minimal changes of the moments can lead to large oscillations of the model function. In particular, the freedom in the moments left by QCD sum rules leads to a nonconverging polynomial expansion. This remains true even if additional constraints on the wave functions are used. As a consequence of this, the widely used procedure of constructing polynomial models of hadronic wave function from QCD sum rule moments does not guarantee even a reasonable approximation to the true wave function. The differences among the model wave functions persist also in the calculations of physical observables like hadronic form factors. This implies that physical observables calculated by means of such model wave functions are in general very unreliable. As specific examples, we examine the pion and nucleon wave functions and show that Gegenbauer as well as Appell polynomial expansions constructed from QCD sum rule moments are ruled out. The implications for the wave functions which are generally used in the literature are discussed.     

Analysis of two neutron (proton) transfer reaction data in the Zr-region

The spectroscopic amplitudes, form factors, angular distributions and total cross-sections for two nucleon transfer reactions in Zr-region in the zero range distorted wave Born approximation are calculated using consistent set of shell model wave functions. A single normalisation factor gives a good fit to all the two neutron transfer reaction data whereas the corresponding fit for the two-proton transfer reaction data is less satisfactory.     

Investigation of the transverse beam dynamics in the thermal wave model with a functional method

We investigated the transverse beam dynamics in a thermal wave model by using a functional method. It can describe the beam optical elements separately with a kernel for a component. The method can be applied to general quadrupole magnets beyond a thin lens approximation as well as drift spaces. We found that the model can successfully describe the PARMILA simulation result through an FODO lattice structure for the Gaussian input beam without space charge effects.     

The Spectral Action and Cosmic Topology

The spectral action functional, considered as a model of gravity coupled to matter, provides, in its non-perturbative form, a slow-roll potential for inflation, whose form and corresponding slow-roll parameters can be sensitive to the underlying cosmic topology. We explicitly compute the non-perturbative spectral action for some of the main candidates for cosmic topologies, namely the quaternionic space, the Poincaré dodecahedral space, and the flat tori. We compute the corresponding slow-roll parameters and we check that the resulting inflation model behaves in the same way as for a simply-connected spherical topology in the case of the quaternionic space and the Poincaré homology sphere, while it behaves differently in the case of the flat tori. We add an appendix with a discussion of the case of lens spaces.     

Spatial correlations of pairing collective states

The properties of the low-energy nuclear spectrum are greatly affected by pairing correlations. We study these effects in the nucleus ²¹⁰Pb which has two particles moving outside closed shells. The configuration-mixed wave functions describe the motion of particles which are on the average closer together than they would be if the particles were confined to particular orbitals. Since the energy associated with pairing correlations is much smaller than the Fermi energy the width of the associated probability distribution is determined by the wavelength of single particles moving close to the Fermi surface. Despite the fact that the amplitudes associated with high-lying configurations are small, their net effect is important, typically changing the collectivity of the states by a factor of about two. The results of the microscopic calculations compare well with a semiclassical pairing transition density calculated on the basis of the Thomas-Fermi approximation.     

Calculation of the differential cross sections of excitation and ionization of a helium atom by electrons

Equations for the amplitudes and differential cross sections of electronic excitation and ionization of a helium atom are derived in the approximation of a frozen ion core. The wave functions of the discrete states are chosen in the form of generalized hydrogenlike orbitals. The radial wave functions of the continuous spectrum are determined by solving the equation of motion numerically. The differential excitation cross sections of excitation of the 2p, 3p, and 4p levels and ionization of a helium atom by electrons are calculated in the energy range up to 50 eV. Estimates are obtained for the nonorthogonal wave functions in the amplitudes of the excitation and ionization processes. It is shown that the given method is more compatible with experiment than the Born method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 48–57, December, 1994.     

Exact treatment of the saturation behaviour of second-harmonic generation

We investigate the interaction between a fundamental plane wave and the second-harmonic wave propagating in a nonlinear medium. Of particular interest is the dependence of the second-harmonic amplitude and of the susceptibility on the amplitude of the fundamental wave in the stationary case. Therefore, spatial structures are assumed as simple as possible (amplitudes constant in space, phase matching direction). The susceptibilities are not calculated by iteration, as it was done so far, but exactly, using a classical model of matter (anharmonic oscillators). The exact solution is expanded into series for small field amplitudes and compared term by term with the results achieved by the usual methods, i.e. calculation of the susceptibilities by perturbation theory, parametric approximation, coupled amplitude approximation. The lowest term is identical with the parametric approximation. The additional term of the coupled amplitude approximation, however, is not consistent with the exact solution.     

The Q2 evolution of flavour singlet wave functions in QCD

We calculate the Q² evolution of the quark-antiquark and gluon-gluon components of helicity-zero, flavour and colour singlet wave functions by summing diagrams to all orders in axial gauge QCD perturbation theory in the leading logarithm approximation. We find that Gegenbauer moments of these components have exactly the same scale-breaking behaviour as moments of singlet quark and gluon distribution functions in leptoproduction. The resulting singlet wave function is used to calculate the amplitudes for quark-antiquark and gluon-gluon jet production in off-shell photon-photon collisions.     

Intersubband optical refractive index changes in an asymmetric quantum dot underlying an external static magnetic field

We theoretically investigate the refractive index (RI) changes in an asymmetric quantum dot (QD) underlying an external static magnetic field. We obtain the confined wave functions and energies of an electron in QD by the effective-mass approximation. Using the compact-density-matrix approach and iterative method, we obtain the analytical expressions of linear, nonlinear and total RI changes. The results of numerical calculations for the typical GaAs/AlGaAs QD show that the RI changes are sensitive to the parameters of the asymmetric potential and incident optical intensity. Moreover, the resonance peaks of the RI changes shift with the value of magnetic field B or the radius of the QD changing.     

Mechanisms of binary and ternary low-energy fission of nuclei with allowance for nonsphericity effects

Within the quantum-mechanical theory of fission, wave functions for fragments of binary nuclear fission and amplitudes of partial fission widths are constructed with allowance for a strong nonsphericity of fragment-interaction potentials. It is shown that, in the strong-coupling approximation, the symmetry axes of fission fragments are oriented along the symmetry axis of a fissile nucleus. The structure of the fragment-interaction potentials is analyzed, and the mechanism that is responsible for the alignment of the spins and relative orbital angular momenta of fission fragments and which explains the emergence of high fragment-spin values in experiments is substantiated. The mechanisms in question are generalized to the case of ternary nuclear fission. The fragment-interaction potentials and fragment wave functions are investigated, along with the partial fission widths with respect to the ternary fission of nuclei.     

A study of the optical transfer function for annular binary filters

The annular binary pupil filters consist of two transparent annuli obstructed by an annular mask. The optical transfer functions for them are analytically derived under paraxial approximation, and three- and two- as well as one-dimensional numerical plots are presented. It is shown that by changing the parameters of transparent regions it is possible to improve the axial resolution whilst the transverse resolution remains unchanged, compared with an annular lens. Results indicate, as is well known, that this kind of filters can be applied to three-dimensional confocal microscopy.     

Gluon cascades and amplitudes in light-front perturbation theory

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.     

Green function and scattering amplitudes in many-dimensional space

Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation.     

Phase effects during parametric conversion in layer structures

Coupled-wave equations that describe the parametric amplification and generation of a sum frequency in a three-layer structure are studied theoretically in the constant-intensity approximation taking into account the inverse effect of the excited wave on the phase of the pumping wave. For this purpose, the approximation of constant intensity of the fundamental radiation is applied not to the layer structure as a whole but to each separately taken layer. In this case, the complex amplitudes of the interacting waves at the output of each layer are the input values of the corresponding complex amplitudes for the next layer. Analytical expressions obtained in the constant-intensity approximation for the efficiency of conversion to the sum frequency were analyzed numerically for different parameters of the problem. The efficiency of parametric amplification at a high frequency was found to depend on the intensity of the signal wave at a low frequency.     

Local properties of nonrenormalizable interactions

The possibility of constructing strictly localizable fields is considered, using generalized S-type spaces as spaces of basis functions. The restrictions imposed on the asymptotic behavior of the amplitudes coincide with the well-known restrictions found by Jaffe. Contrary to previous results, the spatial amplitudes and momenta are regular, and not singular functions, in the case considered. The possibility of formulating spectral conditions is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 76–81, August, 1971.