arXiv subjects
Publications and source records attributed to T. Sato.
Quantization of a system constrained to move on a sphere is considered by taking a square root of the ``on sphere condition''. We arrive at the fibre bundle structure of the Hopf map in the cases of $S^{2} $and $S^{4}$. This leads to more geometrical understanding of monopole and instanton gauge structures that emerge in the course of quantization.
The finite-difference time-domain (FDTD) method is employed to solve the three dimensional Maxwell equation for the situation of near-field microscopy using a sub-wavelength aperture. Experimental result on unexpected high spatial resolution is reproduced by our computer simulation.
We discuss the results of a systematic calculation of the next-to-next-to-leading order amplitude for the pp -> ppπ^0 S-wave production at the threshold in heavy-baryon chiral perturbation theory. We find six new diagrams, two of which can be viewed as vertex corrections, of 15 - 20 %, to the pion-exchange graph, whereas the rest are much larger, one exceeding 900 %. We discuss the reasons for this enhancement, as well as the steps necessary to be taken before the final comparison with experiment.
We study the Fermi surface of Bi2Sr2CaCu2O8 (Bi2212) using angle resolved photoemission (ARPES) with a momentum resolution of ~ 0.01 of the Brillouin zone. We show that, contrary to recent suggestions, the Fermi surface is a large hole barrel centered at (pi,pi), independent of the incident photon energy.
Recent improvements in momentum resolution by a factor of 32 lead to qualitatively new ARPES results on the spectra of Bi2Sr2CaCu2O8 (Bi2212) along the (pi,pi) direction, where there is a node in the superconducting gap. With improved resolution, we now see the intrinsic lineshape, which indicates the presence of true quasiparticles at the Fermi momentum in the superconducting state, and lack thereof in the normal state. The region of momentum space probed here is relevant for charge transport, motivating a comparison of our results to conductivity measurements by infrared reflectivity.
We present a systematic analysis of next-to-next-to-leading-order diagrams that contribute to the $pp \to ppπ^0$ production at threshold. Analytic expressions are given for the effective transition operators, and the relative importance of various types of diagrams is discussed. The vertex-correction-type graphs are found to give only small corrections to lower order graphs in conformity with expectations. By contrast, we find very large contributions from the two-pion graphs which can be interpreted as a part of effective $σ$-meson exchange diagrams. The recoil correction to the pion rescattering diagram also turns out to be large.
A dynamical approach is developed to predict the $πN$ scattering amplitudes starting with the constituent quark models. The first step is to apply a variational method to solve the three-quark bound state problem. The resulting wave functions are used to calculate the $N^* \to πN, ηN, πΔ$ vertex functions by assuming that the $π$ and $η$ mesons couple directly to quarks. These vertex functions and the predicted baryon bare masses then define a Hamiltonian for $πN$ reactions. We apply a unitary transformation method to derive from the constructed Hamiltonian a multi-channel and multi-resonance reaction model for predicting the $πN$ scattering amplitudes up to $W = 2$ GeV. With the parameters constrained by the $Δ(1232$) excitation, we have examined the extent to which the $πN$ scattering in $S_{11}$ channel can be described by the constituent quark models based on the one-gluon-exchange or one-meson-exchange mechanisms. It is found that the data seem to favor the spin-spin interaction due to one-meson-exchange and the tensor interaction due to one-gluon-exchange. A phenomenological quark-quark potential has been constructed to reproduce the $S_{11}$ amplitude.
Photoemission spectra of Bi2Sr2CaCu2O8 reveal that the high energy feature near (pi,0), the "hump", scales with the superconducting gap and persists above Tc in the pseudogap phase. As the doping decreases, the dispersion of the hump increasingly reflects the wavevector (pi,pi) characteristic of the undoped insulator, despite the presence of a large Fermi surface. This can be understood from the interaction of the electrons with a collective mode, supported by our observation that the doping dependence of the resonance observed by neutron scattering is the same as that inferred from our data.
Comparing ARPES measurements on Bi2212 with penetration depth data, we show that a description of the nodal excitations of the d-wave superconducting state in terms of non-interacting quasiparticles is inadequate, and we estimate the magnitude and doping dependence of the Landau interaction parameter which renormalizes the linear T contribution to the superfluid density. Furthermore, although consistent with d-wave symmetry, the gap with underdoping cannot be fit by the simple coskx-cosky form, which suggests an increasing importance of long range interactions as the insulator is approached.
The T matrix of the LambdaN-> NN reaction, which is a strangeness changing weak process, is derived. The explicit formulas of the spin observables are given for s-wave p-Lambda final states which kinematically corresponds to inverse reaction of the weak nonmesonic decay of Lambda hypernuclei. One can study interferences between amplitudes of parity- conserving and violating, spin- singlet and triplet and isospin- singlet and triplet. Most of them are not available in the study of the nonmesonic decay. They clarify structure of the reaction and constrain strongly theoretical models for weak hyperon nucleon interaction.
Quantum mechanics on manifolds is not unique and in general infinite number of inequivalent quantizations can be considered. They are specified by the induced spin and the induced gauge structures on the manifold. The configuration space of collective mode in the Skyrme model can be identified with $S^{3}$ and thus the quantization is not unique. This leads to the different predictions for the physical observables.
We propose a new type of Monte-Carlo method which enables us to study the excited state of many-body systems.
We show the necessity of two-nucleon axial currents and associated pion emission/ absorption operators for the partial conservation of the axial current (PCAC) nuclear matrix elements with arbitrary nuclear dynamics described by a nonrelativistic Schroedinger equation. As examples we construct such nonrelativistic axial two-body currents in the linear- and heterotic (g_A = 1.26) sigma models, with an optional isoscalar vector (omega) meson exchange. The nuclear matrix elements obey PCAC only if the nuclear wave functions used in the calculation are solutions to the Schroedinger equation with the static one-meson-exchange potential constructed in the respective (sigma) model. The same holds true for the nucler pion production amplitude, since it is proportional to the divergence of the axial current matrix element, by virtue of PCAC. Thus we found a new consistency condition between the pion creation/absorption operator and the nuclear Hamiltonian. We present examples drawn from our models and discuss implications for one-pion-two-nucleon processes.
Relaxed States of a slightly resistive and turbulent magnetized plasma is obtained by invoking the principle of minimum dissipation which leads to curl curl curl B = λB . A solution of the above equation is accomplished using the analytic continuation of the Chandrasekhar-Kendall eigenfunctions in the complex domain. The new features of this theory is to show (i) a single fluid can relax to an MHD equilibrium which can support pressure gradient even without a flow, (ii) field reversal (RFP) in states that are not force free.
A particle in quantum mechanics on manifolds couples to the induced topological gauge field that characterises the possible inequivalent quantizations. For instance, the gauge potential induced on $S^2$ is that of a magnetic monopole located at the center of $S^2$. We find that the gauge potential induced on $S^3$ ($S^{2n+1}$) is that of a meron (generalized meron) also sitting at the center of $S^3$ ($S^{2n+1}$).
A chiral-perturbative consideration of the near-threshold pp -> pp pi0 reaction indicates that the pion-rescattering term has a substantial energy and momentum dependence. The existing calculations that incorporate this dependence give pion rescattering contributions significantly larger than those of the conventional treatment, and this enhanced rescattering term interferes destructively with the one-body impulse term, leading to theoretical cross sections that are much smaller than the observed values. However, since the existing calculations are based on coordinate-space representation, they involve a number of simplifying assumptions about the energy-momentum flow in the rescattering diagram, even though the delicate interplay between the one-body and two-body terms makes it desirable to avoid these kinematical assumptions. We carry out here a momentum-space calculation that retains the energy-momentum dependence of the vertices as predicted by chiral perturbation theory. Our improved treatment increases the rescattering amplitude by a factor of 3 over the value obtained in the r-space calculations. The pp -> pp pi0 transition amplitude, which is now dominated by the rescattering term, leads to the cross section much larger than what was reported in the approximate r-space calculations. Thus, the extremely small cross sections obtained in the previous chiral perturbative treatments of this reaction should be considered as an accidental consequence of the approximations employed rather than a general feature.
An effective Hamiltonian consisting of bare $Δ\leftrightarrowπN$, $γN$ vertex interactions and energy-independent meson-exchange $πN \leftrightarrow πN, γN$ transition operators is derived by applying a unitary transformation to a model Lagrangian with $N,Δ,π$, $ρ$, $ω$, and $γ$ fields. With appropraite phenomenological form factors and coupling constants for $ρ$ and $Δ$, the model can give a good description of $πN$ scattering phase shifts up to the $Δ$ excitation energy region. It is shown that the best reproduction of the recent LEGS data of the photon-asymmetry ratios in $γp \rightarrow π^0 p$ reactions provides rather restricted constraints on the coupling strengths $G_E$ of the electric $E2$ and $G_M$ of the magnetic $M1$ transitions of the bare $Δ\leftrightarrow γN$ vertex and the less well-determined coupling constant $g_{ωNN}$ of $ω$ meson. Within the ranges that $G_M = 1.9 \pm 0.05$, $G_E = 0.0 \pm 0.025$, and $7 \leq g_{ωNN}\leq 10.5$, the predicted differential cross sections and photon-asymmetry ratios are in an overall good agreement with the data of $γp \rightarrow π^0 p$, $γp \rightarrow π^+ n$, and $γn\rightarrow π^- p$ reactions from 180 MeV to the $Δ$ excitation region. The predicted $M_{1^+}$ and $E_{1^+}$ multipole amplitudes are also in good agreement with the empirical values determined by the amplitude analyses. The constructed effective Hamiltonian is free of the nucleon renormlization problem and hence is suitable for nuclear many-body calculations. We have also shown that the assumptions made in the $K$-matrix method, commonly used in extracting empirically the $γN \rightarrow Δ$ transition amplitudes from the data, are consistent with
B and N K-edge x-ray absorption spectroscopy measurements have been performed on three BN thin films grown on Si substrates using ion-assisted pulsed laser deposition. Comparison of the films' spectra to those of several single-phase BN powder standards shows that the films consist primarily of $sp^2$ bonds. Other features in the films' spectra suggest the presence of secondary phases, possibly cubic or rhombohedral BN. Films grown at higher deposition rates and higher ion-beam voltages are found to be more disordered, in agreement with previous work.