No Arabic abstract
We take advantage of peculiar properties of three dimensional incompressible turbulence to introduce a nonstandard Exact Renormalization Group method. A Galilean invariance preserving regularizing procedure is utilized and a field truncation is adopted to test the method. Results are encouraging: the energy spectrum E(k) in the inertial range scales with exponent -1.666+/- 0.001 and the Kolmogorov constant C_K, computed for several (realistic) shapes of the stirring force correlator, agrees with experimental data.
The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of the Wilson action in the exact renormalization group (ERG) formalism. By imitating the structure of this connection, we propose an ERG differential equation that preserves manifest gauge invariance in Yang--Mills theory. Our construction in continuum theory can be extended to lattice gauge theory.
We investigate possible renormalization-group fixed points at nonzero coupling in $phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a one-component scalar, (b) a scalar transforming as the fundamental representation of a global ${rm SU}(N)$ symmetry group, and (c) a scalar transforming as a bi-adjoint representation of a global ${rm SU}(N) otimes {rm SU}(N)$ symmetry. We do not find robust evidence for such fixed points in theories (a) or (b). Theory (c) has the special feature that the one-loop term in the beta function is zero; implications of this are discussed.
The exact renormalization group methods is applied to many fermion systems with short-range attractive force. The strength of the attractive fermion-fermion interaction is determined from the vacuum scattering length. A set of approximate flow equations is derived including fermionic and bosonic fluctuations. The numerical solutions show a phase transition to a gapped phase. The inclusion of bosonic fluctuations is found to be significant only in the small-gap regime.
Excited states in 38,40,42Si nuclei have been studied via in-beam gamma-ray spectroscopy with multi-nucleon removal reactions. Intense radioactive beams of 40S and 44S provided at the new facility of the RIKEN Radioactive Isotope Beam Factory enabled gamma-gamma coincidence measurements. A prominent gamma line observed with an energy of 742(8) keV in 42Si confirms the 2+ state reported in an earlier study. Among the gamma lines observed in coincidence with the 2+ -> 0+ transition, the most probable candidate for the transition from the yrast 4+ state was identified, leading to a 4+_1 energy of 2173(14) keV. The energy ratio of 2.93(5) between the 2+_1 and 4+_1 states indicates well-developed deformation in 42Si at N=28 and Z=14. Also for 38,40Si energy ratios with values of 2.09(5) and 2.56(5) were obtained. Together with the ratio for 42Si, the results show a rapid deformation development of Si isotopes from N=24 to N=28.
Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic d=3 physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers, are obtained for Ising, XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.