A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces

We reformulate the Ponzano-Regge quantum gravity model in terms of surfaces on a 3-dimensional simplex lattice. This formulation (1) has a clear relation to the loop representation of the canonical quantum general relativity in 3-dimensions, (2) may have a 4-dimensional analogue, in contrast to the 6-j symbolic formalism of the Ponzano-Regge model, and (3) is purely a theory of surfaces, in the sense that it does not include any field variables; hence it is coordinate-free on the surface and background-free in spacetime. We discuss implications and applications of this formulation.Comment: latex 11 page

Current-Driven Motion of Magnetic Domain Wall with Many Bloch Lines

The current-driven motion of a domain wall (DW) in a ferromagnet with many Bloch lines (BLs) via the spin transfer torque is studied theoretically. It is found that the motion of BLs changes the current-velocity ($j$-$v$) characteristic dramatically. Especially, the critical current density to overcome the pinning force is reduced by the factor of the Gilbert damping coefficient $\alpha$ even compared with that of a skyrmion. This is in sharp contrast to the case of magnetic field driven motion, where the existence of BLs reduces the mobility of the DW

Inertia, diffusion and dynamics of a driven skyrmion

Skyrmions recently discovered in chiral magnets are a promising candidate for magnetic storage devices because of their topological stability, small size ($\sim 3-100$nm), and ultra-low threshold current density ($\sim 10^{6}$A/m$^2$) to drive their motion. However, the time-dependent dynamics has hitherto been largely unexplored. Here we show, by combining the numerical solution of the Landau-Lifshitz-Gilbert equation and the analysis of a generalized Thiele's equation, that inertial effects are almost completely absent in skyrmion dynamics driven by a time-dependent current. In contrast, the response to time-dependent magnetic forces and thermal fluctuations depends strongly on frequency and is described by a large effective mass and a (anti-) damping depending on the acceleration of the skyrmion. Thermal diffusion is strongly suppressed by the cyclotron motion and is proportional to the Gilbert damping coefficient $\alpha$. This indicates that the skyrmion position is stable, and its motion responds to the time-dependent current without delay or retardation even if it is fast. These findings demonstrate the advantages of skyrmions as information carriers.Comment: 9 pages, 10 figure

Two-dimensional Lattice Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Chemical Potential

We investigate the phase structure of the two-dimensional lattice Gross-Neveu model formulated with the Wilson fermion action to leading order of 1/N expansion. Structural change of the parity-broken phase under the influence of finite temperature and chemical potential is studied. The connection between the lattice phase structure and the chiral phase transition of the continuum theory is clarified.Comment: 42 pages, 20 EPS figures, using REVTe

Prognostic Model for Hepatocellular Carcinoma with Time-Dependent Factors

The purpose of this study was to build a prognostic model of hepatocellular carcinoma (HCC) using time-dependent covariates to re-evaluate the prognosis at any stage of the disease. The subjects were consecutive HCC patients who were treated at our institute between 1995 and 2007. We constructed time-fixed and time-dependent prognostic models with a training group (n＝336) and compared the prognostic abilities between conventional Cancer of the Liver Italian Program (CLIP) scores, Japan Integrated Staging (JIS) scores, an Okuda classification, and our prognostic models in the testing group (n＝227) with the c-index. The time-dependent prognostic model consisted of main tumor size, tumor number, portal vein invasion, distant metastasis, alpha-fetoprotein, des-gamma-carboxy prothrombin (DCP), bilirubin, and albumin and the weighted scores were set for each factor depending on the hazard ratio for the prognosis. The prognostic index was determined by summing the scores. The c-index values for the CLIP scores, JIS scores, Okuda classification, and our time-dependent model were 0.741, 0.727, 0.609, and 0.870, respectively. These results indicate that our time-dependent model can estimate the prognosis of HCC more precisely than traditional time-fixed models and can be used to re-predict the prognosis of HCC