Dynamics near QCD critical point by dynamic renormalization group

We work out the basic analysis of dynamics near QCD critical point (CP) by dynamic renormalization group (RG). In addition to the RG analysis by coarse graining, we construct the nonlinear Langevin equation as a basic equation for the critical dynamics. Our construction is based on the generalized Langevin theory and the relativistic hydrodynamics. Applying the dynamic RG to the constructed equation, we derive the RG equation for the transport coefficients and analyze their critical behaviors. We find that the resulting RG equation turns out to be the same as that for the liquid-gas CP except for an insignificant constant. Therefore, the bulk viscosity and the thermal conductivity strongly diverge at the QCD CP. We also show that the thermal and viscous diffusion modes exhibit critical slowing down with the dynamic critical exponents $z_{\rm thermal}\sim 3$ and $z_{\rm viscous}\sim 2$, respectively. In contrast, the sound propagating mode shows critical speeding up with the negative exponent $z_{\rm sound}\sim -0.8$.Comment: 16 pages, 4 figures. accepted version by PRD. A comment on a frame dependence is added in Sec.

Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2

An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c=m/2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.Comment: 23 pages, 1 figure, 3 table

Finding a Style for Presenting Shakespeare on the Japanese Stage

Japanese productions of Shakespeare’s plays are almost always discussed with exclusive focus upon their visual, musical and physical aspects without any due considerations to their verbal elements. Yet the translated texts in the vernacular, in which most of Japanese stage performances of Shakespeare are given, have played crucial part in understanding and analysing them as a whole. This paper aims to illuminate the importance of the verbal styles and phraseology of Shakespeare’s translated texts by analysing Nakayashiki Norihito’s all-female productions of Hamlet (2011) and Macbeth (2012) in the historical contexts of Japanese Shakespeare translation

Dislocation Formation and Work-Hardening in Two-Phase Alloys

A phase field model is presented to investigate dislocation formation (coherency loss) and workhardening in two-phase binary alloys. In our model the elastic energy density is a periodic function of the shear and tetragonal strains, which allows multiple formation of slips (dislocation dipoles). By numerically integrating the dynamic equations in two dimensions, we find that dislocations appear in pairs in the interface region and grow into slips. One end of each slip glides preferentially into the softer region, while the other end remains trapped at the interface. Under uniaxial stretching at deep quenching, slips appear in the softer regions and do not penetrate into the harder domains, giving rise to an increase of the stress with increasing applied strain in plastic flow.Comment: 14 figures (Higher resolution figures can be obtained at http://stat.scphys.kyoto-u.ac.jp/~minami_a/pict/cond-mat0405177/

Extreme value distributions of noncolliding diffusion processes

Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite time interval $(0, T)$, $0 < T < \infty$. We consider four temporally inhomogeneous processes with duration $T$, the noncolliding Brownian bridge, the noncolliding Brownian motion, the noncolliding three-dimensional Bessel bridge, and the noncolliding Brownian meander. Their particle distributions at each time $t \in [0, T]$ are related to the eigenvalue distributions of random matrices in Gaussian ensembles and in some two-matrix models. Extreme values of paths in $[0, T]$ are studied for these noncolliding diffusion processes and determinantal and pfaffian representations are given for the distribution functions. The entries of the determinants and pfaffians are expressed using special functions.Comment: v2: LaTeX2e, 21 pages, 2 figures, correction mad