Theoretical Status of Pentaquarks

We review the current status of the theoretical pentaquark search from the direct QCD calculation. The works from the QCD sum rule and the lattice QCD in the literature are carefully examined. The importance of the framework which can distinguish the exotic pentaquark state (if any) from the NK scattering state is emphasized.Comment: Presented at Yukawa International Seminar (YKIS) 2006 on "New Frontiers in QCD", Kyoto, Japan, 20 Nov. - 8 Dec. 2006, 4 page

Anomalous Electric Fields in n-InSb under High Magnetic Fields. I-Experiment

An investigation was made of the anomalous electric field in its various aspects in n-type InSb subjected to strong magnetic field at 77K and 273K, which lead to the conclusion that no open contradiction arose between a part of the present observations and the predictions attainable from Yoshida's model of semimetals. There remained, however, the other part of the experimental results unexplained, being rather natural since an inner property of indium antimonide does not seem so simple comparing with the compensated metals, bismuth and antimony. Especially as for the mechanism of an inversion phenomenon of the polarity of a negative anomalous field at a critical pulse current, we have no available theory to explain at present stage

Density Functional Theory for Block Copolymer Melts and Blends

We derive an expression for the free energy of the blends of block copolymers expressed as a functional of the density distribution of the monomer of each block. The expression is a generalization of the Flory-Huggins-de Gennes theory for homo polymer blends, and also a generalization of the Ohta-Kawasaki theory for the melts of diblock copolymers. The expression can be used for any blends of homopolymers and block copolymers of any topological structure. The expression gives a fast and stable computational method to calculate the micro and macro phase separation of the blends of homopolymers and block copolymers.Comment: 25 pages, 9 figures, will appear in Macromolecule

On a modification method of Lefschetz thimbles

The QCD at finite density is not well understood yet, where standard Monte Carlo simulation suffers from the sign problem. In order to overcome the sign problem, the method of Lefschetz thimble has been explored. Basically, the original sign problem can be less severe in a complexified theory due to the constancy of the imaginary part of an action on each thimble. However, global phase factors assigned on each thimble still remain. Their interference is not negligible in a situation where a large number of thimbles contribute to the partition function, and this could also lead to a sign problem.In this study, we propose a method to resolve this problem by modifying the structure of Lefschetz thimbles such that only a single thimble is relevant to the partition function. It can be shown that observables measured in the original and modified theories are connected by a simple identity. We exemplify that our method works well in a toy model.Comment: 7 pages, 4 figures, talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Response of Single Polymers to Localized Step Strains

In this paper, the response of single three-dimensional phantom and self-avoiding polymers to localized step strains are studied for two cases in the absence of hydrodynamic interactions: (i) polymers tethered at one end with the strain created at the point of tether, and (ii) free polymers with the strain created in the middle of the polymer. The polymers are assumed to be in their equilibrium state before the step strain is created. It is shown that the strain relaxes as a power-law in time $t$ as $t^{-\eta}$. While the strain relaxes as $1/t$ for the phantom polymer in both cases; the self-avoiding polymer relaxes its strain differently in case (i) than in case (ii): as $t^{-(1+\nu)/(1+2\nu)}$ and as $t^{-2/(1+2\nu)}$ respectively. Here $\nu$ is the Flory exponent for the polymer, with value $\approx0.588$ in three dimensions. Using the mode expansion method, exact derivations are provided for the $1/t$ strain relaxation behavior for the phantom polymer. However, since the mode expansion method for self-avoiding polymers is nonlinear, similar theoretical derivations for the self-avoiding polymer proves difficult to provide. Only simulation data are therefore presented in support of the $t^{-(1+\nu)/(1+2\nu)}$ and the $t^{-2/(1+2\nu)}$ behavior. The relevance of these exponents for the anomalous dynamics of polymers are also discussed.Comment: 10 pages, 1 figure; minor errors corrected, introduction slightly modified and references expanded; to appear in Phys. Rev.

Chain motion and viscoelasticity in highly entangled solutions of semiflexible rods

Brownian dynamics simulations are used to study highly entangled solutions of semiflexible polymers. Bending fluctuations of semiflexible rods are signficantly affected by entanglement only above a concentration $c^{**}$, where $c^{**}\sim 10^{3}L^{-3}$ for chains of similar length $L$ and persistence length. For $c > c^{**}$, the tube radius $R_{e}$ approaches a dependence $R_{e} \propto c^{-3/5}$, and the linear viscoelastic response develops an elastic contribution that is absent for $c < c^{**}$. Experiments on isotropic solutions of $F$-actin span concentrations near $c^{**}$ for which the predicted asymptotic scaling of the plateau modulus $G \propto c^{7/5}$ is not yet valid.Comment: 4 pages, 5 figures, submitted to PR