Transfer matrix method to study electromagnetic shower

Transfer matrix method gives underlying dynamics of a multifractal. In the present studies transfer matrix method is applied to multifractal properties of Cherenkov image from which probabilities of electromagnetic components are obtained.Comment: 7 page

Improved transfer matrix method without numerical instability

A new improved transfer matrix method (TMM) is presented. It is shown that the method not only overcomes the numerical instability found in the original TMM, but also greatly improves the scalability of computation. The new improved TMM has no extra cost of computing time as the length of homogeneous scattering region becomes large. The comparison between the scattering matrix method(SMM) and our new TMM is given. It clearly shows that our new method is much faster than SMM.Comment: 5 pages,3 figure

Free field approach to diagonalization of boundary transfer matrix : recent advances

We diagonalize infinitely many commuting operators $T_B(z)$. We call these operators $T_B(z)$ the boundary transfer matrix associated with the quantum group and the elliptic quantum group. The boundary transfer matrix is related to the solvable model with a boundary. When we diagonalize the boundary transfer matrix, we can calculate the correlation functions for the solvable model with a boundary. We review the free field approach to diagonalization of the boundary transfer matrix $T_B(z)$ associated with $U_q(A_2^{(2)})$ and $U_{q,p}(\hat{sl_N})$. We construct the free field realizations of the eigenvectors of the boundary transfer matrix $T_B(z)$. This paper includes new unpublished formula of the eigenvector for $U_q(A_2^{(2)})$. It is thought that this diagonalization method can be extended to more general quantum group $U_q(g)$ and elliptic quantum group $U_{q,p}(g)$.Comment: To appear in Group 28 : Group Theoretical Method in Physic

Inward continuation of the scalp potential distribution by means of the (vector) BEM

The vector Boundary Element Method (vBEM) is used for the calculation of a matrix that links the tangential components of the current density on the cortical and scalp surface. This so-called transfer matrix is compared to the transfer matrix that links the potential distribution on both surfaces. Forward and inverse calculations are performed to evaluate both types of transfer matrice

Corner Transfer Matrix Renormalization Group Method

We propose a new fast numerical renormalization group method,the corner transfer matrix renormalization group (CTMRG) method, which is based on a unified scheme of Baxter's corner transfer matrix method and White's density matrix renormalization groupmethod. The key point is that a product of four corner transfer matrices gives the densitymatrix. We formulate the CTMRG method as a renormalization of 2D classical models.Comment: 8 pages, LaTeX and 4 figures. Revised version is converted to a latex file and added an example of a computatio

Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.Comment: 15 pages, uses IOP styl

Density matrix renormalization group for 19-vertex model

We embody the density matrix renormalization group method for the 19-vertex model on a square lattice; the 19-vertex model is regarded to be equivalent to the XY model for small interaction. The transfer matrix of the 19-vertex model is classified by the total number of arrows incoming into one layer of the lattice. By using this property, we reduce the dimension of the transfer matrix appearing in the density matrix renormalizaion group method and obtain a very nice value of the conformal anomaly which is consistent with the value at the Berezinskii-Kosterlitz-Thouless transition point. Keyword : Kosterlitz-Thouless, Renormalization groupComment: 7 pages, 1 figure , REVTE