Takashi Odagaki

An admittance for localized physical quantities is generally related to a random walk on the basis of linear-response theory. A coherent-medium approximation is introduced to solve a master equation which is assumed to govern the random walk. The general formalism is specialized to ac hopping conduction and applied to the bond-percolation model in one- and three-dimensional systems and to a lattice model for impurity conduction in doped semiconductors. For the one-dimensional bond-percolation mo

Dynamics of atoms near the glass transition of simple classical liquids is studied on the basis of the mesoscopic stochastic-trapping diffusion model recently developed by Odagaki [J. Phys. A 20, 6455 (1987); Phys. Rev. B. 38, 9044 (1988)]. The jump rate of an atom (tracer) is assumed to have a distribution following a power-law function with exponent \ensuremath{\rho}, where \ensuremath{\rho} is a phenomenological parameter. A sharp transition is predicted at \ensuremath{\rho}=0, that is, the s

The tight-binding electronic structure of two-dimensional quasicrystals is studied numerically for three patterns of Penrose tiling with up to 426 vertices. According to the range of interactions, three different models are considered. For the simplest model, two different interactions are assigned to long and short edges of the Penrose tile. Energy spectra show several significant gaps whose width and position depend on the relative strength of the interactions. The cumulative density of states

The exact frequency dependence of the ac hopping conductivity of a one-dimensional chain with random interruptions is obtained. The real and imaginary parts of the ac conductivity are shown to vanish quadratically and linearly, respectively, with frequency at the static limit. Critical behavior of the ac conductivity in the limit of no interruptions is discussed.

The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable. It is assumed that the society consists of four compartments; susceptible individuals (S), infected individuals at large (I), quarantined patients (Q) and recovered individuals (R), and the time evolution of the pandemic is described by a set of ordinary differential equations. It is shown that the quarantine rate can be determined fro

We devise a method based on an analysis of the non-Gaussian parameter in a finite time domain to determine the transition between Gaussian and non-Gaussian dynamics in a stochastic trapping model of a glass transition. We find evidence of the Gaussian--to--non-Gaussian transition in the supercooled region of soft-sphere fluids. We propose an alternative analysis of the incoherent scattering function for glass-forming systems to observe the transition.

Quantum percolation problems are studied with the use of a real-space renormalization-group method. A quantum effect is taken into account by calculating the quantum-mechanical efficiency of the Kadanoff cell in opening a channel for an electron in the cell. The quantum percolation threshold and the critical index for the correlation length are obtained for both the site and bond problems in the square and simplecubic lattices.

The ac conductivity of carriers which perform a random walk in a random environment is studied. Irreducible clusters of hopping sites are introduced by connecting sites which share a nonzero jump rate. A finite irreducible random-walk matrix is shown to be negative semidefinite and have a nondegenerate zero eigenvalue. As a result, the real and imaginary parts of the ac conductivity of systems without infinite irreducible clusters vanish, respectively, quadratically and linearly with the frequen

Hopping conduction of a bond-percolation model in $d$-dimensional lattices is studied by making use of the coherent-medium approximation. The dc conductivity vanishes when $p<{p}_{c} (\ensuremath{\equiv}\frac{2}{z})$ and is proportional to $p\ensuremath{-}{p}_{c}$ when $p\ensuremath{\ge}{p}_{c}$, where $p$ is the probability that a given bond is not broken and $z$ is the coordination number of the lattice. In the low frequency region, the leading term of the imaginary and real parts of the ac

A percolation process concerned with the properties of quantum mechanical particles moving in a random medium is investigated numerically. The random characteristics of the medium are introduced in the same manner as in the classical method: in the site problem, any site has a fixed probability x of being unblocked, whereas in the bond problem, any bond has a fixed probability p of being unblocked. If xcQ (or pcQ) is a maximum value of x (or p) for which a quantum mechanical particle attached to

The percolation theory is extended to a thermal equilibrium state of an interacting particle system. By a computer simulation method, percolation process in a square lattice gas model is studied in super-critical regions. Critical percolation density is found to be an increasing function of temperature. The critical index of percolation probability is almost independent of temperature and 0.145±0.027. The result obtained in the lattice gas model is applied to the metal-insulator transition in su

Slow dynamics in supercooled liquids is investigated on the basis of the trapping diffusion model which takes account of two types of diffusive dynamics, jump motion and stray motion. Parameters of the model are determined in such a way that the waiting-time distribution of the model agrees with those found for a binary soft-sphere system through molecular-dynamics simulation. With the use of the coherent-medium approximation, the frequency dependence of the self-part of the dynamical structure