Step Bunching with Alternation of Structural Parameters

By taking account of the alternation of structural parameters, we study bunching of impermeable steps induced by drift of adatoms on a vicinal face of Si(001). With the alternation of diffusion coefficient, the step bunching occurs irrespective of the direction of the drift if the step distance is large. Like the bunching of permeable steps, the type of large terraces is determined by the drift direction. With step-down drift, step bunches grows faster than those with step-up drift. The ratio of the growth rates is larger than the ratio of the diffusion coefficients. Evaporation of adatoms, which does not cause the step bunching, decreases the difference. If only the alternation of kinetic coefficient is taken into account, the step bunching occurs with step-down drift. In an early stage, the initial fluctuation of the step distance determines the type of large terraces, but in a late stage, the type of large terraces is opposite to the case of alternating diffusion coefficient.Comment: 8pages, 16 figure

On correlation functions of integrable models associated to the six-vertex R-matrix

We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum models. This generalized master equation allows us to obtain multiple integral representations for the correlation functions of these models. We apply this method to derive the density-density correlation functions of the quantum non-linear Schrodinger model.Comment: 21 page

The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations

In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wave functions. From this, we derive the Lax representation for the $N$-component KP hierarchy, which are equations satisfied by some pseudodifferential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in \cite{2}, we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in \cite{3}.Comment: 19 page

Metric perturbation from inflationary magnetic field and generic bound on inflation models

There is an observational indication of extragalactic magnetic fields. No known astrophysical process can explain the origin of such large scale magnetic fields, which motivates us to look for their origin in primordial inflation. By solving the linearized Einstein equations, we study metric perturbations sourced by magnetic fields that are produced during inflation. This leads to a simple but robust bound on the inflation models by requiring that the induced metric perturbation should not exceed the observed value 10^-5. In case of the standard single field inflation model, the bound can be converted into a lower bound on the Hubble parameter during inflation.Comment: 14 page

Towards unravelling the structural distribution of ultra-high-energy cosmic ray sources

We investigate the possibility that near future observations of ultra-high-energy cosmic rays (UHECRs) can unveil their local source distribution, which reflects the observed local structures if their origins are astrophysical objects. In order to discuss this possibility, we calculate the arrival distribution of UHE protons taking into account their propagation process in intergalactic space i.e. energy losses and deflections by extragalactic magnetic field (EGMF). For a realistic simulation, we construct and adopt a model of a structured EGMF and UHECR source distribution, which reproduce the local structures actually observed around the Milky Way. The arrival distribution is compared statistically to their source distribution using correlation coefficient. We specially find that UHECRs above $10^{19.8}$eV are best indicators to decipher their source distribution within 100 Mpc, and detection of about 500 events on all the sky allows us to unveil the local structure of UHE universe for plausible EGMF strength and the source number density. This number of events can be detected by five years observation by Pierre Auger Observatory.Comment: 7pages, 4 figures, submitted to Ap

An Isomonodromy Cluster of Two Regular Singularities

We consider a linear $2\times2$ matrix ODE with two coalescing regular singularities. This coalescence is restricted with an isomonodromy condition with respect to the distance between the merging singularities in a way consistent with the ODE. In particular, a zero-distance limit for the ODE exists. The monodromy group of the limiting ODE is calculated in terms of the original one. This coalescing process generates a limit for the corresponding nonlinear systems of isomonodromy deformations. In our main example the latter limit reads as $P_6\to P_5$, where $P_n$ is the $n$-th Painlev\'e equation. We also discuss some general problems which arise while studying the above-mentioned limits for the Painlev\'e equations.Comment: 44 pages, 8 figure

Thermal background can solve the cosmological moduli problem

It is shown that the coherent field oscillation of moduli fields with weak or TeV scale masses can dissipate its energy efficiently if they have a derivative coupling to standard bosonic fields in a thermal state. This mechanism may provide a new solution to the cosmological moduli problem in some special situations.Comment: 4 pages. revised versio

Risk Adjusted Deposit Insurance for Japanese Banks

The purpose of this paper is to evaluate the Japanese deposit insurance scheme by contrasting the flat insurance rate with a market-determined risk-adjusted rate. The model used to calculate the risk-adjusted rate is that of Ronn and Verrna (1986) . It utilizes the notion of Merton(1977) that the deposit insurance can be based on a one-to-one relation between it and the put option; this permits the application of Black and Scholes(1973) model for the calculation of the insurance rate. The risk adjusted premiums are calculated for the thirteen city banks and twenty-two regional banks. The inter-bank spread in risk-adjusted rates in Japan is found to be as wide as in the United States. But the insurance system is only one component of the safety network for a county's banking system. The difference in the American and Japanese networks is described and its implications for the evaluation of the insurance system is discussed.