Constraints and Period Relations in Bosonic Strings at Genus-g

We examine some of the implications of implementing the usual boundary conditions on the closed bosonic string in the hamiltonian framework. Using the KN formalism, it is shown that at the quantum level, the resulting constraints lead to relations among the periods of the basis 1-forms. These are compared with those of Riemanns' which arise from a different consideration.Comment: 16 pages, (Plain Tex), NUS/HEP/9320

On Phase Transition of NH4H2PO4NH_{4}H_{2}PO_{4}-Type Crystals by Cluster Variation Method

The Cluster Variation Method (CVM) is applied to the Ishibashi model for ammonium dihydrogen phosphate ($\rm NH_{4}H_{2}PO_{4}$) of a typical hydrogen bonded anti-ferroelectric crystal. The staggered and the uniform susceptibility without hysteresis are calculated at equilibrium. On the other hand, by making use of the natural iteration method (NIM) for the CVM, hysteresis phenomena of uniform susceptibility versus temperature observed in experiments is well explained on the basis of local minimum in Landau type variational free energy. The polarization $P$ curves against the uniform field is also calculated.Comment: 14 pages, 10 figure

Effect of Material Properties on Soil Liquefaction

Four material constants included in the pore-pressure buildup equation for saturated sands under earthquake loadings are determined as functions of grain size, soil angularity, coefficient of uniformity, and void ratio. This would allow engineers to readily calculate pore-pressure buildup as a function of time, and hence assess the liquefaction potential, for a given soil without conducting cyclic tests

Modeling the momentum distributions of annihilating electron-positron pairs in solids

Measuring the Doppler broadening of the positron annihilation radiation or the angular correlation between the two annihilation gamma quanta reflects the momentum distribution of electrons seen by positrons in the material.Vacancy-type defects in solids localize positrons and the measured spectra are sensitive to the detailed chemical and geometric environments of the defects. However, the measured information is indirect and when using it in defect identification comparisons with theoretically predicted spectra is indispensable. In this article we present a computational scheme for calculating momentum distributions of electron-positron pairs annihilating in solids. Valence electron states and their interaction with ion cores are described using the all-electron projector augmented-wave method, and atomic orbitals are used to describe the core states. We apply our numerical scheme to selected systems and compare three different enhancement (electron-positron correlation) schemes previously used in the calculation of momentum distributions of annihilating electron-positron pairs within the density-functional theory. We show that the use of a state-dependent enhancement scheme leads to better results than a position-dependent enhancement factor in the case of ratios of Doppler spectra between different systems. Further, we demonstrate the applicability of our scheme for studying vacancy-type defects in metals and semiconductors. Especially we study the effect of forces due to a positron localized at a vacancy-type defect on the ionic relaxations.Comment: Submitted to Physical Review B on September 1 2005. Revised manuscript submitted on November 14 200

Scalar Field Probes of Power-Law Space-Time Singularities

We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in hep-th/0403252 for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x^{-2}-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.Comment: v2: 21 pages, JHEP3.cls, one reference adde

Origin of second-harmonic generation in the incommensurate phase of K2SeO4

We show that a ferroelectric phase transition takes place in the incommensurate phase of the K2SeO4 crystal. The ferroelectric character of the IC phase explains the second-harmonic generation observed in the corresponding temperature range.Comment: 5 pages, 1 figur

Excited state g-functions from the Truncated Conformal Space

In this paper we consider excited state g-functions, that is, overlaps between boundary states and excited states in boundary conformal field theory. We find a new method to calculate these overlaps numerically using a variation of the truncated conformal space approach. We apply this method to the Lee-Yang model for which the unique boundary perturbation is integrable and for which the TBA system describing the boundary overlaps is known. Using the truncated conformal space approach we obtain numerical results for the ground state and the first three excited states which are in excellent agreement with the TBA results. As a special case we can calculate the standard g-function which is the overlap with the ground state and find that our new method is considerably more accurate than the original method employed by Dorey et al.Comment: 21 pages, 6 figure

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Compton scattering in Noncommutative Space-Time at the NLC

We study the Compton scattering in the noncommutative counter part of QED (NC QED). Interactions in NC QED have momentum dependent phase factors and the gauge fields have Yang Mills type couplings, this modifies the cross sections and are different from the commuting Standard Model. Collider signals of noncommutative space-time are studied at the Next Linear Collider (NLC) operating in the $e \gamma$ mode. Results for different polarised cases are presented and it is shown that the Compton process can probe the noncommutative scale in the range of 1 - 2.5 TeV for typical proposed NLC energies.Comment: 12 pages, 5 Postscript figures, version to appear in Phys. Rev.

Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations

We analyze the tensor mode perturbations of static, spherically symmetric solutions of the Einstein equations with a quadratic Gauss-Bonnet term in dimension $D > 4$. We show that the evolution equations for this type of perturbations can be cast in a Regge-Wheeler-Zerilli form, and obtain the exact potential for the corresponding Schr\"odinger-like stability equation. As an immediate application we prove that for $D \neq 6$ and $\alpha >0$, the sign choice for the Gauss-Bonnet coefficient suggested by string theory, all positive mass black holes of this type are stable. In the exceptional case $D =6$, we find a range of parameters where positive mass asymptotically flat black holes, with regular horizon, are unstable. This feature is found also in general for $\alpha < 0$.Comment: 7 pages, 1 figure, minor corrections, references adde