Fitting two nucleons inside a box: exponentially suppressed corrections to the Luscher's formula

Scattering observables can be computed in lattice field theory by measuring the volume dependence of energy levels of two particle states. The dominant volume dependence, proportional to inverse powers of the volume, is determined by the phase shifts. This universal relation (\Lu's formula) between energy levels and phase shifts is distorted by corrections which, in the large volume limit, are exponentially suppressed. They may be sizable, however, for the volumes used in practice and they set a limit on how small the lattice can be in these studies. We estimate these corrections, mostly in the case of two nucleons. Qualitatively, we find that the exponentially suppressed corrections are proportional to the {\it square} of the potential (or to terms suppressed in the chiral expansion) and the effect due to pions going ``around the world'' vanishes. Quantitatively, the size of the lattice should be greater than $\approx(5 {fm})^3$ in order to keep finite volume corrections to the phase less than $1^\circ$ for realistic pion mass.Comment: 18 pages, 5 figures, 6 figure

Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field

We present systematic study of zero modes and gaps by introducing effects of anisotropy of hopping integrals for a tight-binding model on the honeycomb lattice in a magnetic field. The condition for the existence of zero modes is analytically derived. From the condition, it is found that a tiny anisotropy for graphene is sufficient to open a gap around zero energy in a magnetic field. This gap behaves as a non-perturbative and exponential form as a function of the magnetic field. The non-analytic behavior with respect to the magnetic field can be understood as tunneling effects between energy levels around two Dirac zero modes appearing in the honeycomb lattice, and an explicit form of the gap around zero energy is obtained by the WKB method near the merging point of these Dirac zero modes. Effects of the anisotropy for the honeycomb lattices with boundaries are also studied. The condition for the existence of zero energy edge states in a magnetic field is analytically derived. On the basis of the condition, it is recognized that anisotropy of the hopping integrals induces abrupt changes of the number of zero energy edge states, which depend on the shapes of the edges sensitively.Comment: 36 pages, 20 figures; added discussion on experiments in Sec.VI, cited Refs.[35]-[40], and reworded Sec.IV

Phytohaemagglutinin on maternal and umbilical leukocytes

Almost all the umbilical lymphocytes showed more extensive blast cell formation than that of their mother's lymphocytes with PHA. Pathological conditions of mother in pregnancy and labor such as anemia, gestational toxicosis, difficult labor and asphyxia of babies, inhibited the normal response of both maternal and umbilical lymphocytes to PHA.</p

A transceiver module of the Mu radar

The transceiver (TR) module of a middle and upper atmospheric radar is described. The TR module used in the radar is mainly composed of two units: a mixer (MIX unit) and a power amplifier (PA unit). The former generates the RF wave for transmission and converts the received echo to the IF signal. A 41.5-MHz local signal fed to mixers passes through a digitally controlled 8-bit phase shifter which can change its value up to 1,000 times in a second, so that the MU radar has the ability to steer its antenna direction quickly and flexibly. The MIX unit also contains a buffer amplifier and a gate for the transmitting signal and preamplifier for the received one whose noise figure is less than 5 dB. The PA unit amplifies the RF signal supplied from the MIX unit up to 63.7 dBm (2350 W), and feeds it to the crossed Yagi antenna

A two micron polarization survey toward dark clouds

A near infrared (2.2 micron) polarization survey of about 190 sources was conducted toward nearby dark clouds. The sample includes both background field stars and embedded young stellar objects. The aim is to determine the magnetic field structure in the densest regions of the dark clouds and study the role of magnetic fields in various phases of star formation processes, and to study the grain alignment efficiency in the dark cloud cores. From the polarization of background field stars and intrinsically unpolarized embedded sources, the magnetic field structure was determined in these clouds. From the intrinsic polarization of young stellar objects, the spatial distribution was determined of circumstellar dust around young stars. Combining the perpendicularity between the disks and magnetic fields with perpendicularity between the cloud elongation and magnetic fields, it is concluded that the magnetic fields might have dominated nearly all aspects of cloud dynamics, from the initial collapse of the clouds right through to the formation of disks/tori around young stars in these low to intermediate mass star forming clouds of the Taurus, Ophiuchus, and Perseus

Baryonic sources using irreducible representations of the double-covered octahedral group

Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states. Complete sets of local and nonlocal straight-link operators are explicitly shown for isospin 1/2 and 3/2 baryons. The orthogonality relations of the IR operators are confirmed in a quenched lattice simulation.Comment: Talk presented at Lattice2004(heavy), Fermilab, June 21-26, 2004, 3 page

Multi-Instantons and Multi-Cuts

We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the one-cut matrix model case as a degeneration of the two-cut case. These formulae show that the instanton gas is ultra-dilute, due to the repulsion among the matrix model eigenvalues. We exemplify and test our general results in the cubic matrix model, where multi-instanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multi-instanton contributions in two-dimensional quantum gravity, verifying them by computing the instanton corrections to the string equation. The resulting amplitudes can be interpreted as regularized partition functions for multiple ZZ-branes, which take into full account their back-reaction on the target geometry. Finally, we also derive structural properties of the trans-series solution to the Painleve I equation.Comment: 34 pages, 3 figures, JHEP3.cls; v2: added references, minor changes; v3: added 1 reference, more minor changes, final version for JMP; v4: more typos correcte

Robust strongly-modulated transmission of a TT-shaped structure with local Rashba interaction

We propose a scheme of spin transistor using a $T$-shaped structure with local Rashba interaction. A wide antiresonance energy gap appears due to the interplay of two types of interference, the Fano-Rashba interference and the structure interference. A large current from the gap area can be obtained via changing the Rashba strength and/or the length of the sidearm by using gate voltage. The robustness of the antiresonance gap against strong disorder is demonstrated and shows the feasibility of this structure for the real application.Comment: 4 pages, 3 figures, To be published in PR

The fractional Schr\"{o}dinger operator and Toeplitz matrices

Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices. We determine the asymptotic behaviour of the product of eigenvalues for the $\alpha$-stable symmetric laws by employing the Szeg\"o's strong limit theorem. The results of the present work can be applied to a recently proposed model for a particle hopping on a bounded interval in one dimension whose hopping probability is given a discrete representation of the fractional Laplacian.Comment: 10 pages, 2 figure