On Kernel Formulas and Dispersionless Hirota Equations

We rederive dispersionless Hirota equations of the dispersionless Toda hierarchy from the method of kernel formula provided by Carroll and Kodama. We then apply the method to derive dispersionless Hirota equations of the extended dispersionless BKP(EdBKP) hierarchy proposed by Takasaki. Moreover, we verify associativity equations (WDVV equations) in the EdBKP hierarchy from dispersionless Hirota equations and give a realization of associative algebra with structure constants expressed in terms of residue formula.Comment: 30 pages, minor corrections, references adde

Spin transport properties of a quantum dot coupled to ferromagnetic leads with noncollinear magnetizations

A correct general formula for the spin current through an interacting quantum dot coupled to ferromagnetic leads with magnetization at an arbitrary angle $\theta$ is derived within the framework of the Keldysh formalism. Under asymmetric conditions, the spin current component J_{z} may change sign for $0<\theta<\pi$. It is shown that the spin current and spin tunneling magnetoresistance exhibit different angle dependence in the free and Coulomb blockade regimes. In the latter case, the competition of spin precession and the spin-valve effect could lead to an anomaly in the angle dependence of the spin current.Comment: 7 pages, 4 figures; some parts of the text has been revised in this version accepted by J. Phys.: Condens. Matte

Valence bond spin liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets

Fermionic valence bond approach in terms of SU(4) representation is proposed to describe the $J_{1}-J_{2}$ frustrated Heisenberg antiferromagnetic (AF) model on a {\it bipartite} square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence bond spin liquid state, interpolating the two different AF ordered states in the large $J_{1}$ and large $J_{2}$ limits, respectively. This novel spin liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structure factor is predicted for momenta ${\bf q}=(0,0)$ and $(\pi ,\pi)$ in the strongly frustrated limit $J_{2}/J_{1}\sim 1/2$, which can be checked by neutron scattering experiment.Comment: Revtex file, 4 pages, 4 figure

Understanding the in vivo Uptake Kinetics of a Phosphatidylethanolamine-binding Agent \u3csup\u3e99m\u3c/sup\u3eTc-Duramycin

Introduction 99mTc-Duramycin is a peptide-based molecular probe that binds specifically to phosphatidylethanolamine (PE). The goal was to characterize the kinetics of molecular interactions between 99mTc-Duramycin and the target tissue. Methods High level of accessible PE is induced in cardiac tissues by myocardial ischemia (30 min) and reperfusion (120 min) in Sprague–Dawley rats. Target binding and biodistribution of 99mTc-duramycin were captured using SPECT/CT. To quantify the binding kinetics, the presence of radioactivity in ischemic versus normal cardiac tissues was measured by gamma counting at 3, 10, 20, 60 and 180 min after injection. A partially inactivated form of 99mTc-Duramycin was analyzed in the same fashion. A compartment model was developed to quantify the uptake kinetics of 99mTc-Duramycin in normal and ischemic myocardial tissue. Results 99mTc-duramycin binds avidly to the damaged tissue with a high target-to-background radio. Compartment modeling shows that accessibility of binding sites in myocardial tissue to 99mTc-Duramycin is not a limiting factor and the rate constant of target binding in the target tissue is at 2.2 ml/nmol/min/g. The number of available binding sites for 99mTc-Duramycin in ischemic myocardium was estimated at 0.14 nmol/g. Covalent modification of D15 resulted in a 9-fold reduction in binding affinity. Conclusion 99mTc-Duramycin accumulates avidly in target tissues in a PE-dependent fashion. Model results reflect an efficient uptake mechanism, consistent with the low molecular weight of the radiopharmaceutical and the relatively high density of available binding sites. These data help better define the imaging utilities of 99mTc-Duramycin as a novel PE-binding agent

Charmless Two-body B(Bs)→VPB(B_s)\to VP decays In Soft-Collinear-Effective-Theory

We provide the analysis of charmless two-body $B\to VP$ decays under the framework of the soft-collinear-effective-theory (SCET), where $V(P)$ denotes a light vector (pseudoscalar) meson. Besides the leading power contributions, some power corrections (chiraly enhanced penguins) are also taken into account. Using the current available $B\to PP$ and $B\to VP$ experimental data on branching fractions and CP asymmetry variables, we find two kinds of solutions in $\chi^2$ fit for the 16 non-perturbative inputs which are essential in the 87 $B\to PP$ and $B\to VP$ decay channels. Chiraly enhanced penguins can change several charming penguins sizably, since they share the same topology. However, most of the other non-perturbative inputs and predictions on branching ratios and CP asymmetries are not changed too much. With the two sets of inputs, we predict the branching fractions and CP asymmetries of other modes especially $B_s\to VP$ decays. The agreements and differences with results in QCD factorization and perturbative QCD approach are analyzed. We also study the time-dependent CP asymmetries in channels with CP eigenstates in the final states and some other channels such as $\bar B^0/B^0\to\pi^\pm\rho^\mp$ and $\bar B_s^0/B_s^0\to K^\pm K^{*\mp}$. In the perturbative QCD approach, the $(S-P)(S+P)$ penguins in annihilation diagrams play an important role. Although they have the same topology with charming penguins in SCET, there are many differences between the two objects in weak phases, magnitudes, strong phases and factorization properties.Comment: 34 pages, revtex, 2 figures, published at PR

Generating entanglement of photon-number states with coherent light via cross-Kerr nonlinearity

We propose a scheme for generating entangled states of light fields. This scheme only requires the cross-Kerr nonlinear interaction between coherent light-beams, followed by a homodyne detection. Therefore, this scheme is within the reach of current technology. We study in detail the generation of the entangled states between two modes, and that among three modes. In addition to the Bell states between two modes and the W states among three modes, we find plentiful new kinds of entangled states. Finally, the scheme can be extend to generate the entangled states among more than three modes.Comment: 2 figure