Analyses of multiplicity distributions by means of the Modified Negative Binomial Distribution and its KNO scaling function

We analyze various data of multiplicity distributions by means of the Modified Negative Binomial Distribution (MNBD) and its KNO scaling function, since this MNBD explains the oscillating behavior of the cumulant moment observed in e^+e^- annihilations, h-h collisions and e-p collisions. In the present analyses, we find that the MNBD(discrete distributions) describes the data of charged particles in e^+e^- annihilations much better than the Negative Binomial Distribution (NBD). To investigate stochastic property of the MNBD, we derive the KNO scaling function from the discrete distribution by using a straightforward method and the Poisson transform. It is a new KNO function expressed by the Laguerre polynomials. In analyses of the data by using the KNO scaling function, we find that the MNBD describes the data better than the gamma function.Thus, it can be said that the MNBD is one of useful formulas as well as NBD.Comment: 12 pages, latex, 3 figure

SU(3) lattice QCD study for octet and decuplet baryon spectra

The spectra of octet and decuplet baryons are studied using SU(3) lattice QCD at the quenched level. As an implementation to reduce the statistical fluctuation, we employ the anisotropic lattice with $O(a)$ improved quark action. In relation to $\Lambda(1405)$, we measure also the mass of the SU(3) flavor-singlet negative-parity baryon, which is described as a three quark state in the quenched lattice QCD, and its lowest mass is measured about 1.6 GeV. Since the experimentally observed negative-parity baryon $\Lambda(1405)$ is much lighter than 1.6 GeV, $\Lambda(1405)$ may include a large component of a $N \bar K$ bound state rather than the three quark state. The mass splitting between the octet and the decuplet baryons are also discussed in terms of the current quark mass.Comment: 8 pages, 3 figures, proceeding of "International Symposium on Hadron and Nuclei" at Yonsei Univ., Seoul, Korea 20-22 Feb. 200

Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: We construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial models for each highest weight crystal. Applying this construction to the crystal of the fundamental representation recovers a family of combinatorial realizations recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as a generalization to higher level. We also discuss a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some references; v3: many small correction

The Gauge-Bethe Correspondence and Geometric Representation Theory

The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason for its existence remaining elusive. We argue here that geometrical representation theory is the mathematical foundation of the Gauge/Bethe correspondence, and it provides a framework to study families of gauge theories in a unified way.Comment: 8 page

Negative-Parity Baryons in Quenched Anisotropic Lattice QCD

We study negative-parity baryon spectra in quenched anisotropic lattice QCD. The negative-parity baryons are measured as the parity partner of the ground-state baryons. In addition to the flavor octet and decuplet baryons, we pay much attention to the flavor-singlet negative-parity baryon as a three-quark state and compare it with the Lambda(1405) baryon. Numerical results of the flavor octet and decuplet negative-parity baryon masses are close to experimental values of lowest-lying negative-parity baryons, while the flavor-singlet baryon is much heavier than Lambda(1405). This indicates that the Lambda(1405) would be a multi-quark state such as the N-Kbar molecule rather than the flavor-singlet 3 quark state.Comment: 4 pages, 4 figs. Talk given at 16th International Conference on Particles and Nuclei (PANIC 02), Osaka, Japan, 30 Sep - 4 Oct 200

Quantum Coherence and Correlations of optical radiation by atomic ensembles interacting with a two-level atom in microwave cavity

We examine quantum statistics of optical photons emitted from atomic ensembles which are classically driven and simultaneously coupled to a two-level atom via microwave photon exchange. Quantum statistics and correlations are analyzed by calculating second order coherence degree, von Neumann entropy, spin squeezing for multi-particle entanglement, as well as genuine two and three-mode entanglement parameters for steady state and non-equilibrium situations. Coherent transfer of population between the radiation modes and quantum state mapping between the two-level atom and the optical modes are discussed. A potential experimental realization of the theoretical results in a superconducting coplanar waveguide resonator containing diamond crystals with Nitrogen-Vacancy color centers and a superconducting artificial two-level atom is discussed.Comment: 15 pages, 17 figures, submitted to Phys. Rev.