Explicit solutions of the classical Calogero & Sutherland systems for any root system

Explicit solutions of the classical Calogero (rational with/without harmonic confining potential) and Sutherland (trigonometric potential) systems is obtained by diagonalisation of certain matrices of simple time evolution. The method works for Calogero & Sutherland systems based on any root system. It generalises the well-known results by Olshanetsky and Perelomov for the A type root systems. Explicit solutions of the (rational and trigonometric) higher Hamiltonian flows of the integrable hierarchy can be readily obtained in a similar way for those based on the classical root systems.Comment: 18 pages, LaTeX, no figur

Virtual photon structure functions and positivity constraints

We study the three positivity constraints among the eight virtual photon structure functions, derived from the Cauchy-Schwarz inequality and which are hence model-independent. The photon structure functions obtained from the simple parton model show quite different behaviors in a massive quark or a massless quark case, but they satisfy, in both cases, the three positivity constraints. We then discuss an inequality which holds among the unpolarized and polarized photon structure functions $F_1^\gamma$, $g_1^\gamma$ and $W_{TT}^\tau$, in the kinematic region $\Lambda^2\ll P^2 \ll Q^2$, where $-Q^2 (-P^2)$ is the mass squared of the probe (target) photon, and we examine whether this inequality is satisfied by the perturbative QCD results.Comment: 24 pages, 13 eps figure

QCD phase diagram and charge fluctuations

We discuss the phase structure and fluctuations of conserved charges in two flavor QCD. The importance of the density fluctuations to probe the existence of the critical end point is summarized. The role of these fluctuations to identify the first order phase transition in the presence of spinodal phase separation is also discussed.Comment: 8 pages, 8 figures, plenary talk given at the 19th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions: Quark Matter 2006 (QM 2006), Shanghai, China, 14-20 Nov 200

The alphaalphas2alpha alpha_s^2 corrections to the first moment of the polarized virtual photon structure function g1gamma(x,Q2,P2)g_1^gamma(x,Q^2,P^2)

We present the next-to-next-to-leading order ($alpha alpha_s^2$) corrections to the first moment of the polarized virtual photon structure function $g_1^gamma(x,Q^2,P^2)$ in the kinematical region $Lambda^2 ll P^2 ll Q^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $Lambda$ is the QCD scale parameter. In order to evaluate the three-loop-level photon matrix element of the flavor singlet axial current, we resort to the Adler-Bardeen theorem for the axial anomaly and we calculate in effect the two-loop diagrams for the photon matrix element of the gluon operator. The $alpha alpha_s^2$ corrections are found to be about 3% of the sum of the leading order ($alpha$) andthe next-to-leading order ($alpha alpha_s$) contributions, when $Q^2=30 sim 100 {rm GeV}^2$and $P^2=3{rm GeV}^2$, and the number of active quark flavors $n_f$ is three to five.Comment: 21 page

Gauge field for edge state in graphene

By considering the continuous model for graphene, we analytically study a special gauge field for the edge state. The gauge field explains the properties of the edge state such as the existence only on the zigzag edge, the partial appearance in the $k$-space, and the energy position around the Fermi energy. It is demonstrated utilizing the gauge field that the edge state is robust for surface reconstruction, and the next nearest-neighbor interaction which breaks the particle-hole symmetry stabilizes the edge state.Comment: 9 pages, 5 figure

Magnetism as a mass term of the edge states in graphene

The magnetism by the edge states in graphene is investigated theoretically. An instability of the pseudo-spin order of the edge states induces ferrimagnetic order in the presence of the Coulomb interaction. Although the next nearest-neighbor hopping can stabilize the pseudo-spin order, a strong Coulomb interaction makes the pseudo-spin unpolarized and real spin polarized. The magnetism of the edge states makes two peaks of the density of states in the conduction and valence energy bands near the Fermi point. Using a continuous model of the Weyl equation, we show that the edge-induced gauge field and the spin dependent mass terms are keys to make the magnetism of the edge states. A relationship between the magnetism of the edge states and the parity anomaly is discussed.Comment: 7 pages, 5 figure

Soliton Trap in Strained Graphene Nanoribbons

The wavefunction of a massless fermion consists of two chiralities, left-handed and right-handed, which are eigenstates of the chiral operator. The theory of weak interactions of elementally particle physics is not symmetric about the two chiralities, and such a symmetry breaking theory is referred to as a chiral gauge theory. The chiral gauge theory can be applied to the massless Dirac particles of graphene. In this paper we show within the framework of the chiral gauge theory for graphene that a topological soliton exists near the boundary of a graphene nanoribbon in the presence of a strain. This soliton is a zero-energy state connecting two chiralities and is an elementally excitation transporting a pseudospin. The soliton should be observable by means of a scanning tunneling microscopy experiment.Comment: 7 pages, 4 figure

Sigma Model BPS Lumps on Torus

We study doubly periodic Bogomol'nyi-Prasad-Sommerfield (BPS) lumps in supersymmetric CP^{N-1} non-linear sigma models on a torus T^2. Following the philosophy of the Harrington-Shepard construction of calorons in Yang-Mills theory, we obtain the n-lump solutions on compact spaces by suitably arranging the n-lumps on R^2 at equal intervals. We examine the modular invariance of the solutions and find that there are no modular invariant solutions for n=1,2 in this construction.Comment: 15 pages, 3 figures, published versio

Scaling Analysis of Domain-Wall Free-Energy in the Edwards-Anderson Ising Spin Glass in a Magnetic Field

The stability of the spin-glass phase against a magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glasses. Effective couplings and effective fields associated with length scale L are measured by a numerical domain-wall renormalization group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H goes to zero but remains finite for any non-zero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.Comment: 4 pages, 5 figures; The text is slightly changed, the figures 3, 4 and 5 are changed, and a few references are adde