19,186 research outputs found
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 , and
, in the kinematic region , where 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 corrections to the first moment of the polarized virtual photon structure function
We present the next-to-next-to-leading order () corrections
to the first moment of the polarized virtual photon structure function
in the kinematical region ,
where is the mass squared of the probe (target) photon and
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
corrections are found to be about 3% of the sum of the
leading order () andthe next-to-leading order ()
contributions, when and , and the
number of active quark flavors 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 -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
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