# Chinese Journal of Physics- Taipei-

Print ISSN: 0577-9073

Print ISSN: 0577-9073

Publications

With the measurement of positron flux published recently by AMS-02
collaboration, we show how the leptophilic dark matter fits the observation. We
obtain the percentages of different products of dark matter annihilation that
can best describe the flux of high energy positrons observed by AMS. We show
that dark matter annihilates predominantly into $\tau\tau$ pair, while both
$ee$ and $\mu\mu$ final states should be less than $20\%$. When gauge boson
final states are included, the best branching ratio of needed $\tau\tau$ mode
reduces.

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The properties of the Das-Popowicz Moyal momentum algebra that we introduce in hep-th/0207242 are reexamined in details and used to discuss some aspects of integrable models and 2d conformal field theories. Among the results presented, we setup some useful convention notations which lead to extract some non trivial properties of the Moyal momentum algebra. We use the particular sub-algebra sl(n)-{Sigma}_{n}^{(0,n)} to construct the sl(2)-Liouville conformal model and its sl(3)-Toda extension. We show also that the central charge, a la Feigin-Fuchs, associated to the spin-2 conformal current of the (theta)-Liouville model is given by c(theta)=1+24.theta^{2}. Moreover, the results obtained for the Das-Popowicz Mm algebra are applied to study systematically some properties of the Moyal KdV and Boussinesq hierarchies generalizing some known results. We discuss also the primarity condition of conformal $w_{\theta}$-currents and interpret this condition as being a dressing gauge symmetry in the Moyal momentum space. Some computations related to the dressing gauge group are explicitly presented.

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In the present work we attempt to study the cluster model in the transition metal region. The spectrum fitting method is studied for the selected even-even nuclei (Sr88-92, Zr-92,Zr-94, Mo-98,Mo-100, (100-106) Ru, Pd-108,Pd-110, and Cd112-118) with proton number (38 <= Z(T) <= 48) and mass number (88 <= A(T) <= 118). The core-cluster charge products are correlated with the transition probability B(E-2 down arrow, 2(+) -> 0(+)), the excitation energies, and the product of valence nucleon numbers of the parent nuclei.

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A brief summary of talks relating to massless lattice fermions is presented.
This summary is not a review and reading it certainly is no substitute to
reading the various original contributions.

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We report on recent progress with the gauge-fixing approach to lattice chiral gauge theories. The bosonic sector of the gauge-fixing approach is studied with fully dynamical U(1) gauge fields. We demonstrate that it is important to formulate the Lorentz gauge-fixing action such that the dense set of lattice Gribov copies is removed, and the gauge-fixing action has a unique absolute minimum. We then show that the spectrum in the continuum limit contains only the desired massless photon, as expected.

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We define the model of hydrogen atom for twist-deformed acceleration-enlarged
Newton-Hooke space-time. Further, using time-dependent perturbation theory, we
find in first step of iteration procedure the solution of corresponding
Schroedinger equation as well as the probability of transition between two
different energy-eigenstates.

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The paper presents a discussion on localization of acoustic waves. Some important questions about wave localization are addressed. Particular attention is paid to acoustic localization in liquid media containing many air-filled bubbles. It is shown that an amazing collective behavior appears when localization occurs. The study sheds new light to the much discussed subject.

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We have investigated the time-resolved vibrational properties of terahertz quantum cascade lasers by means of ultra-fast laser spectroscopy. By the observation of the acoustic folded branches, and by analyzing the involved phonon modes it is possible to extract accurate structural information of these devices, which are essential for their design and performance. Comment: 8 pages, 5 figures

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By using the conformal symmetry between Brans-Dicke action with
$\omega=-\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in
Einstein frame respecting the Noether symmetry. Since the Noether symmetry is
preserved under conformal transformations, the existence of Noether symmetry in
the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in
Einstein frame. Therefore, the potentials respecting Noether symmetry in
Brans-Dicke action give the corresponding potentials respecting Noether
symmetry in O'Hanlon action in Einstein frame.

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The scattering amplitude of a charged particle from a long hard cylinderical
solenoid is derived by solving the time independent Schr\"{o}dinger equation on
a double connected plane. It is a summation over the angular momentum quantum
number (partial wave summation). It is shown that only negative mechanical
angular momenta contribute to the amplitude when the radius of the solenoid
goes to zero limit without varying the magnetic induction flux (Flux line).
Original Aharonov-Bohm result is obtained with this limit.

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Berry and Balazs showed that an initial Airy packet Ai(b x) under time
evolution is nonspreading in free space and also in a homogeneous time-varying
linear potential V(x,t)=-F(t) x. We find both results can be derived from the
time evolution operator U(t). We show that U(t) can be decomposed into ordered
product of operators and is essentially a shift operator in x; hence, Airy
packets evolve without distortion. By writing the Hamiltonian H as H=H_b+H_i,
where H_b is the Hamiltonian such that Ai(b x) is its eigenfunction. Then, H_i
is shown to be as an interacting Hamiltonian that causes the Airy packet into
an accelerated motion of which the acceleration a=(-H_i/( x))/m. Nonspreading
Airy packet then acts as a classical particle of mass m, and the motion of it
can be described classically by H_i.

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We present in this work a systematic study of integrable models and supersymmetric extensions of the Gelfand-Dickey algebra of pseudo differential operators. We describe in detail the relation existing between the algebra of super pseudo-differential operators on the ring of superfields $u_{\frac{s}{2}}(z,\theta),s\in Z$ and the higher and lower spin extensions of the conformal algebra.

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A simple heuristic argument to understand the existence of branch points in
the unphysical sheet for pi-N scattering amplitude is presented. It is based on
a hypothesis that the singularity structure of the pi-N scattering amplitude is
a smooth varying function of the pion mass. We find that, in general, multiple
poles structure of a resonance is a direct mathematical consequence when
additional Riemann surface is included in the study and the two-pole structure
found to correspond to the Roper resonance is a good example.

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Intense ultrafast laser excitation can produce transient states of condensed
matter that would otherwise be inaccessible. At high excitation level, the
interatomic forces can be altered resulting in an unusual lattice dynamics.
Here we report the study of coherent lattice dynamics in Bi made for various
excitation levels at helium temperature. We demonstrate that under certain
conditions the fully symmetric phonons of large amplitude exhibit anomalous
decay and phase rigidity, both of which possibly signaling the attainment of
transient supersolid state.

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We provide a direct proof for the positivity of Chen-Nester-Tung quasi-local
energy with analytic reference in spherical symmetry. A hoop-type theorem for
this energy is also established. Finally, the relation between Chen-Nester-Tung
and Brown-York quasi-local energies will be discussed.

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We study the thermopower of diffusive Andreev interferometers, which are hybrid loops with one normal-metal arm and one superconducting arm. The thermopower oscillates as a function of the magnetic flux through the loop with a fundamental period corresponding to one flux quantum $\Phi_0=h/2e$. Unlike the electrical resistance oscillations and the thermal resistance oscillations, which are always symmetric with respect to the magnetic field, the symmetry of the thermopower oscillations can be either symmetric or antisymmetric depending on the geometry of the sample. We also observe that the symmetry of the thermopower oscillations is related to the distribution of the supercurrent between the normal-metal/superconductor interfaces. We compare our experimental results with recent theoretical work.

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The boundary term of the gravitational Hamiltonian can be used to give the
values of the quasi-local quantities as long as one can provide a suitable
evolution vector field and an appropriate reference. On the two-surface
boundary of a region we have proposed using {\em four dimensional isometric
matching} between the dynamic spacetime and the reference geometry along with
energy extremization to find both the optimal reference matching and the
appropriate quasi-Killing vectors. Here we consider the axisymmetric spacetime
case. For the Kerr metric in particular we can explicitly solve the equations
to find the best matched reference and quasi-Killing vectors. This leads to the
exact expression for the quasi-local boundary term and the values of our
optimal quasi-local energy and angular momentum.

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We consider a self-consistent system of Bianchi type-I (BI) gravitational
field and a binary mixture of perfect fluid and dark energy. The perfect fluid
is taken to be the one obeying the usual equation of state, i.e., $p = \zeta
\ve$, with $\zeta \in [0, 1]$ whereas, the dark energy density is considered to
be either the quintessence or the Chaplygin gas. Exact solutions to the
corresponding Einstein equations are obtained.

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We study the consequences of timelike and spaccelike conformal Ricci and conformal matter collineations for anisotropic fluid in the context of General Relativity. Necessary and sufficient conditions are derived for a spacetime with anisotropic fluid to admit conformal Ricci and conformal matter collineations parallel to u^a and x^a. These conditions for timelike and spacelike conformal Ricci and conformal matter collineations for anisotropic fluid reduce to the conditions of perfect fluid when the heat flux and the traceless anisotropic stress tensor vanish. Further, for $\alpha=0$ (the conformal factor), we recover the earlier results of Ricci collineations and matter collineations in each case of timelike and spacelike conformal Ricci collineations and conformal matter collineations for the perfect fluid. Thus our results give the generalization of the results already available in the literature. It is worth noticing that the conditions of conformal matter collineations can be derived from the conditions of conformal Ricci collineations or vice versa under certain constraints.

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The stability of the Bianchi type I anisotropic brane cosmology is analyzed in this paper. We also study the effect of the brane solution by comparing the models on the 3-brane and the models in the conventional Einstein's space. Analysis is presented for two different models: one with a perfect fluid and the other one with a dilaton field. It is shown that the anisotropic expansion is smeared out dynamically for both theories in the large time limit independent of the models with different types of matter. The initial states are, however, dramatically different. A primordial anisotropic expansion will grow for the conventional Einstein's theory. On the other hand, it is shown that the initial state is highly isotropic for the brane universe except for a very particular case. Moreover, it is also shown that the Bianchi type I anisotropic cosmology is stable against any anisotropic perturbation for both theories in the large time limit.

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We describe effects of anisotropy caused by the crystal lattice in d-wave superconductors using effective free energy approach in which only one order parameter, the d-wave order parameter field, is used. All the effects of rotational symmetry breaking, including that of the s-wave mixing, can be parametrized by a single four derivative term. We find solutions for single vortex and the vortex lattice. Extending the formalism to include the time dependence, effects of anisotropy on moving vortex structure are calculated. Both direct and Hall I-V curves as functions of the angle between the current and the crystal lattice orientation are obtained.

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Phase diagram of the spin-1 quantum Heisenberg model with both exchange as well as single-ion anisotropy is constructed within the framework of pair approximation formulated as a variational procedure based on the Gibbs-Bogoliubov inequality. In this form adapted variational approach is used to obtain the results equivalent with the Oguchi's pair approximation. It is shown that the single-ion anisotropy induces a tricritical behaviour in the considered model system and a location of tricritical points is found in dependence on the exchange anisotropy strength.

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It is argued on general ground and demonstrated in the particular example of
the Chiral Schwinger Model that there is nothing wrong with apparently
anomalous chiral gauge theory. If quantised correctly, there should be no gauge
anomaly and chiral gauge theory should be renormalisable and unitary, even in
higher dimensions and with non-abelian gauge groups. Furthermore, mass terms
for gauge bosons and chiral fermions can be generated without spoiling the
gauge invariance.

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Electron-impact ionization of atomic hydrogen with the electron's anomalous
mag- netic moment (AMM) effects are examined. The formulas for the
laser-assisted relativis- tic triple differential cross section (TDCS) in the
coplanar binary geometry developed earlier by Y. Attaourti and S. Taj [Phys.
Rev. A 69, 063411 (2004)] are used to check the consistency of our computations
when the anomaly $\kappa$ is taken to be zero. We show that the contribution of
the terms containing the AMM effects even in the first Born approximation has
an important contribution, so it must be included in any reliable analysis. A
full analytical calculation for the TDCS is presented.

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Analogous to Peierls' arguments for the `anomalous' Hall in metals I demonstrate that the Hall anomaly in the mixed state of superconductors, the sign change of the Hall resistivity, is a property of a vortex many-body correlation, and show that the anomaly is due to the competition between vortex vacancies and interstitials. Within this vortex many-body effect picture, many features of the complicated Hall effect can be understood in quantitative terms. For example, the expression for the vacancy formation energy is obtained, the scaling relation between the Hall and longitudinal resistivities with the power varying between 1 and 2 is found to depend on sample details, and near the superconducting transition temperature and for small magnetic fields the Hall conductivity is proportional to the inverse of the magnetic field and to the quadratic of the difference between the measured and the transition temperatures.

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Gravitational field is the manifestation of space-time translational ($T_4$)
gauge symmetry, which enables gravitational interaction to be unified with the
strong and the electroweak interactions. Such a total-unified model is based on
a generalized Yang-Mills framework in flat space-time. Following the idea of
Glashow-Salam-Ward-Weinberg, we gauge the groups $T_4 \times (SU_3)_{color}
\times SU_2 \times U_1\times U_{1b}$ on equal-footing, so that we have the
total-unified gauge covariant derivative ${\bf \d}_{\mu} = \p_{\mu} -
ig\phi_{\mu}^{\nu} p_{\nu}+ig_{s}{G_{\mu}^{a}}(\ld^a/2) +if{W_{\mu}^{k}}{t^k} +
if' U_{\mu}t_{o} + ig_{b}B_{\mu}$. The generators of the external $T_4$ group
have the representation $p_{\mu}=i\p_{\mu}$, which differs from other
generators of all internal groups, which have constant matrix representations.
Consequently, the total-unified model leads to the following new results: (a)
All internal $(SU_3)_{color}, SU_2, U_1$ and baryonic $U_{1b}$ gauge symmetries
have extremely small violations due to the gravitational interaction. (b) The
$T_4$ gauge symmetry remains exact and dictates the universal coupling of
gravitons. (c) Such a gravitational violation of internal gauge symmetries
leads to modified eikonal and Hamilton-Jacobi type equations, which are
obtained in the geometric-optics limit and involve effective Riemann metric
tensors. (d) The rules for Feynman diagrams involving new couplings of
photon-graviton, gluon-graviton and quark-gaviton are obtained.

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Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry, respectively. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations, and the corresponding wave functions are obtained by using the generalization of the Nikiforov-Uvarov method. Comment: 14 pages

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In this research has been studied the possibility of existence the neutral
triplet collective mode in undoped graphene and graphite without one-cone
approximation. This work tries to study this collective mode from different
points of view. It also studies the effects of on-site Hubbard interaction on
neutral collective mode in honeycomb lattice via two representations
(sub-lattice and eigenvector). The effective long rang interaction in honeycomb
lattice has been introduced for studying the spin collective mode. This work
shows that short and effective long range interactions are not responsible for
the formation of neutral triplet collective mode in graphene without {\it
one-cone} approximation.

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We show theoretically that a strongly spin-polarized current can be generated in semiconductors by taking advantage of the ferromagnetic phase of a quantum dot array (QDA). A Hubbard model with coupling to leads is used to study the tunneling current of the QDA system as a function of gate voltage. Due to the weak interdot coupling and strong Coulomb repulsion, it is found that a ferromagnetic phase exists in QDA within a window of gate voltage. Therefore QDA can be used as a spin filter to detect and control spin states in quantum information devices.

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It is argued that (a) In the quantum realm test-particle masses have non-trivial observability which induces a non-geometric element in gravity, (b) Any theory of quantum gravity, on fundamental grounds, must contain an element of non-locality that makes position measurements non-commutative, and (c) The classical notion of free fall does not readily generalize to the quantum regime.

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Besides its various applications in string and D-brane physics, the $\theta$-deformation of space (-time) coordinates (naively called the noncommutativity of coordinates), based on the $\star$-product, behaves as a more general framework providing more mathematical and physical informations about the associated system. Similarly to the Gelfand-Dickey framework of pseudo differential operators, the Moyal $\theta$-deformation applied to physical problems makes the study more systematic. Using these facts as well as the backgrounds of Moyal momentum algebra introduced in previous works [21, 25, 26], we look for the important task of studying integrability in the $\theta$-deformation framework. The main focus is on the $\theta$-deformation version of the Lax representation of two principal examples: the $sl_2$ KdV$_{\theta}$ equation and the Moyal $\theta$-version of the Burgers systems. Important properties are presented.

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The excitation of H ($1s-2s$) by electron impact in the presence and in the
absence of the laser field is studied in the framework of the first Born
approximation. The angular variation of the laser-assisted differential cross
section (DCS) for atomic hydrogen by electronic impact is presented at various
kinetic energies for the incident electron. The use of Darwin wave function as
a semirelativistic state to represent the atomic hydrogen gives interesting
results when the condition $z/c\ll1$ is fulfilled. A comparison with the non
relativistic theory and experimental data gives good agreement. It was observed
that beyond (2700 $eV$) which represents the limit between the two approaches,
the non relativistic theory does not yield close agreement with our theory and
that, over certain ranges of energy, it can be in error by several orders of
magnitude. The sum rule given by Bunkin and Fedorov and by Kroll and Watson
\cite{22} has been verified in both nonrelativistic and relativistic regimes.

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In this research, the totally asymmetric exclusion process without particle
number conservation is discussed. Based on the mean field approximation and the
Rankine-Hugoniot condition, the necessary and sufficient conditions of the
existence of the domain wall have been obtained. Moreover, the properties of
the domain wall, including the location and height, have been studied
theoretically. All the theoretical results are demonstrated by the computer
simulations.

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A technique is proposed for obtaining solutions of various quantum optical Hamiltonians within the framework of the asymptotic iteration method. We extend the notion of the asymptotic iteration method to solve 2×2 matrix Hamiltonians. As particular cases, the eigenvalues of the Rabi and Rashba Hamiltonians are computed. The method presented here reproduces a number of earlier results in a natural way, as well as leading to some novel findings. Possible generalizations of the method are also suggested.

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Based on a simple model, classical walking behaviors of a polarized atom in standing wave field are intensively investigated. By adjusting the control parameters of the frequency and amplitude of the light field as well as the initial conditions, the polarized atom conducts a variety of interesting behaviors in the standing wave lattice. For some specific cases, the corresponding models are analyzed in details. Comment: 9 pages, 9 figures

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We present a theoretical model for atomic hydrogen ionization by electron impact in the instantaneous approximation and the more accurate non-instantaneous approach using the methods of Quantum Electrodynamics, for the binary coplanar and the coplanar asymmetric geometries. All electrons are described by plane wave functions in the coplanar binary geometry but in the asymmetric geometry the ejected electron is described by a Sommerfeld-Maue wave function. It is shown that the two models give the same results in the non relativistic limit for the binary coplanar geometry where the interactions can be treated as instantaneous. However, this is no longer true for the relativistic case where one has to take into account both the instantaneous interaction and the radiation interaction. These results are obtained in the first order of perturbation theory. Comment: 8 pages, 5 figures, REVTEX, Atomic Physics

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Around 1950, Wigner introduced the idea of modelling physical reality with an
ensemble of random matrices while studying the energy levels of heavy atomic
nuclei. Since then, the field of random-matrix theory has grown tremendously,
with applications ranging from fluctuations on the economic markets to complex
atomic spectra. The purpose of this short article is to review several attempts
to apply the basic concepts of random-matrix theory to the structure and
radiative transitions of atoms and ions, using the random matrices originally
introduced by Wigner in the framework of the gaussian orthogonal ensemble. Some
intrinsic properties of complex-atom physics, which could be enlightened by
random-matrix theory, are presented.

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Keeping in mind the several models of M(atrix) theory we attempt to understand the possible structure of the topological M(atrix) theory ``underlying'' these approaches. In particular we raise the issue about the nature of the structure of the vacuum of the topological M(atrix) theory and how this could be related to the vacuum of the electroweak theory. In doing so we are led to a simple Topological Matrix Model. Moreover it is expected from the current understanding that the noncommutative nature of ``spacetime'' and background independence should lead to Topological Model. The main purpose of this note is to propose a simple Topological Matrix Model which bears relation to F and M theories. Suggestions on the origin of the chemical potential term appearing in the matrix models are given.

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We take an axisymmetric rotating universe model by crossing with a time dependent factor and evaluate its force and momentum in this evolving universe. It is concluded that it behaves exactly like a Friedmann model. We also extend this conclusion to the most general cosmological model.

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Symmetry tests provide an important probe for the structure of elementary
particle interactions and for the validity of the standard model. However, it
is pointed out that in the interpretation of such experiments one must keep in
mind that in many cases apparent "violations" of such tests are actually the
result of ordinary effects within the standard model.

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We have calculated the temperature profiles for phonon heat transport in a
suspended membrane with a radially symmetric heat source in the two extreme
cases of either fully ballistic or fully diffusive transport. Theoretical
results confirm that it is possible to distinguish these two transport
mechanisms from the radial temperature profiles alone. Models are also compared
to experimental data measured with 40 nm thick, free standing silicon nitride
membranes below 1 K by using tunnel junction (SINIS) thermometers. The measured
temperature profile is qualitatively in agreement with the ballistic model.

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The decay width of the rare decay Z \to \nu\bar{\nu}\gamma\gamma is strictly
constrained from the LEP data. Tensor unparticles provide a tree-level
contribution to this rare decay. We have calculated the tensor unparticle
contribution to the rare decay Z\to \nu\bar{\nu}\gamma\gamma. The current
experimental limit have been used to constrain unparticle couplings
\nu\bar{\nu}Z {U}^{\mu\nu} and \gamma\gamma {U}^{\mu\nu}.

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The hypercentral Constituent Quark Model (hCQM) for the baryon structure is
reviewed and its applications are systematically discussed. The model is based
on a simple form of the quark potential, which contains a Coulomb-like
interaction and a confinement, both expressed in terms of a collective space
coordinate, the hyperradius. The model has only three free parameters,
determined in order to describe the baryon spectrum. Once the parameters have
been fixed, the model, in its non relativistic version, is used to predict
various quantities of physical interest, namely the elastic nucleon form
factors, the photocouplings and the helicity amplitudes for the electromagnetic
excitation of the baryon resonances. In particular, the $Q^2$ dependence of the
helicity amplitude is quite well reproduced, thanks to the Coulomb-like
interaction. The model is reformulated in a relativistic version by means of
the Point Form hamilton dynamics. While the inclusion of relativity does not
alter the results for the helicity amplitudes, a good description of the
nucleon elastic form factors is obtained.

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Within the relativistic quantum field theory, we analyze the differences between the $\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.

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The complex patterns of the hadronic spectrum have puzzled physicists since
the early discovery of the "particle zoo" in the 1960s. Today, the properties
of these myriad particles are understood to be the result of quantum
chromodynamics (QCD) with some modification by the electroweak interactions.
Despite the discovery of this fundamental theory, the description of the
hadronic spectrum has long been dominated by phenomenological models, due to
the difficulties of addressing QCD in the strong-coupling regime, where
nonperturbative effects are essential. By making numerical calculations in
discretized spacetime, lattice gauge theory enables the ab initio study of many
low-energy properties of QCD. Significant efforts are underway internationally
to use lattice QCD to directly compute properties of ground and excited-state
baryons. Detailed knowledge of the hadronic spectrum will provide insight into
the character of these states beyond what can be extracted from models.
In this review, I will focus on the latest progress in lattice calculations
of the $P_{11}(1440)$, the poorly known hyperon spectrum and the energies of
highly-excited states of the nucleon, Delta and other light-flavor baryons. In
the heavy-flavor sector, I will concentrate on recent lattice-QCD calculations
of baryon masses, particularly those that make predictions concerning
yet-to-be-discovered baryons, such as $\Omega_{cc}$, $\Xi^\prime_b$ or
triply-heavy baryons.

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We analyze the Okubo SU(3) relation among the hyperon magnetic moments in the usual scheme of chiral perturbation theory (ChPT). We classify the one-loop diagrams, including those with intermediate decuplet baryons, in a simple way according to whether or not they satisfy the Okubo relation. Contrary to the conventional wisdom, we find that one-loop contributions to the hyperon magnetic moments in general violate the Okubo relation if the physical masses are employed for the meson propagators in the loops.

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We show that the magnetic moments of the octet baryons can be fitted to an accuracy of 1.5 percent by a phenomenological Lagrangian in which SU(3) breaking corrections appear only linearly. This is in contrast to conventional chiral perturbation theory in which corrections non-analytic in SU(3) breaking dominate and tend to spoil the agreement with the data. Motivated by this observation, we propose a modified scheme for chiral perturbation theory that gives rise to a similar linear breaking of SU(3) symmetry. (Pacs 13.40.Em, 14.20.-c, 11.30.Rd)

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We consider radiation-dominated Friedmann universe and evaluate its force four-vector and momentum. We analyse and compare the results with the already evaluated for the matter-dominated Friedmann model. It turns out that the results are physically acceptable.

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The integrability of the generalized Benney hierarchy with three primary fields is investigated from the point of view of two-dimensional topological field theories coupled to gravity. The associated primary free energy and correlation functions at genus zero are obtained via Landau-Ginzburg formulation and the string equation is derived using the twistor construction for the Orlov operators. By adopting the approach of Dubrovin and Zhang we obtain the genus-one corrections of the Poisson brackets of the generalized Benney hierarchy.

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For certain models, the energy of the universe which includes the energy of both the matter and the gravitational fields is obtained by using the quasilocal energy-momentum in teleparallel gravity. It is shown that in the case of the Bianchi type I and II universes, not only the total energy but also the quasilocal energy-momentum for any region vanishes independently of the three dimensionless coupling constants of teleparallel gravity.

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