Interactions of fast ions with carbon nanotubes: Self-energy and stopping power
The interactions of charged particles with carbon nanotubes are studied by means of the linearized hydrodynamic theory for electronic excitations on the nanotube surface. General expressions are derived for the induced potential, the self-energy, and the stopping power for a charged particle moving paraxially in a nanotube. Numerical results are obtained showing the influence of the damping factor, the nanotube radius, and the particle position on its self-energy and the stopping power. Results for stopping power in the linearized hydrodynamic model are compared with those obtained by means of the dielectric formalism in random-phase approximation, showing a close agreement between the two approaches for high speeds of charged particles.

title: Kinetic Study on Channelling of Protons in Metallic Carbon Nanotubes
abstract: Based on the kinetic model and the dielectric response theory, a theoretical model is put forward to describe the transport of protons along nanotube axes. With the introduction of electron band structure for different nanotubes like zigzag and armchair nanotubes of metallic properties, the collective excitation of electrons on the cylinders induced by the incident ions is studied, showing several distinct peaks in the curves of the energy loss function. Furthermore, the stopping power and the self-energy are calculated as functions of ion velocities, especially taking into account the influence of damping coefficients. It is conceivable from the results that, in the kinetic formulation, plasmon excitation plays a major role in the stopping. And as the damping increases, the peaks of the stopping power shift to the lower velocities, with the broadening of the plasmon resonance.

title: Effects of Tune Modulation on Particles Trapped in 1D Resonance Islands
abstract: The response of particles trapped in 1D resonance islands to betatron tune modulation resembles, yet is not equivalent to, that of a parametric resonant system. Experimental data obtained at Indiana University Cyclotron Facility for the 4th order resonance islands has confirmed this characteristic feature. The beam, driven by betatron tune modulation, was observed for the first time to travel from near the center of resonance islands toward the separatrix. The experimental data are characterized by the onset of large response at a critical modulation amplitude and frequency, which are compared with theoretical models. Possible future experiments are suggested. Work supported in part by grants from the National Science Foundation NSF PHY-9221402 and from the U.S.DoE DE-FGO2-93ER40801; a IUCF, Indiana University, Bloomington, IN 47405; b The SSC laboratory, 2550 Beckleymeade Avenue, Dallas, TX 75X37-3946; ’ Fermilab, P.0. Box 500, Batavia, IL 60510.

title: A note on Friedmann equation of FRW universe in deformed Horava-Lifshitz gravity from entropic force
abstract: With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann—Robertson—Walker universe for the deformed Hořava—Lifshitz gravity. It is shown that, when the parameter of Hořava—Lifshitz gravity ω → ∞, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Hořava—Lifshitz gravity.

title: Exact results on a Dirac-like Lee model
abstract: A one‐dimensional massive Lee model is studied via the Bethe ansatz method. The exact engenstates and the energy spectrum are obtained. The general picture of the excitations is discussed.

title: System-size dependence of transverse momentum correlations at √s NN=62.4 and 200 GeV at the BNL Relativistic Heavy Ion Collider
abstract: We present a study of the average transverse momentum ($p_t$) fluctuations and $p_t$ correlations for charged particles produced in Cu+Cu collisions at midrapidity for $\sqrt{s_{NN}} =$ 62.4 and 200 GeV. These results are compared with those published for Au+Au collisions at the same energies, to explore the system size dependence. In addition to the collision energy and system size dependence, the $p_t$ correlation results have been studied as functions of the collision centralities, the ranges in $p_t$, the pseudorapidity $\eta$, and the azimuthal angle $\phi$. The square root of the measured $p_t$ correlations when scaled by mean $p_t$ is found to be independent of both colliding beam energy and system size studied. Transport-based model calculations are found to have a better quantitative agreement with the measurements compared to models which incorporate only jetlike correlations.

title: Emergence of Cosmic Space and the Generalized Holographic Equipartition
abstract: Recently, a novel idea about our expanding Universe was proposed by T. Padmanabhan . He suggested that the expansion of our Universe can be thought of as the emergence of space as cosmic time progresses. The emergence is governed by the basic relation that the increase rate of Hubble volume is linearly determined by the difference between the number of degrees of freedom on the horizon surface and the one in the bulk. In this paper, following this idea, we generalize the basic relation to derive the Friedmann equations of an (n + 1)-dimensional Friedmann-Robertson-Walker universe corresponding to general relativity, Gauss-Bonnet gravity, and Lovelock gravity.