Quarkyonic Matter and Chiral Spirals

The nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region are classified based on the 1/Nc expansion. The chiral symmetry in the Quarkyonic matter is investigated by taking into account condensations of chiral particle-hole pairs. It is argued that the chiral symmetry and parity are locally violated by the formation of chiral spirals, < psibar exp(2 i mu z gamma^0 gamma^z) psi >. An extension to multiple chiral spirals is also briefly discussed.Comment: Prepared for Hot Quark 2010, 4 page

Gap Condition and Self-Dualized N=4{\cal N}=4 Super Yang-Mills Theory for ADE Gauge Group on K3

We try to determine the partition function of ${\cal N}=4$ super Yang-Mills theoy for ADE gauge group on K3 by self-dualizing our previous ADE partition function. The resulting partition function satisfies gap condition.Comment: 17 page

Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles

The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. Firstly, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Secondly, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e, the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type1 and type2 (dual) superconductor. These results are summarized that the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.Comment: 11 pages, 14 figure

The Advantage of Increased Resolution in the Study of Quasar Absorption Systems

We compare a new R = 120,000 spectrum of PG1634+706 (z_QSO = 1.337,m_V = 14.9) obtained with the HDS instrument on Subaru to a R = 45, 000 spectrum obtained previously with HIRES/Keck. In the strong MgII system at z = 0.9902 and the multiple cloud, weak MgII system at z = 1.0414, we find that at the higher resolution, additional components are resolved in a blended profile. We find that two single-cloud weak MgII absorbers were already resolved at R = 45,000, to have b = 2 - 4 km/s. The narrowest line that we measure in the R = 120, 000 spectrum is a component of the Galactic NaI absorption, with b = 0.90+/-0.20 km/s. We discuss expectations of similarly narrow lines in various applications, including studies of DLAs, the MgI phases of strong MgII absorbers, and high velocity clouds. By applying Voigt profile fitting to synthetic lines, we compare the consistency with which line profile parameters can be accurately recovered at R = 45,000 and R = 120,000. We estimate the improvement gained from superhigh resolution in resolving narrowly separated velocity components in absorption profiles. We also explore the influence of isotope line shifts and hyperfine splitting in measurements of line profile parameters, and the spectral resolution needed to identify these effects. Super high resolution spectra of quasars, which will be routinely possible with 20-meter class telescopes, will lead to greater sensitivity for absorption line surveys, and to determination of more accurate physical conditions for cold phases of gas in various environments.Comment: To appear in AJ. Paper with better resolution images available at http://www.astro.psu.edu/users/anand/superhigh.AJ.pd

Abelian dominance and the dual Meissner effect in local unitary gauges in SU(2) gluodynamics

Performing highly precise Monte-Carlo simulations of SU(2) gluodynamics, we observe for the first time Abelian dominance in the confining part of the static potential in local unitary gauges such as the F12 gauge. We also study the flux-tube profile between the quark and antiquark in these local unitary gauges and find a clear signal of the dual Meissner effect. The Abelian electric field is found to be squeezed into a flux tube by the monopole supercurrent. This feature is the same as that observed in the non-local maximally Abelian gauge. These results suggest that the Abelian confinement scenario is gauge independent. Observing the important role of space-like monopoles in the Polyakov gauge also indicates that the monopoles defined on the lattice do not necessarily correspond to those proposed by 't Hooft in the context of Abelian projection.Comment: 4 pages, 7 figure

Analytical modelling of planar potential and current distributions in electrodes of lithium-Ion batteries

Mathematical modelling can play an important role in the design of a lithium-ion cell in that many design iterations can be performed at relatively little cost. • Electrochemical models are useful for cell design and optimization but can be typically high-order and complex and hence computationally expensive, and, are therefore not suitable for real-time applications. • Much reduced order electrochemical models for lithium-ion cells have been developed, with these type of models more suitable for use with real-time on-board electronic control units. • However, a difficulty with these methods is that the current-voltage behavior for different operating conditions cannot be predicted

Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials

We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials. We derive a formula for the power series expansion of reflection coefficients in terms of the wave number, and apply it to the low-energy expansion of the Green function

An Approach to N=4{\cal N}=4 ADE Gauge Theory on K3

We propose a recipe for determination of the partition function of ${\cal N}=4$ $ADE$ gauge theory on $K3$ by generalizing our previous results of the SU(N) case. The resulting partition function satisfies Montonen-Olive duality for $ADE$ gauge group.Comment: 28 pages, Latex, enlarged published versio