Chiral Lagrangian and spectral sum rules for dense two-color QCD

We analytically study two-color QCD with an even number of flavors at high baryon density. This theory is free from the fermion sign problem. Chiral symmetry is broken spontaneously by the diquark condensate. Based on the symmetry breaking pattern we construct the low-energy effective Lagrangian for the Nambu-Goldstone bosons. We identify a new epsilon-regime at high baryon density in which the quark mass dependence of the partition function can be determined exactly. We also derive Leutwyler-Smilga-type spectral sum rules for the complex eigenvalues of the Dirac operator in terms of the fermion gap. Our results can in principle be tested in lattice QCD simulations.Comment: 24 pages, 1 table, no figur

Relation between fundamental estimation limit and stability in linear quantum systems with imperfect measurement

From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4. This fundamental lower-bound may become bigger when taking the structure and quality of a specific measurement apparatus into account. In this paper, we consider a particle subjected to a linear dynamics that is continuously monitored with efficiency $\eta\in(0,1]$. It is then clarified that the above Heisenberg uncertainty relation is replaced by \mean{\Delta \hat{q}^2}\mean{\Delta \hat{p}^2}\geq \hbar^2/4\eta if the monitored system is unstable, while there exists a stable quantum system for which the Heisenberg limit is reached.Comment: 4 page

Hadron-quark continuity induced by the axial anomaly in dense QCD

We investigate the interplay between the chiral and diquark condensates on the basis of the Ginzburg-Landau potential with QCD symmetry. We demonstrate that the axial anomaly drives a new critical point at low temperature in the QCD phase diagram and leads to a smooth crossover between the hadronic and color superconducting phases.Comment: 4 pages, 5 figures, to appear in the Proceedings of Quark Matter 2006 held in Shangha

Effect of tangential traction and roughness on crack initiation/propagation during rolling contact

Rolling fatigue tests of 0.45 percent carbon steel rollers were carried out using a four roller type rolling contact fatigue tester. Tangential traction and surface roughness of the harder mating rollers were varied and their effect was studied. The results indicate that the fatigue life decreases when fraction is applied in the same direction as that of rolling. When the direction of fraction is reversed, the life increases over that obtained with zero traction. The roughness of harder mating roller also has a marked influence on life. The smoother the mating roller, the longer the life. Microscopic observation of specimens revealed that the initiation of cracks during the early stages of life is more strongly influenced by the surface roughness, while the propagation of these cracks in the latter stages is affected mainly by the tangential traction

Certifying isolated singular points and their multiplicity structure

This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is that it does not introduce new variables and the increase in the number of equations is linear instead of the quadratic increase of previous methods. The second construction gives the coefficients of the so-called inverse system or dual basis, which defines the multiplicity structure at the singular root. We present a system of equations in the original variables plus a relatively small number of new vari-ables. We show that the roots of this new system include the original singular root but now with multiplicity one, and the new variables uniquely determine the multiplicity structure. Both constructions are "exact", meaning that they permit one to treat all conjugate roots simultaneously and can be used in certification procedures for singular roots and their multiplicity structure with respect to an exact rational polynomial system

Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice

Within the zero-temperature linear spin-wave theory we have investigated the effect of frustration and dimerization of a Heisenberg system with alternating spins $s_{1}$ and $s_{2}$ on one- and two-dimensional lattices. The combined effect most visibly appears in the elementary excitation spectra. In contrast to the ground state energy that decreases with dimerization and increases with frustration, the excitation energies are shown to be suppressed in energy by both dimerization and frustration. The threshold value of frustration that signals a transition from a classical ferrimagnetic state to a spiral state, decreases with dimerization, showing that dimerization further helps in the phase transition. The correlation length and sublattice magnetization decrease with both dimerization and frustration indicating the destruction of the long-range classical ferrimagnetic. The linear spin wave theory shows that in the case of a square lattice, dimerization initially opposes the frustration-led transition to a spiral magnetic state, but then higher magnitudes of lattice deformation facilitate the transition. It also shows that the transition to spiral state is inhibited in a square lattice beyond a certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure

Hyperon mixing and universal many-body repulsion in neutron stars

A multi-pomeron exchange potential (MPP) is proposed as a model for the universal many-body repulsion in baryonic systems on the basis of the Extended Soft Core (ESC) bryon-baryon interaction. The strength of MPP is determined by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The interaction in $\Lambda N$ channels is shown to reproduce well the experimental $\Lambda$ binding energies. The equation of state (EoS) in neutron matter with hyperon mixing is obtained including the MPP contribution, and mass-radius relations of neutron stars are derived. It is shown that the maximum mass can be larger than the observed one $2M_{\odot}$ even in the case of including hyperon mixing on the basis of model-parameters determined by terrestrial experiments

First-order quantum correction to the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field

First-order quantum correction to the Larmor radiation is investigated on the basis of the scalar QED on a homogeneous background of time-dependent electric field, which is a generalization of a recent work by Higuchi and Walker so as to be extended for an accelerated charged particle in a relativistic motion. We obtain a simple approximate formula for the quantum correction in the limit of the relativistic motion when the direction of the particle motion is parallel to that of the electric field.Comment: 12 pages, 2 figures, accepted for publication in Physical Review