On the phase of quark determinant in lattice QCD with finite chemical potential

We investigate the phase of the quark determinant with finite chemical potential in lattice QCD using both analytic and numerical methods. Applying the winding number expansion and the hopping parameter expansion to the logarithm of the determinant, we show that the absolute value of the phase has an upper bound that grows with the spatial volume but decreases exponentially with an increase in the temporal extent of the lattice. This analytic but approximate result is confirmed with a numerical study in four-flavor QCD in which the phase is calculated exactly. Since the phase is well controlled on lattices with larger time extents, we try the phase reweighting method in a region beyond $\mu/T=1$ where the Taylor expansion method cannot be applied. Working in four-flavor QCD, we find a first-order like behavior on a $6^3\times 4$ lattice at $\mu /T\approx 0.8$ which was previously observed by Kentucky group with the canonical method. We also show that the winding number expansion has a nice convergence property beyond $\mu/T=1$. We expect that this expansion is useful to study the high density region of the QCD phase diagram at low temperatures.Comment: 21 page

Absolute continuity of symmetric Markov processes

We study Girsanov's theorem in the context of symmetric Markov processes, extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov transformations of ``gradient type.'' We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward-backward martingale method of Lyons-Zheng, to cover the case of processes with jumps.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000043

The survival and destruction of X-ray coronae of early-type galaxies in the rich cluster environments: a case study of Abell 1367

A new Chandra observation of the northwest region of the galaxy cluster A1367 reveals four cool galaxy coronae (0.4 - 1.0 keV) embedded in the hot intracluster medium (ICM) (5 - 6 keV). While the large coronae of NGC 3842 and NGC 3837 appear symmetric and relaxed, the galaxy coronae of the \lsim L* galaxies (NGC 3841 and CGCG 97090) are disturbed and being stripped. Massive galaxies, with dense cooling cores, are better able to resist ram pressure stripping and survive in rich environments than \lsim L* galaxies whose galactic coronae are much less dense. The survival of these cool coronae implies that thermal conduction from the hot surrounding ICM has to be suppressed by a factor of at least 60, at the corona boundary. Within the galaxy coronae of NGC 3842 and NGC 3837, stellar mass loss or heat conduction with the Spitzer value may be sufficient to balance radiative cooling. Energy deposition at the ends of collimated jets may heat the outer coronae, but allow the survival of a small, dense gas core (e.g., NGC 3842 in A1367 and NGC 4874 in Coma). The survived X-ray coronae become significantly smaller and fainter with the increasing ambient pressure.Comment: 11 pages, 7 figures, emulateapj5, accepted by Ap

Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices

A conjecture is given for the exact location of the multicritical point in the phase diagram of the +/- J Ising model on the triangular lattice. The result p_c=0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, p_c=0.9327041, again in excellent agreement with a numerical study. The method is a variant of duality transformation to relate the triangular lattice directly with its dual triangular lattice without recourse to the hexagonal lattice, in conjunction with the replica method.Comment: 9 pages, 1 figure; Minor corrections in notatio

Generation of 10^15 - 10^17 eV photons by UHE CR in the Galactic magnetic filed

We show that the deep expected in the diffuse photon spectrum above the threshold of e+e- pair production, i.e., at energies 10^15 - 10^17 eV, may be absent due to the synchrotron radiation by the electron component of the extragalactic Ultra-High Energy Cosmic Rays (UHE CR) in the Galactic magnetic filed. The mechanism we propose requires small (less than 2x10^-12 G) extragalactic magnetic fields and large fraction of photons in the UHE CR. For a typical photon flux expected in top-down scenarios of UHE CR, the predicted flux in the region of the deep is close to the existing experimental limit. The sensitivity of our mechanism to the extragalactic magnetic field may be used to improve existing bounds on the latter by two orders of magnitude.Comment: 11 pages, LaTeX, 1 .ps figure. Numerical error corrected; references adde

Structural Transition of Li2RuO3 Induced by Molecular-Orbit Formation

A pseudo honeycomb system Li2RuO3 exhibits a second-order-like transition at temperature T=Tc=540 K to a low-T nonmagnetic phase with a significant lattice distortion forming Ru-Ru pairs. For this system, we have calculated the band structure, using the generalized gradient approximation (GGA) in both the high- and low- T phases, and found that the results of the calculation can naturally explain the insulating behavior observed in the low-T phase. The detailed characters of the Ru 4d t2g bands obtained by the tight-binding fit to the calculated dispersion curves show clear evidence that the structural transition is driven by the formation of the Ru-Ru molecular-orbits, as proposed in our previous experimental studies.Comment: 5 pages, 5 figures, 4 tables, submitted to J. Phys. Soc. Jp

Statistics of clustering of ultra-high energy cosmic rays and the number of their sources

Observation of clustering of ultra-high energy cosmic rays (UHECR) suggests that they are emitted by compact sources. Assuming small deflection of UHECR during the propagation, the statistical analysis of clustering allows to estimate the spatial density of the sources, h, including those which have not yet been observed directly. When applied to astrophysical models involving extra-galactic sources, the estimate based on 14 events with energy E>10^{20} eV gives h ~ 6 X 10^{-3} Mps^{-3}. With increasing statistics, this estimate may lead to exclusion of the models which associate the production of UHECR with exceptional galaxies such as AGN, powerful radio-galaxies, dead quasars, and models based on gamma ray bursts.Comment: The version accepted for publication in Phys. Rev. Lett. Notations changed to conventional ones. The estimate of the effective GZK radius replaced by the result of numerical simulatio

Anomalous Hall Effect and Magnetoresistance of SrFe1-xCoxO3-d

Transport and magnetic studies on polycrystalline samples of SrFe1-xCoxO3-d have been carried out to investigate the relationship between the magnetic structure and the anomalous Hall resistivity rH. The hysteretic behavior of the magnetization observed in the measurements with varying temperature T up and then down after zero field cooling indicates that the system has the reentrant spin-glass phase, which is supported by the increasing width of the magnetic reflections observed by neutron diffraction with decreasing T below the Curie temperature TC. Detailed analyses of the observed Hall resistivity rH indicate that the anomalous Hall coefficient exhibits unusual behavior in the reentrant spin-glass phase. The magnetic field (H)- and T-dependence of the magnetoresistance of the present system can be understood by a spin dependent tunneling model.Comment: 10 pages, 11 figures, J. Phys. Soc. Jpn. 72 (2003) No.

Nonexponential decay of an unstable quantum system: Small-QQ-value s-wave decay

We study the decay process of an unstable quantum system, especially the deviation from the exponential decay law. We show that the exponential period no longer exists in the case of the s-wave decay with small $Q$ value, where the $Q$ value is the difference between the energy of the initially prepared state and the minimum energy of the continuous eigenstates in the system. We also derive the quantitative condition that this kind of decay process takes place and discuss what kind of system is suitable to observe the decay.Comment: 17 pages, 6 figure