Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarks

We present the first results for lattice QCD at finite temperature $T$ and chemical potential $\mu$ with four flavors of Wilson quarks. The calculations are performed using the imaginary chemical potential method at $\kappa=0$, 0.001, 0.15, 0.165, 0.17 and 0.25, where $\kappa$ is the hopping parameter, related to the bare quark mass $m$ and lattice spacing $a$ by $\kappa=1/(2ma+8)$. Such a method allows us to do large scale Monte Carlo simulations at imaginary chemical potential $\mu=i \mu_I$. By analytic continuation of the data with $\mu_I < \pi T/3$ to real values of the chemical potential, we expect at each $\kappa\in [0,\kappa_{chiral}]$, a transition line on the $(\mu, T)$ plane, in a region relevant to the search for quark gluon plasma in heavy-ion collision experiments. The transition is first order at small or large quark mass, and becomes a crossover at intermediate quark mass.Comment: Published versio

Time dependent diffusion in a disordered medium with partially absorbing walls: A perturbative approach

We present an analytical study of the time dependent diffusion coefficient in a dilute suspension of spheres with partially absorbing boundary condition. Following Kirkpatrick (J. Chem. Phys. 76, 4255) we obtain a perturbative expansion for the time dependent particle density using volume fraction $f$ of spheres as an expansion parameter. The exact single particle $t$-operator for partially absorbing boundary condition is used to obtain a closed form time-dependent diffusion coefficient $D(t)$ accurate to first order in the volume fraction $f$. Short and long time limits of $D(t)$ are checked against the known short-time results for partially or fully absorbing boundary conditions and long-time results for reflecting boundary conditions. For fully absorbing boundary condition the long time diffusion coefficient is found to be $D(t)=5 a^2/(12 f D_{0} t) +O((D_0t/a^2)^{-2})$, to the first order of perturbation theory. Here $f$ is small but non-zero, $D_0$ the diffusion coefficient in the absence of spheres, and $a$ the radius of the spheres. The validity of this perturbative result is discussed

Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and nonequilibrium conformational fluctuations of the single molecule. It is identified as the free energy difference associated with a fluctuating density in equilibrium, and is associated with the distribution deviate from the equilibrium in nonequilibrium relaxation. This result can be generalized to any other isothermal macromolecular systems using the mathematical theories of large deviations and Markov processes, and at the same time provides the well-known mathematical results with an interesting physical interpretations.Comment: 5 page

Neutrino Mass Hierarchy and Stepwise Spectral Swapping of Supernova Neutrino Flavors

We examine a phenomenon recently predicted by numerical simulations of supernova neutrino flavor evolution: the swapping of supernova $\nu_e$ and $\nu_{\mu,\tau}$ energy spectra below (above) energy \EC for the normal (inverted) neutrino mass hierarchy. We present the results of large-scale numerical calculations which show that in the normal neutrino mass hierarchy case, \EC decreases as the assumed $\nu_e\rightleftharpoons\nu_{\mu,\tau}$ effective $2\times 2$ vacuum mixing angle ($\simeq \theta_{1 3}$) is decreased. However, these calculations also indicate that \EC is essentially independent of the vacuum mixing angle in the inverted neutrino mass hierarchy case. With a good neutrino signal from a future Galactic supernova, the above results could be used to determine the neutrino mass hierarchy even if $\theta_{13}$ is too small to be detected in terrestrial neutrino oscillation experiments.Comment: 4 pages, 2 figures. Version accepted by PR

The Spin Mass of an Electron Liquid

We show that in order to calculate correctly the {\it spin current} carried by a quasiparticle in an electron liquid one must use an effective "spin mass" $m_s$, that is larger than both the band mass, $m_b$, which determines the charge current, and the quasiparticle effective mass $m^*$, which determines the heat capacity. We present microscopic calculations of $m_s$ in a paramagnetic electron liquid in three and two dimensions, showing that the mass enhancement $m_s/m_b$ can be a very significant effect.Comment: 10 pages, 1 figur

Flavor Evolution of the Neutronization Neutrino Burst from an O-Ne-Mg Core-Collapse Supernova

We present results of 3-neutrino flavor evolution simulations for the neutronization burst from an O-Ne-Mg core-collapse supernova. We find that nonlinear neutrino self-coupling engineers a single spectral feature of stepwise conversion in the inverted neutrino mass hierarchy case and in the normal mass hierarchy case, a superposition of two such features corresponding to the vacuum neutrino mass-squared differences associated with solar and atmospheric neutrino oscillations. These neutrino spectral features offer a unique potential probe of the conditions in the supernova environment and may allow us to distinguish between O-Ne-Mg and Fe core-collapse supernovae.Comment: 4 pages, 2 figures. Version accepted by PR

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati