35,254 research outputs found
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 and
chemical potential with four flavors of Wilson quarks. The calculations
are performed using the imaginary chemical potential method at ,
0.001, 0.15, 0.165, 0.17 and 0.25, where is the hopping parameter,
related to the bare quark mass and lattice spacing by
. Such a method allows us to do large scale Monte Carlo
simulations at imaginary chemical potential . By analytic
continuation of the data with to real values of the chemical
potential, we expect at each , a transition line
on the 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 of
spheres as an expansion parameter. The exact single particle -operator for
partially absorbing boundary condition is used to obtain a closed form
time-dependent diffusion coefficient accurate to first order in the
volume fraction . Short and long time limits of 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
, to the first order of
perturbation theory. Here is small but non-zero, the diffusion
coefficient in the absence of spheres, and 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, , 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 and
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
effective vacuum mixing angle () 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 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"
, that is larger than both the band mass, , which determines the
charge current, and the quasiparticle effective mass , which determines
the heat capacity. We present microscopic calculations of in a
paramagnetic electron liquid in three and two dimensions, showing that the mass
enhancement 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 and be two integers with , and let and be
integers with and . In this paper, we prove that , where is a constant depending on and .Comment: 8 pages. To appear in Archiv der Mathemati
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