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Evolution models for mass transportation problems
No full textSUMMARY We present a survey on several mass transportation problems, in which a given
mass dynamically moves from an initial configuration to a final one. The
approach we consider is the one introduced by Benamou and Brenier in [5], where
a suitable cost functional , depending on the density and on
the velocity (which fulfill the continuity equation), has to be minimized.
Acting on the functional various forms of mass transportation problems can
be modeled, as for instance those presenting congestion effects, occurring in
traffic simulations and in crowd motions, or concentration effects, which give
rise to branched structures
Exact relations between particle fluctuations and entanglement in Fermi gases
No full textWe derive exact relations between the Renyi entanglement entropies and the
particle number fluctuations of spatial connected regions in systems of N
noninteracting fermions in arbitrary dimension. We prove that the asymptotic
large-N behavior of the entanglement entropies is proportional to the variance
of the particle number. We also consider 1D Fermi gases with a localized
impurity, where all particle cumulants contribute to the asymptotic large-N
behavior of the entanglement entropies. The particle cumulant expansion turns
out to be convergent for all integer-order Renyi entropies (except for the von
Neumann entropy) and the first few cumulants provide already a good
approximation. Since the particle cumulants are accessible to experiments,
these relations may provide a measure of entanglement in these systems
A distributed infrastructure for monitoring network resources
No full textWhen an infrastructure is used to process complex workflows by way of an Infrastructure as a Service
(IaaS), network monitoring becomes mandatory to ensure the required quality of service and to optimize
the utilization of the whole infrastructure.
In this paper we explore this scenario, evaluate the issues that come with the network monitoring
operation, and propose a practical solution. To support our claims, we introduce a network monitoring
infrastrucure that has been implemented as a proof of concept for the foundations of our solution
Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields
No full textWe investigate two flavor QCD in presence of CP-odd electromagnetic
background fields and determine, by means of lattice QCD simulations, the
induced effective theta term to the first order in the scalar product of E and
B. We employ a rooted staggered discretization and study lattice spacings down
to 0.1 fm and Goldstone pion masses around 480 MeV. In order to deal with a
positive measure, we consider purely imaginary electric fields and real
magnetic fields, then exploiting analytic continuation. Our results are
relevant to a description of the effective pseudoscalar QED-QCD interactions
Optimal-transport formulation of electronic density-functional theory
No full textSUMMARY The most challenging scenario for Kohn-Sham density functional theory, that
is when the electrons move relatively slowly trying to avoid each other as much
as possible because of their repulsion (strong-interaction limit), is
reformulated here as an optimal transport (or mass transportation theory)
problem, a well established field of mathematics and economics. In practice, we
show that solving the problem of finding the minimum possible internal
repulsion energy for electrons in a given density \rho(\rv) is equivalent
to find the optimal way of transporting times the density into
itself, with cost function given by the Coulomb repulsion. We use this link to
put the strong-interaction limit of density functional theory on firm grounds
and to discuss the potential practical aspects of this reformulation
The critical line of two-flavor QCD at finite isospin or baryon densities from imaginary chemical potentials
No full textWe determine the (pseudo)critical lines of QCD with two degenerate staggered
fermions at nonzero temperature and quark or isospin density, in the region of
imaginary chemical potentials; analytic continuation is then used to prolongate
to the region of real chemical potentials. We obtain an accurate determination
of the curvatures at zero chemical potential, quantifying the deviation between
the case of finite quark and of finite isospin chemical potential. Deviations
from a quadratic dependence of the pseudocritical lines on the chemical
potential are clearly seen in both cases: we try different extrapolations and,
for the case of nonzero isospin chemical potential, confront them with the
results of direct Monte Carlo simulations. Finally we find that, as for the
finite quark density case, an imaginary isospin chemical potential can
strengthen the transition till turning it into strong first order
Two-flavor QCD at finite quark or isospin density
No full textWe exploit analytic continuation to prolongate to the region of real chemical
potentials the (pseudo)critical lines of QCD with two degenerate staggered
fermions at nonzero temperature and quark or isospin density obtained in the
region of imaginary chemical potentials. We determine the curvatures at zero
chemical potential and quantify the deviation between the cases of finite quark
and of finite isospin chemical potential. In both circumstances deviations from
a quadratic dependence of the pseudocritical lines on the chemical potential
are clearly seen. We try different extrapolations and, for the nonzero isospin
chemical potential, confront them with the results of direct Monte Carlo
simulations. We also find that, as for the finite quark chemical potential, an
imaginary isospin chemical potential can strengthen the transition till turning
it into strong first order
Wave Function Renormalization Effects in Resonantly Enhanced Tunneling
No full textWe study the time evolution of ultra-cold atoms in an accelerated optical
lattice. For a Bose- Einstein condensate with a narrow quasi-momentum
distribution in a shallow optical lattice the decay of the survival probability
in the ground band has a step-like structure. In this regime we establish a
connection between the wave function renormalization parameter Z introduced in
[Phys. Rev. Lett. 86, 2699 (2001)] to characterize non-exponential decay and
the phenomenon of resonantly enhanced tunneling, where the decay rate is peaked
for particular values of the lattice depth and the accelerating force
Non-perturbative features of driven scattering systems
No full textSUMMARY We investigate the scattering properties of one-dimensional, periodically and
non-periodically forced oscillators. The pattern of singularities of the
scattering function, in the periodic case, shows a characteristic hierarchical
structure where the number Nc of zeros of the solutions plays the role of an
order parameter marking the level of the observed self-similar structure. The
behavior is understood both in terms of the return map and of the intersections
pattern of the invariant manifolds of the outermost fixed points. In the
non-periodic case the scattering function does not provide a complete
development of the hierarchical structure. The singularities pattern of the
outgoing energy as a function of the driver amplitude is connected to the
arrangement of gaps in the fundamental regions. The survival probability
distribution of temporarily bound orbits is shown to decay asymptotically as a
power law. The "stickiness" of regular regions of phase space, given by KAM
surfaces and remnant of KAM curves, is responsible for this observation