325 research outputs found
Recovering the chiral critical end-point via delocalization of quark interactions
We show that for the lower branch of the quark condensate and values higher
than approximately the chiral critical end-point in
the Nambu--Jona-Lasinio model does not occur in the phase diagram. By using
lattice motivated non-local quark interactions, we demonstrate that the
critical end-point can be recovered. We study this behavior for a range of
condensate values and find that the variation in the position of the critical
end-point is more pronounced as the condensate is increased.Comment: title changed, minor changes in text, version to match the one
published in PR
Medium induced Lorentz symmetry breaking effects in nonlocal PNJL models
In this paper we detail the thermodynamics of two flavor nonlocal
Polyakov-Nambu-Jona-Lasinio models for different parametrizations of the quark
interaction regulators. The structure of the model is upgraded in order to
allow for terms in the quark selfenergy which violate Lorentz invariance due to
the presence of the medium. We examine the critical properties, the phase
diagram as well as the equation of state. Furthermore, some aspects of the Mott
effect for pions and sigma mesons are discussed explicitly within a nonlocal
Polyakov-Nambu-Jona-Lasinio model. In particular, we continued the meson
polarization function in the complex energy plane and under certain
approximations, we were able to extract the imaginary part as a function of the
meson energy. We were not able to calculate the dynamical meson mass, and
therefore resorted to a technical study of the temperature dependence of the
meson width by replacing the meson energy with the temperature dependent
spatial meson mass. Our results show that while the temperature behavior of the
meson widths is qualitatively the same for a wide class of covariant
regulators, the special case where the nonlocal interactions are introduced via
the instanton liquid model singles out with a drastically different behavior.Comment: version to match the one published in PR
A symmetry restoration scenario supported by the generalized Witten-Veneziano relation and its analytic solution
The Witten-Veneziano relation, or, alternatively, its generalization proposed
by Shore, facilitates understanding and describing the complex of eta and eta'
mesons. We present an analytic, closed-form solution to Shore's equations which
gives results on the eta-eta' complex in full agreement with results previously
obtained numerically. Although the Witten-Veneziano relation and Shore's
equations are related, the ways they were previously used in the context of
dynamical models to calculate eta and eta' properties, were rather different.
However, with the analytic solution, the calculation can be formulated
similarly to the approach through the Witten-Veneziano relation, and with some
conceptual improvements. In the process, one strengthens the arguments in favor
of a possible relation between the U_A(1) and SU_A(3) chiral symmetry breaking
and restoration. To test this scenario, the experiments such as those at RHIC,
NICA and FAIR, which extend the RHIC (and LHC) high-temperature scans also to
the finite-density parts of the QCD phase diagram, should pay particular
attention to the signatures from the eta'-eta complex indicating the symmetry
restoration.Comment: elsarticle style, 6 page
Scale invariant properties of public debt growth
Public debt is one of the important economic variables that quantitatively
describes a nation's economy. Because bankruptcy is a risk faced even by
institutions as large as governments (e.g. Iceland), national debt should be
strictly controlled with respect to national wealth. Also, the problem of
eliminating extreme poverty in the world is closely connected to the study of
extremely poor debtor nations. We analyze the time evolution of national public
debt and find "convergence": initially less-indebted countries increase their
debt more quickly than initially more-indebted countries. We also analyze the
public debt-to-GDP ratio R, a proxy for default risk, and approximate the
probability density function P(R) with a Gamma distribution, which can be used
to establish thresholds for sustainable debt. We also observe "convergence" in
R: countries with initially small R increase their R more quickly than
countries with initially large R. The scaling relationships for debt and R have
practical applications, e.g. the Maastricht Treaty requires members of the
European Monetary Union to maintain R < 0.6.Comment: 9 pages, 8 figure
The competitiveness versus the wealth of a country
Politicians world-wide frequently promise a better life for their citizens.
We find that the probability that a country will increase its {\it per capita}
GDP ({\it gdp}) rank within a decade follows an exponential distribution with
decay constant . We use the Corruption Perceptions Index (CPI)
and the Global Competitiveness Index (GCI) and find that the distribution of
change in CPI (GCI) rank follows exponential functions with approximately the
same exponent as , suggesting that the dynamics of {\it gdp}, CPI, and
GCI may share the same origin. Using the GCI, we develop a new measure, which
we call relative competitiveness, to evaluate an economy's competitiveness
relative to its {\it gdp}. For all European and EU countries during the
2008-2011 economic downturn we find that the drop in {\it gdp} in more
competitive countries relative to {\it gdp} was substantially smaller than in
relatively less competitive countries, which is valuable information for
policymakers.Comment: 11 pages, 7 figures, accepted for publication in Nature Scientific
Report
Systemic risk in dynamical networks with stochastic failure criterion
Complex non-linear interactions between banks and assets we model by two
time-dependent Erd\H{o}s Renyi network models where each node, representing
bank, can invest either to a single asset (model I) or multiple assets (model
II). We use dynamical network approach to evaluate the collective financial
failure---systemic risk---quantified by the fraction of active nodes. The
systemic risk can be calculated over any future time period, divided on
sub-periods, where within each sub-period banks may contiguously fail due to
links to either (i) assets or (ii) other banks, controlled by two parameters,
probability of internal failure and threshold ("solvency" parameter).
The systemic risk non-linearly increases with and decreases with average
network degree faster when all assets are equally distributed across banks than
if assets are randomly distributed. The more inactive banks each bank can
sustain (smaller ), the smaller the systemic risk---for some values
in I we report a discontinuity in systemic risk. When contiguous spreading
becomes stochastic (ii) controlled by probability ---a condition for the
bank to be solvent (active) is stochastic---the systemic risk decreases with
decreasing . We analyse asset allocation for the U.S. banks.Comment: 7 pages, 7 figure
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