379 research outputs found
Fluctuations and the QCD phase diagram
In this contribution the role of quantum fluctuations for the QCD phase
diagram is discussed. This concerns in particular the importance of the matter
back-reaction to the gluonic sector. The impact of these fluctuations on the
location of the confinement/deconfinement and the chiral transition lines as
well as their interrelation are investigated. Consequences of our findings for
the size of a possible quarkyonic phase and location of a critical endpoint in
the phase diagram are drawn.Comment: 7 pages, 3 figures, to appear in Physics of Atomic Nucle
On the ground states of the Bernasconi model
The ground states of the Bernasconi model are binary +1/-1 sequences of
length N with low autocorrelations. We introduce the notion of perfect
sequences, binary sequences with one-valued off-peak correlations of minimum
amount. If they exist, they are ground states. Using results from the
mathematical theory of cyclic difference sets, we specify all values of N for
which perfect sequences do exist and how to construct them. For other values of
N, we investigate almost perfect sequences, i.e. sequences with two-valued
off-peak correlations of minimum amount. Numerical and analytical results
support the conjecture that almost perfect sequences do exist for all values of
N, but that they are not always ground states. We present a construction for
low-energy configurations that works if N is the product of two odd primes.Comment: 12 pages, LaTeX2e; extended content, added references; submitted to
J.Phys.
Tree-based Coarsening and Partitioning of Complex Networks
Many applications produce massive complex networks whose analysis would
benefit from parallel processing. Parallel algorithms, in turn, often require a
suitable network partition. For solving optimization tasks such as graph
partitioning on large networks, multilevel methods are preferred in practice.
Yet, complex networks pose challenges to established multilevel algorithms, in
particular to their coarsening phase.
One way to specify a (recursive) coarsening of a graph is to rate its edges
and then contract the edges as prioritized by the rating. In this paper we (i)
define weights for the edges of a network that express the edges' importance
for connectivity, (ii) compute a minimum weight spanning tree with
respect to these weights, and (iii) rate the network edges based on the
conductance values of 's fundamental cuts. To this end, we also (iv)
develop the first optimal linear-time algorithm to compute the conductance
values of \emph{all} fundamental cuts of a given spanning tree. We integrate
the new edge rating into a leading multilevel graph partitioner and equip the
latter with a new greedy postprocessing for optimizing the maximum
communication volume (MCV). Experiments on bipartitioning frequently used
benchmark networks show that the postprocessing already reduces MCV by 11.3%.
Our new edge rating further reduces MCV by 10.3% compared to the previously
best rating with the postprocessing in place for both ratings. In total, with a
modest increase in running time, our new approach reduces the MCV of complex
network partitions by 20.4%
Two flavor chiral phase transition from nonperturbative flow equations
We employ nonperturbative flow equations to compute the equation of state for
two flavor QCD within an effective quark meson model. This yields the
temperature and quark mass dependence of quantities like the chiral condensate
or the pion mass. A precision estimate of the universal critical equation of
state for the three-dimensional O(4) Heisenberg model is presented. We
explicitly connect the O(4) universal behavior near the critical temperature
and zero quark mass with the physics at zero temperature and a realistic pion
mass. For realistic quark masses the pion correlation length near T_c turns out
to be smaller than its zero temperature value.Comment: 49 pages including 15 figures, LaTeX, uses epsf.sty and rotate.st
Structural Characterization And Condition For Measurement Statistics Preservation Of A Unital Quantum Operation
We investigate the necessary and sufficient condition for a convex cone of
positive semidefinite operators to be fixed by a unital quantum operation
acting on finite-dimensional quantum states. By reducing this problem to
the problem of simultaneous diagonalization of the Kraus operators associated
with , we can completely characterize the kind of quantum states that are
fixed by . Our work has several applications. It gives a simple proof of
the structural characterization of a unital quantum operation that acts on
finite-dimensional quantum states --- a result not explicitly mentioned in
earlier studies. It also provides a necessary and sufficient condition for what
kind of measurement statistics is preserved by a unital quantum operation.
Finally, our result clarifies and extends the work of St{\o}rmer by giving a
proof of a reduction theorem on the unassisted and entanglement-assisted
classical capacities, coherent information, and minimal output Renyi entropy of
a unital channel acting on finite-dimensional quantum state.Comment: 9 pages in revtex 4.1, minor revision, to appear in J.Phys.
Propagators in Coulomb gauge from SU(2) lattice gauge theory
A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is
performed using large scale lattice simulations. The (equal-time) transverse
gluon propagator, the ghost form factor d(p) and the Coulomb potential V_{coul}
(p) ~ d^2(p) f(p)/p^2 are calculated. For large momenta p, the gluon propagator
decreases like 1/p^{1+\eta} with \eta =0.5(1). At low momentum, the propagator
is weakly momentum dependent. The small momentum behavior of the Coulomb
potential is consistent with linear confinement. We find that the inequality
\sigma_{coul} \ge \sigma comes close to be saturated. Finally, we provide
evidence that the ghost form factor d(p) and f(p) acquire IR singularities,
i.e., d(p) \propto 1/\sqrt{p} and f(p) \propto 1/p, respectively. It turns out
that the combination g_0^2 d_0(p) of the bare gauge coupling g_0 and the bare
ghost form factor d_0(p) is finite and therefore renormalization group
invariant.Comment: 10 pages, 7 figure
Brownian Motions on Metric Graphs
Brownian motions on a metric graph are defined. Their generators are
characterized as Laplace operators subject to Wentzell boundary at every
vertex. Conversely, given a set of Wentzell boundary conditions at the vertices
of a metric graph, a Brownian motion is constructed pathwise on this graph so
that its generator satisfies the given boundary conditions.Comment: 43 pages, 7 figures. 2nd revision of our article 1102.4937: The
introduction has been modified, several references were added. This article
will appear in the special issue of Journal of Mathematical Physics
celebrating Elliott Lieb's 80th birthda
On the Convergence of the Expansion of Renormalization Group Flow Equation
We compare and discuss the dependence of a polynomial truncation of the
effective potential used to solve exact renormalization group flow equation for
a model with fermionic interaction (linear sigma model) with a grid solution.
The sensitivity of the results on the underlying cutoff function is discussed.
We explore the validity of the expansion method for second and first-order
phase transitions.Comment: 12 pages with 10 EPS figures included; revised versio
Heisenberg frustrated magnets: a nonperturbative approach
Frustrated magnets are a notorious example where the usual perturbative
methods are in conflict. Using a nonperturbative Wilson-like approach, we get a
coherent picture of the physics of Heisenberg frustrated magnets everywhere
between and . We recover all known perturbative results in a single
framework and find the transition to be weakly first order in . We compute
effective exponents in good agreement with numerical and experimental data.Comment: 5 pages, Revtex, technical details available at
http://www.lpthe.jussieu.fr/~tissie
Non-perturbative dynamics and charge fluctuations in effective chiral models
We discuss the properties of fluctuations of the electric charge in the
vicinity of the chiral crossover transition within effective chiral models at
finite temperature and vanishing net baryon density. The calculation includes
non-perturbative dynamics implemented within the functional renormalization
group approach. We study the temperature dependence of the electric charge
susceptibilities in the linear sigma model and explore the role of quantum
statistics. Within the Polyakov loop extended quark-meson model, we study the
influence of the coupling of quarks to mesons and to an effective gluon field
on charge fluctuations. We find a clear signal for the chiral crossover
transition in the fluctuations of the electric charge. Accordingly, we stress
the role of higher order cumulants as probes of criticality related to the
restoration of chiral symmetry and deconfinement.Comment: 12 pages, 3 figure
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