784 research outputs found
Resolving the instability of the Savvidy vacuum by dynamical gluon mass
In this paper we apply the formalism of local composite operators as
developed by Verschelde et al. in combination with a constant chromomagnetic
field as considered in the seventies by Savvidy and others. We find that a
nonzero minimizes the vacuum energy, as in the case with no
chromomagnetic field, and that the chromomagnetic field itself is near-to zero.
The Nielsen-Olesen instability, caused by the imaginary part in the action,
also vanishes. We further investigate the effect of an external chromomagnetic
field on the value of , finding that this condensate is destroyed by
sufficiently strong fields. The inverse scenario, where is considered
as external, results in analogous findings: when this condensate is
sufficiently large, the induced chromomagnetic field is lowered to a
perturbative value slightly below the applied .Comment: 11 pages, 8 figure
The anomalous dimension of the composite operator A^2 in the Landau gauge
The local composite operator A^2 is analysed in pure Yang-Mills theory in the
Landau gauge within the algebraic renormalization. It is proven that the
anomalous dimension of A^2 is not an independent parameter, being expressed as
a linear combination of the gauge beta function and of the anomalous dimension
of the gauge fields.Comment: 12 pages, LaTeX2e, final version to appear in Phys. Lett.
Modernizing PHCpack through phcpy
PHCpack is a large software package for solving systems of polynomial
equations. The executable phc is menu driven and file oriented. This paper
describes the development of phcpy, a Python interface to PHCpack. Instead of
navigating through menus, users of phcpy solve systems in the Python shell or
via scripts. Persistent objects replace intermediate files.Comment: Part of the Proceedings of the 6th European Conference on Python in
Science (EuroSciPy 2013), Pierre de Buyl and Nelle Varoquaux editors, (2014
The mass gap and vacuum energy of the Gross-Neveu model via the 2PPI expansion
We introduce the 2PPI (2-point-particle-irreducible) expansion, which sums
bubble graphs to all orders. We prove the renormalizibility of this summation.
We use it on the Gross-Neveu model to calculate the mass gap and vacuum energy.
After an optimization of the expansion, the final results are qualitatively
good.Comment: 14 pages,19 eps figures, revtex
Sampling algebraic sets in local intrinsic coordinates
Numerical data structures for positive dimensional solution sets of
polynomial systems are sets of generic points cut out by random planes of
complimentary dimension. We may represent the linear spaces defined by those
planes either by explicit linear equations or in parametric form. These
descriptions are respectively called extrinsic and intrinsic representations.
While intrinsic representations lower the cost of the linear algebra
operations, we observe worse condition numbers. In this paper we describe the
local adaptation of intrinsic coordinates to improve the numerical conditioning
of sampling algebraic sets. Local intrinsic coordinates also lead to a better
stepsize control. We illustrate our results with Maple experiments and
computations with PHCpack on some benchmark polynomial systems.Comment: 13 pages, 2 figures, 2 algorithms, 2 table
Optimal teleportation with a mixed state of two qubits
We consider a single copy of a mixed state of two qubits and derive the
optimal trace-preserving local operations assisted by classical communication
(LOCC) such as to maximize the fidelity of teleportation that can be achieved
with this state. These optimal local operations turn out to be implementable by
one-way communication, and always yields a teleportation fidelity larger than
2/3 if the original state is entangled. This maximal achievable fidelity is an
entanglement measure and turns out to quantify the minimal amount of mixing
required to destroy the entanglement in a quantum state.Comment: 5 pages, expanded version of part II of quant-ph/0203073(v2
Variational principle for non-linear wave propagation in dissipative systems
The dynamics of many natural systems is dominated by non-linear waves
propagating through the medium. We show that the dynamics of non-linear wave
fronts with positive surface tension can be formulated as a gradient system.
The variational potential is simply given by a linear combination of the
occupied volume and surface area of the wave front, and changes monotonically
in time. Finally, we demonstrate that vortex filaments can be written as a
gradient system only if their binormal velocity component vanishes, which
occurs in chemical system with equal diffusion of reactants
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