3,911 research outputs found
On periodic points of free inverse monoid endomorphisms
It is proved that the periodic point submonoid of a free inverse monoid
endomorphism is always finitely generated. Using Chomsky's hierarchy of
languages, we prove that the fixed point submonoid of an endomorphism of a free
inverse monoid can be represented by a context-sensitive language but, in
general, it cannot be represented by a context-free language.Comment: 18 page
Fixed points of endomorphisms of graph groups
It is shown, for a given graph group , that the fixed point subgroup
Fix is finitely generated for every endomorphism of if
and only if is a free product of free abelian groups. The same conditions
hold for the subgroup of periodic points. Similar results are obtained for
automorphisms, if the dependence graph of is a transitive forest.Comment: 9 page
Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme
We introduce a new regularization scheme for Quantum Cosmology in Loop
Quantum Gravity (LQG) using the tools of Quantum Reduced Loop Gravity (QRLG).
It is obtained considering density matrices for superposition of graphs based
on statistical countings of microstates compatible with macroscopic
configurations. We call this procedure statistical regularization scheme. In
particular, we show how the and schemes introduced in Loop
Quantum Cosmology (LQC) emerge with specific choices of density matrices.
Within this new scheme we compute effective Hamiltonians suitable to describe
quantum corrected Friedmann and Bianchi I universes and their leading orders
coincide with the corresponding effective LQC Hamiltonians in the
scheme. We compute the next to the leading orders corrections and numerical
investigation of the resulting dynamics shows evidence for the
emergent-bouncing universe scenario to be a general property of the isotropic
sector of QRLG.Comment: 22 pages, 4 figures. Two small typos fixed. Conclusions unchange
Three-quark potentials in an effective Polyakov loop model
Three-quark potentials are studied in great details in the three-dimensional
pure gauge theory at finite temperature, for the cases of static
sources in the fundamental and adjoint representations. For this purpose, the
corresponding Polyakov loop model in its simplest version is adopted. The
potentials in question, as well as the conventional quark--anti-quark
potentials, are calculated numerically both in the confinement and
deconfinement phases. Results are compared to available analytical predictions
at strong coupling and in the limit of large number of colors . The
three-quark potential is tested against the expected and laws and
the string tension entering these laws is compared to the conventional
string tension. As a byproduct of this investigation, essential
features of the critical behaviour across the deconfinement transition are
elucidated.Comment: 28 pages, 18 figures, 4 tables; some text and a few references added;
version accepted for publication on Nucl. Phys.
Bianchi I effective dynamics in Quantum Reduced Loop Gravity
The effective quantum dynamics of Bianchi I spacetime is addressed within the
statistical regularization scheme in Quantum Reduced Loop Gravity. The case of
a minimally coupled massless scalar field is studied and compared with the
effective Loop Quantum Cosmology. The dynamics provided by the two
approaches match in the semiclassical limit but differ significantly after the
bounces. Analytical and numerical inspections show that energy density,
expansion scalar and shear are bounded also in Quantum Reduced Loop Gravity and
the classical singularity is resolved for generic initial conditions in all
spatial directions.Comment: 19 pages, 23 figures, 1 tabl
Homogenization of the linear Boltzmann equation in a domain with a periodic distribution of holes
Consider a linear Boltzmann equation posed on the Euclidian plane with a
periodic system of circular holes and for particles moving at speed 1. Assuming
that the holes are absorbing -- i.e. that particles falling in a hole remain
trapped there forever, we discuss the homogenization limit of that equation in
the case where the reciprocal number of holes per unit surface and the length
of the circumference of each hole are asymptotically equivalent small
quantities. We show that the mass loss rate due to particles falling into the
holes is governed by a renewal equation that involves the distribution of
free-path lengths for the periodic Lorentz gas. In particular, it is proved
that the total mass of the particle system at time t decays exponentially fast
as t tends to infinity. This is at variance with the collisionless case
discussed in [Caglioti, E., Golse, F., Commun. Math. Phys. 236 (2003), pp.
199--221], where the total mass decays as Const./t as the time variable t tends
to infinity.Comment: 29 pages, 1 figure, submitted; figure 1 corrected in new versio
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