153 research outputs found
Induced and non-induced forbidden subposet problems
The problem of determining the maximum size that a -free
subposet of the Boolean lattice can have, attracted the attention of many
researchers, but little is known about the induced version of these problems.
In this paper we determine the asymptotic behavior of , the maximum
size that an induced -free subposet of the Boolean lattice can have
for the case when is the complete two-level poset or the complete
multi-level poset when all 's either equal 4 or
are large enough and satisfy an extra condition. We also show lower and upper
bounds for the non-induced problem in the case when is the complete
three-level poset . These bounds determine the asymptotics of
for some values of independently of the values of and
Supersaturation and stability for forbidden subposet problems
We address a supersaturation problem in the context of forbidden subposets. A
family of sets is said to contain the poset if there is an
injection such that implies . The poset on four elements with is
called butterfly. The maximum size of a family
that does not contain a butterfly is as proved by De Bonis, Katona, and
Swanepoel. We prove that if contains
sets, then it has to contain at least copies of the butterfly provided for some positive . We show by a
construction that this is asymptotically tight and for small values of we
show that the minimum number of butterflies contained in is
exactly
Prethermalisation and the Build Up of the Higgs Effect
Real time field excitations in the broken symmetry phase of the classical
abelian Gauge+Higgs model are studied numerically in the unitary gauge, for
systems starting from the unstable maximum of the Higgs potential.Comment: 5 pages, 6 figures, to appear in proceedings of SEWM'0
Spontaneously broken ground states of the U(n)_L x U(n)_R linear sigma model at large n
Symmetry breaking patterns of the U(n)_L x U(n)_R symmetric meson model are
investigated in a formulation involving three auxiliary composite fields. The
effective potential is constructed at leading order in the 1/n expansion for a
condensate belonging to the center of the U(n) group. A wide region is found in
the coupling space where in addition to the condensate proportional to the unit
matrix, also metastable minima exist, in which a further breakdown of the
diagonal U_V(n) symmetry to U_V(n-1) is realized. Application of a moderate
external field conjugate to this component of the order parameter changes this
state into the true ground state of the system.Comment: ReVTeX4, 10 pages, 5 figures. Extended introduction and conclusion.
Version published in Phys. Rev.
Beyond HTL: The Classical Kinetic Theory of Landau Damping for Selfinteracting Scalar Fields in the Broken Phase
The effective theory of low frequency fluctuations of selfinteracting scalar
fields is constructed in the broken symmetry phase. The theory resulting from
integrating fluctuations with frequencies much above the spontanously generated
mass scale is found to be local. Non-local dynamics, especially
Landau damping emerges under the effect of fluctuations in the
region. A kinetic theory of relativistic scalar gas particles interacting via
their locally variable mass with the low frequency scalar field is shown to be
equivalent to this effective field theory for scales below the characteristic
mass, that is beyond the accuracy of the Hard Thermal Loop (HTL) approximation.Comment: 5 pages, Latex, uses sprocl.sty, to be published in the Proceedings
of SEWM 98 Conference Copenhagen, Denmark 2-5 December 199
The scalar-isoscalar spectral function of strong matter in a large N approximation
The enhancement of the scalar-isoscalar spectral function near the two-pion
threshold is studied in the framework of an effective linear model,
using a large N approximation in the number of the Goldstone bosons. The effect
is rather insensitive to the detailed T=0 characteristics of the pole,
it is accounted by a pole moving with increasing along the real axis of the
second Riemann sheet towards the threshold location from below.Comment: 5 pages, poster presented at SEWM2002, Heidelberg, October 200
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