1,169 research outputs found
On the spatial Markov property of soups of unoriented and oriented loops
We describe simple properties of some soups of unoriented Markov loops and of
some soups of oriented Markov loops that can be interpreted as a spatial Markov
property of these loop-soups. This property of the latter soup is related to
well-known features of the uniform spanning trees (such as Wilson's algorithm)
while the Markov property of the former soup is related to the Gaussian Free
Field and to identities used in the foundational papers of Symanzik, Nelson,
and of Brydges, Fr\"ohlich and Spencer or Dynkin, or more recently by Le Jan
Duality of Chordal SLE
We derive some geometric properties of chordal SLE
processes. Using these results and the method of coupling two SLE processes, we
prove that the outer boundary of the final hull of a chordal
SLE process has the same distribution as the image of a
chordal SLE trace, where ,
, and the forces and are suitably
chosen. We find that for , the boundary of a standard chordal
SLE hull stopped on swallowing a fixed x\in\R\sem\{0\} is the image
of some SLE trace started from . Then we obtain a
new proof of the fact that chordal SLE trace is not reversible for
. We also prove that the reversal of SLE trace has
the same distribution as the time-change of some SLE trace for
certain values of and .Comment: In this third version, the referee's suggestions are taken into
consideration. More details are added. Some typos are corrected. The paper
has been accepted by Inventiones Mathematica
LERW as an example of off-critical SLEs
Two dimensional loop erased random walk (LERW) is a random curve, whose
continuum limit is known to be a Schramm-Loewner evolution (SLE) with parameter
kappa=2. In this article we study ``off-critical loop erased random walks'',
loop erasures of random walks penalized by their number of steps. On one hand
we are able to identify counterparts for some LERW observables in terms of
symplectic fermions (c=-2), thus making further steps towards a field theoretic
description of LERWs. On the other hand, we show that it is possible to
understand the Loewner driving function of the continuum limit of off-critical
LERWs, thus providing an example of application of SLE-like techniques to
models near their critical point. Such a description is bound to be quite
complicated because outside the critical point one has a finite correlation
length and therefore no conformal invariance. However, the example here shows
the question need not be intractable. We will present the results with emphasis
on general features that can be expected to be true in other off-critical
models.Comment: 45 pages, 2 figure
Nuclear Flow Excitation Function
We consider the dependence of collective flow on the nuclear surface
thickness in a Boltzmann--Uehling--Uhlenbeck transport model of heavy ion
collisions. Well defined surfaces are introduced by giving test particles a
Gaussian density profile of constant width. Zeros of the flow excitation
function are as much influenced by the surface thickness as the nuclear
equation of state, and the dependence of this effect is understood in terms of
a simple potential scattering model. Realistic calculations must also take into
account medium effects for the nucleon--nucleon cross section, and impact
parameter averaging. We find that balance energy scales with the mass number as
, where has a numerical value between 0.35 and 0.5, depending on
the assumptions about the in-medium nucleon-nucleon cross section.Comment: 11 pages (LaTeX), 7 figures (not included), MSUCL-884, WSU-NP-93-
Hamiltonian light-front field theory within an AdS/QCD basis
Non-perturbative Hamiltonian light-front quantum field theory presents
opportunities and challenges that bridge particle physics and nuclear physics.
Fundamental theories, such as Quantum Chromodynmamics (QCD) and Quantum
Electrodynamics (QED) offer the promise of great predictive power spanning
phenomena on all scales from the microscopic to cosmic scales, but new tools
that do not rely exclusively on perturbation theory are required to make
connection from one scale to the next. We outline recent theoretical and
computational progress to build these bridges and provide illustrative results
for nuclear structure and quantum field theory. As our framework we choose
light-front gauge and a basis function representation with two-dimensional
harmonic oscillator basis for transverse modes that corresponds with
eigensolutions of the soft-wall AdS/QCD model obtained from light-front
holography.Comment: To appear in the proceedings of Light-Cone 2009: Relativistic
Hadronic and Particle Physics, July 8-13, 2009, Sao Jose dos Campos, Brazi
Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
We present a method of short-distance analysis in quantum field theory that
does not require choosing a renormalization prescription a priori. We set out
from a local net of algebras with associated pointlike quantum fields. The net
has a naturally defined scaling limit in the sense of Buchholz and Verch; we
investigate the effect of this limit on the pointlike fields. Both for the
fields and their operator product expansions, a well-defined limit procedure
can be established. This can always be interpreted in the usual sense of
multiplicative renormalization, where the renormalization factors are
determined by our analysis. We also consider the limits of symmetry actions. In
particular, for suitable limit states, the group of scaling transformations
induces a dilation symmetry in the limit theory.Comment: minor changes and clarifications; as to appear in Commun. Math.
Phys.; 37 page
Critical scaling of the a.c. conductivity for a superconductor above Tc
We consider the effects of critical superconducting fluctuations on the
scaling of the linear a.c. conductivity, \sigma(\omega), of a bulk
superconductor slightly above Tc in zero applied magnetic field. The dynamic
renormalization- group method is applied to the relaxational time-dependent
Ginzburg-Landau model of superconductivity, with \sigma(\omega) calculated via
the Kubo formula to O(\epsilon^{2}) in the \epsilon = 4 - d expansion. The
critical dynamics are governed by the relaxational XY-model
renormalization-group fixed point. The scaling hypothesis \sigma(\omega) \sim
\xi^{2-d+z} S(\omega \xi^{z}) proposed by Fisher, Fisher and Huse is explicitly
verified, with the dynamic exponent z \approx 2.015, the value expected for the
d=3 relaxational XY-model. The universal scaling function S(y) is computed and
shown to deviate only slightly from its Gaussian form, calculated earlier. The
present theory is compared with experimental measurements of the a.c.
conductivity of YBCO near Tc, and the implications of this theory for such
experiments is discussed.Comment: 16 pages, submitted to Phys. Rev.
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