421 research outputs found
Symmetric random walks on Homeo+(R)
We study symmetric random walks on finitely generated groups of
orientation-preserving homeomorphisms of the real line. We establish an
oscillation property for the induced Markov chain on the line that implies a
weak form of recurrence. Except for a few special cases, which can be treated
separately, we prove a property of "global stability at a finite distance":
roughly speaking, there exists a compact interval such that any two
trajectories get closer and closer whenever one of them returns to the compact
interval. The probabilistic techniques employed here lead to interesting
results for the study of group actions on the line. For instance, we show that
under a suitable change of the coordinates, the drift of every point becomes
zero provided that the action is minimal. As a byproduct, we recover the fact
that every finitely generated group of homeomorphisms of the real line is
topologically conjugate to a group of (globally) Lipschitz homeomorphisms.
Moreover, we show that such a conjugacy may be chosen in such a way that the
displacement of each element is uniformly bounded
The Pressure of Hot Theory at order
The order contribution to the pressure of massless theory
at nonzero temperature is obtained explicitly. Lower order contributions are
reconsidered and two issues leading to the optimal choice of rearranged
Lagrangian for such calculations are clarified.Comment: 15 pages, Latex, postscript file attached at the en
Integrable Hierarchies and Information Measures
In this paper we investigate integrable models from the perspective of
information theory, exhibiting various connections. We begin by showing that
compressible hydrodynamics for a one-dimesional isentropic fluid, with an
appropriately motivated information theoretic extension, is described by a
general nonlinear Schrodinger (NLS) equation. Depending on the choice of the
enthalpy function, one obtains the cubic NLS or other modified NLS equations
that have applications in various fields. Next, by considering the integrable
hierarchy associated with the NLS model, we propose higher order information
measures which include the Fisher measure as their first member. The lowest
members of the hiearchy are shown to be included in the expansion of a
regularized Kullback-Leibler measure while, on the other hand, a suitable
combination of the NLS hierarchy leads to a Wootters type measure related to a
NLS equation with a relativistic dispersion relation. Finally, through our
approach, we are led to construct an integrable semi-relativistic NLS equation.Comment: 11 page
On the screening of static electromagnetic fields in hot QED plasmas
We study the screening of static magnetic and electric fields in massless
quantum electrodynamics (QED) and massless scalar electrodynamics (SQED) at
temperature . Various exact relations for the static polarisation tensor are
first reviewed and then verified perturbatively to fifth order (in the
coupling) in QED and fourth order in SQED, using different resummation
techniques. The magnetic and electric screening masses squared, as defined
through the pole of the static propagators, are also calculated to fifth order
in QED and fourth order in SQED, and their gauge-independence and
renormalisation-group invariance is checked. Finally, we provide arguments for
the vanishing of the magnetic mass to all orders in perturbation theory.Comment: 37 pages, 8 figure
The Free Energy Of Hot Gauge Theories
The total perturbative contribution to the free-energy of hot SU(3) gauge
theory is argued to lie significantly higher than the full result obtained by
lattice simulations. This then suggests the existence of large non-perturbative
corrections even at temperatures a few times above the critical temperature.
Some speculations are then made on the nature and origin of the
non-perturbative corrections. The analysis is then carried out for quantum
chromodynamics, gauge theories, and quantum electrodynamics, leading
to a conjecture and one more speculation.Comment: Revised Journal version;25 pages Latex and 11 .eps figures in
separate file. Requires epsf.st
Solution to the 3-loop -derivable Approximation for Scalar Thermodynamics
We solve the 3-loop -derivable approximation to the thermodynamics of
the massless field theory by reducing it to a 1-parameter variational
problem. The thermodynamic potential is expanded in powers of and ,
where is the coupling constant, is a variational mass parameter, and
is the temperature. There are ultraviolet divergences beginning at 6th
order in that cannot be removed by renormalization. However the finite
thermodynamic potential obtained by truncating after terms of 5th order in
and defines a stable approximation to the thermodynamic functions.Comment: 4 pages, 1 figur
Ewing Sarcoma/Primitive Neuroectodermal Tumor of the Kidney: Two Unusual Presentations of a Rare Tumor
Only few cases of primary renal Ewing's sarcoma have been reported in the literature to date. We present here two cases of renal ES/PNET with an uncanny presentation. The first case was discovered after the patient presented clinically with irradiating flank pain, mimicking the pain related with kidney stones. The second case had clinical presentation of pulmonary thromboembolism after the patient was involved in an automobilist accident. The tumors were mainly composed of small blue cells which by immunohistochemical were positive for neural markers, and FISH revealed the translocation 22q12 for the EWSR1 gene. The diagnosis of renal primitive neuroectodermal tumor/EWING tumor is very rare and usually involves several different diagnostic techniques. The differential diagnosis is usually broad with frequent overlapping features between the entities. The cases presented in this paper illustrated the difficulties with which routine anatomical pathologist is faced when dealing with rare renal poorly differentiated neoplasm in adults
The Free Energy of High Temperature QED to Order From Effective Field Theory
Massless quantum electrodynamics is studied at high temperature and zero
chemical potential. We compute the Debye screening mass to order and
the free energy to order } by an effective field theory approach,
recently developed by Braaten and Nieto. Our results are in agreement with
calculations done in resummed perturbation theory. This method makes it
possible to separate contributions to the free energy from different momentum
scales (order and ) and provides an economical alternative to
computations in the full theory which involves the dressing of internal
propagators.Comment: 10 pages Latex, 6 figure
Gap equation in scalar field theory at finite temperature
We investigate the two-loop gap equation for the thermal mass of hot massless
theory and find that the gap equation itself has a non-zero finite
imaginary part. This indicates that it is not possible to find the real thermal
mass as a solution of the gap equation beyond order in perturbation
theory. We have solved the gap equation and obtain the real and the imaginary
part of the thermal mass which are correct up to order in perturbation
theory.Comment: 13 pages, Latex with axodraw, Minor corrections, Appendix adde
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