200,194 research outputs found
Quadrature domains and kernel function zipping
It is proved that quadrature domains are ubiquitous in a very strong sense in
the realm of smoothly bounded multiply connected domains in the plane. In fact,
they are so dense that one might as well assume that any given smooth domain
one is dealing with is a quadrature domain, and this allows access to a host of
strong conditions on the classical kernel functions associated to the domain.
Following this string of ideas leads to the discovery that the Bergman kernel
can be zipped down to a strikingly small data set. It is also proved that the
kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati
Enhanced non-perturbative effects through the collinear anomaly
We show that non-perturbative effects are logarithmically enhanced for
transverse-momentum-dependent observables such as q_T-spectra of electroweak
bosons in hadronic collisions and jet broadening at e^+e^- colliders. This
enhancement arises from the collinear anomaly, a mechanism characteristic for
transverse observables, which induces logarithmic dependence on the hard scale
in the product of the soft and collinear matrix elements. Our analysis is based
on an operator product expansion and provides, for the first time, a
systematic, model-independent way to study non-perturbative effects for this
class of observables. For the case of jet broadening, we relate the leading
correction to the non-perturbative shift of the thrust distribution.Comment: 5 pages, 2 figures. v2: Minor changes, references added. Journal
versio
Conditions for negative specific heat in systems of attracting classical particles
We identify conditions for the presence of negative specific heat in
non-relativistic self-gravitating systems and similar systems of attracting
particles.
The method used, is to analyse the Virial theorem and two soluble models of
systems of attracting particles, and to map the sign of the specific heat for
different combinations of the number of spatial dimensions of the system,
(), and the exponent, (), in the force potential,
. Negative specific heat in such systems is found to be present
exactly for , at least for . For many combinations of and
representing long-range forces, the specific heat is positive or zero,
for both models and the Virial theorem. Hence negative specific heat is not
caused by long-range forces as such. We also find that negative specific heat
appears when is negative, and there is no singular point in a certain
density distribution. A possible mechanism behind this is suggested.Comment: 11 pages, 1 figure, Published version (including correlation between
positive specific heat and singular points
Relaxation to a Perpetually Pulsating Equilibrium
Paper in honour of Freeman Dyson on the occasion of his 80th birthday.
Normal N-body systems relax to equilibrium distributions in which classical
kinetic energy components are 1/2 kT, but, when inter-particle forces are an
inverse cubic repulsion together with a linear (simple harmonic) attraction,
the system pulsates for ever. In spite of this pulsation in scale, r(t), other
degrees of freedom relax to an ever-changing Maxwellian distribution. With a
new time, tau, defined so that r^2d/dt =d/d tau it is shown that the remaining
degrees of freedom evolve with an unchanging reduced Hamiltonian. The
distribution predicted by equilibrium statistical mechanics applied to the
reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature
pulsates like r^-2. Numerical simulation with 1000 particles demonstrate a
rapid relaxation to this pulsating equilibrium.Comment: 9 pages including 4 figure
Adaptive Mesh Refinement for Singular Current Sheets in Incompressible Magnetohydrodynamic Flows
The formation of current sheets in ideal incompressible magnetohydrodynamic
flows in two dimensions is studied numerically using the technique of adaptive
mesh refinement. The growth of current density is in agreement with simple
scaling assumptions. As expected, adaptive mesh refinement shows to be very
efficient for studying singular structures compared to non-adaptive treatments.Comment: 8 pages RevTeX, 13 Postscript figure
Bell's inequalities I: An explanation for their experimental violation
Derivations of two Bell's inequalities are given in a form appropriate to the
interpretation of experimental data for explicit determination of all the
correlations. They are arithmetic identities independent of statistical
reasoning and thus cannot be violated by data that meets the conditions for
their validity. Two experimentally performable procedures are described to meet
these conditions. Once such data are acquired, it follows that the measured
correlations cannot all equal a negative cosine of angular differences. The
relation between this finding and the predictions of quantum mechanics is
discussed in a companion paper.Comment: 15 pages, 2 figure
On Spontaneous Wave Function Collapse and Quantum Field Theory
One way of obtaining a version of quantum mechanics without observers, and
thus of solving the paradoxes of quantum mechanics, is to modify the
Schroedinger evolution by implementing spontaneous collapses of the wave
function. An explicit model of this kind was proposed in 1986 by Ghirardi,
Rimini, and Weber (GRW), involving a nonlinear, stochastic evolution of the
wave function. We point out how, by focussing on the essential mathematical
structure of the GRW model and a clear ontology, it can be generalized to
(regularized) quantum field theories in a simple and natural way.Comment: 14 pages LaTeX, no figures; v2 minor improvement
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