12,477 research outputs found
Correction-to-scaling exponent for two-dimensional percolation
We show that the correction-to-scaling exponents in two-dimensional
percolation are bounded by Omega <= 72/91, omega = D Omega <= 3/2, and Delta_1
= nu omega <= 2, based upon Cardy's result for the critical crossing
probability on an annulus. The upper bounds are consistent with many previous
measurements of site percolation on square and triangular lattices, and new
measurements for bond percolation presented here, suggesting this result is
exact. A scaling form evidently applicable to site percolation is also found
PHENIX Measurement of High- Hadron-hadron and Photon-hadron Azimuthal Correlations
High- hadron-hadron correlations have been measured with the PHENIX
experiment in \Cu and \pp collisions at GeV. A
comparison of the jet widths and yields between the two colliding systems
allows us to study the medium effect on jets. We also present a first
measurement of direct photon-hadron correlations in \Au and \pp collisions.
We find that the near-side yields are consistent with zero in both systems. By
comparing the jet yields on the away side, we observe a suggestion of the
expected suppression of hadrons associated with photons in \Au collisions.Comment: 5 pages, proceeding for parallel talk on Quark Matter 200
Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schr\"odinger Equation
We generalize the Weisskopf-Wigner theory for the line shape and transition
rates of decaying states to the case of the energy-driven stochastic
Schr\"odinger equation that has been used as a phenomenology for state vector
reduction. Within the standard approximations used in the Weisskopf-Wigner
analysis, and assuming that the perturbing potential inducing the decay has
vanishing matrix elements within the degenerate manifold containing the
decaying state, the stochastic Schr\"odinger equation linearizes. Solving the
linearized equations, we find no change from the standard analysis in the line
shape or the transition rate per unit time. The only effect of the stochastic
terms is to alter the early time transient behavior of the decay, in a way that
eliminates the quantum Zeno effect. We apply our results to estimate
experimental bounds on the parameter governing the stochastic effects.Comment: 29 pages in RevTeX, Added Note, references adde
Quantum Black Holes as the Link Between Microphysics and Macrophysics
There appears to be a duality between elementary particles, which span the
mass range below the Planck scale, and black holes, which span the mass range
range above it. In particular, the Black Hole Uncertainty Principle
Correspondence posits a smooth transition between the Compton and Schwarzschild
scales as a function of mass. This suggests that all black holes are in some
sense quantum, that elementary particles can be interpreted as sub-Planckian
black holes, and that there is a subtle connection between quantum and
classical physics.Comment: 9 pages, 7 figures, 2015 Karl Schwarzschild Meeting on Gravitational
Physics, eds. P. Nicolini, J. Mureika, M. Kaminski and M. Bleiche
Gravitomagnetism in Quantum Mechanics
We give a systematic treatment of the quantum mechanics of a spin zero
particle in a combined electromagnetic field and a weak gravitational field,
which is produced by a slow moving matter source. The analysis is based on the
Klein-Gordon equation expressed in generally covariant form and coupled
minimally to the electromagnetic field. The Klein-Gordon equation is recast
into Schroedinger equation form (SEF), which we then analyze in the
non-relativistic limit. We include a discussion of some rather general
observable physical effects implied by the SEF, concentrating on
gravitomagnetism. Of particular interest is the interaction of the orbital
angular momentum of the particle with the gravitomagnetic field.Comment: 9 page
Billiard algebra, integrable line congruences, and double reflection nets
The billiard systems within quadrics, playing the role of discrete analogues
of geodesics on ellipsoids, are incorporated into the theory of integrable
quad-graphs. An initial observation is that the Six-pointed star theorem, as
the operational consistency for the billiard algebra, is equivalent to an
integrabilty condition of a line congruence. A new notion of the
double-reflection nets as a subclass of dual Darboux nets associated with
pencils of quadrics is introduced, basic properies and several examples are
presented. Corresponding Yang-Baxter maps, associated with pencils of quadrics
are defined and discussed.Comment: 18 pages, 8 figure
Collapse models with non-white noises
We set up a general formalism for models of spontaneous wave function
collapse with dynamics represented by a stochastic differential equation driven
by general Gaussian noises, not necessarily white in time. In particular, we
show that the non-Schrodinger terms of the equation induce the collapse of the
wave function to one of the common eigenstates of the collapsing operators, and
that the collapse occurs with the correct quantum probabilities. We also
develop a perturbation expansion of the solution of the equation with respect
to the parameter which sets the strength of the collapse process; such an
approximation allows one to compute the leading order terms for the deviations
of the predictions of collapse models with respect to those of standard quantum
mechanics. This analysis shows that to leading order, the ``imaginary'' noise
trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J.
Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509
QCD Accurately Predicts the Induced Pseudoscalar Coupling Constant
Using chiral Ward identities of QCD, we derive a relation for the induced
pseudoscalar coupling constant which is accurate within a few percent, .Comment: 5pp, LaTeX, CRN-94/1
- …