31,308 research outputs found
On the divine clockwork: the spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state
The correspondence limit of the atomic elliptic state in three dimensions is
discussed in terms of Nelson's stochastic mechanics. In previous work we have
shown that this approach leads to a limiting Nelson diffusion and here we
discuss in detail the invariant measure for this process and show that it is
concentrated on the Kepler ellipse in the plane z=0. We then show that the
limiting Nelson diffusion generator has a spectral gap; thereby proving that in
the infinite time limit the density for the limiting Nelson diffusion will
converge to its invariant measure. We also include a summary of the Cheeger and
Poincare inequalities both of which are used in our proof of the existence of
the spectral gap.Comment: 30 pages, 5 figures, submitted to J. Math. Phy
The generalized Fenyes-Nelson model for free scalar field theory
The generalized Fenyes--Nelson model of quantum mechanics is applied to the
free scalar field. The resulting Markov field is equivalent to the Euclidean
Markov field with the times scaled by a common factor which depends on the
diffusion parameter. This result is consistent between Guerra's earlier work on
stochastic quantization of scalar fields. It suggests a deep connection between
Euclidean field theory and the stochastic interpretation of quantum mechanics.
The question of Lorentz covariance is also discussed.Comment: 6 page
The formation of silver /I/ chloride by the action of silver /I/ ion on carbon tetrachloride in 2-butanol and methanol
Formation of silver chloride by action of silver ion on carbon tetrachloride in 2-butanol and methano
Maximal violation of Bell inequalities by position measurements
We show that it is possible to find maximal violations of the CHSH-Bell
inequality using only position measurements on a pair of entangled
non-relativistic free particles. The device settings required in the CHSH
inequality are done by choosing one of two times at which position is measured.
For different assignments of the "+" outcome to positions, namely to an
interval, to a half line, or to a periodic set, we determine violations of the
inequalities, and states where they are attained. These results have
consequences for the hidden variable theories of Bohm and Nelson, in which the
two-time correlations between distant particle trajectories have a joint
distribution, and hence cannot violate any Bell inequality.Comment: 13 pages, 4 figure
The relation between gas density and velocity power spectra in galaxy clusters: qualitative treatment and cosmological simulations
We address the problem of evaluating the power spectrum of the velocity field
of the ICM using only information on the plasma density fluctuations, which can
be measured today by Chandra and XMM-Newton observatories. We argue that for
relaxed clusters there is a linear relation between the rms density and
velocity fluctuations across a range of scales, from the largest ones, where
motions are dominated by buoyancy, down to small, turbulent scales:
, where
is the spectral amplitude of the density perturbations at wave number ,
is the mean square component of the velocity field,
is the sound speed, and is a dimensionless constant of order unity.
Using cosmological simulations of relaxed galaxy clusters, we calibrate this
relation and find . We argue that this value is set at
large scales by buoyancy physics, while at small scales the density and
velocity power spectra are proportional because the former are a passive scalar
advected by the latter. This opens an interesting possibility to use gas
density power spectra as a proxy for the velocity power spectra in relaxed
clusters, across a wide range of scales.Comment: 6 pages, 3 figures, submitted to ApJ Letter
Studies of Yeast V - Is Bios a Single Substance
In previous communication (Journal of Biological Chemistry, March, 1922) Fulmer and Nelson showed that the water extract of alfalfa is much richer in the yeast growth stimulant, Bois, than is the 95 per cent alcoholic extract of the same material. In the work here described two extracts were prepared as follows from alfalfa which had been previously extracted with ether. Extract A was an extract by long extraction with absolute alcohol. Extract B was an extract prepared by long extraction of the absolute-alcohol-extracted material with water. Both extracts showed optimum concentrations for maximum stimulation and were about equally potent. Combinations of the two extracts were much more potent than the optimum concentration of either alone. Detailed studies are being made of the properties of the two extracts. Bois is not a single substance but is composed of at least two materials. Bois A is soluble in absolute alcohol and in water. Bois B is insoluble in absolute alcohol and is soluble in water
Vortex pinning by meandering line defects in planar superconductors
To better understand vortex pinning in thin superconducting slabs, we study
the interaction of a single fluctuating vortex filament with a curved line
defect in (1+1) dimensions. This problem is also relevant to the interaction of
scratches with wandering step edges in vicinal surfaces. The equilibrium
probability density for a fluctuating line attracted to a particular fixed
defect trajectory is derived analytically by mapping the problem to a straight
line defect in the presence of a space and time-varying external tilt field.
The consequences of both rapid and slow changes in the frozen defect
trajectory, as well as finite size effects are discussed. A sudden change in
the defect direction leads to a delocalization transition, accompanied by a
divergence in the trapping length, near a critical angle.Comment: 9 pages, 9 figure
Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes
We examine the shapes and energies of 5- and 7-fold disclinations in
low-temperature hexatic membranes. These defects buckle at different values of
the ratio of the bending rigidity, , to the hexatic stiffness constant,
, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation
temperatures. Seven-fold disclinations are studied in detail numerically for
arbitrary . We argue that thermal fluctuations always drive
into an ``unbuckled'' regime at long wavelengths, so that
disclinations should, in fact, proliferate at the {\em same} critical
temperature. We show analytically that both types of defects have power law
shapes with continuously variable exponents in the ``unbuckled'' regime.
Thermal fluctuations then lock in specific power laws at long wavelengths,
which we calculate for 5- and 7-fold defects at low temperatures.Comment: LaTeX format. 17 pages. To appear in Phys. Rev.
The dependence of the viscosity-parameter on the disk scale height profile
It is shown that the height scale for accretion disks is a constant whenever
hydrostatic equilibrium and sub-sonic turbulence regime hold in the disk. In
order to have a variable height scale, processes that do contribute with an
extra term to the continuity equation are needed. This makes the viscosity
parameter much greater in the outer region and much smaller in the inner
region. Under these circumstances, turbulence is a presumable source of
viscosity in the disk.Comment: 8 pages, submitted to Apj
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