7,978 research outputs found
Hypersurface Bohm-Dirac models
We define a class of Lorentz invariant Bohmian quantum models for N entangled
but noninteracting Dirac particles. Lorentz invariance is achieved for these
models through the incorporation of an additional dynamical space-time
structure provided by a foliation of space-time. These models can be regarded
as the extension of Bohm's model for N Dirac particles, corresponding to the
foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to
more general foliations. As with Bohm's model, there exists for these models an
equivariant measure on the leaves of the foliation. This makes possible a
simple statistical analysis of position correlations analogous to the
equilibrium analysis for (the nonrelativistic) Bohmian mechanics.Comment: 17 pages, 3 figures, RevTex. Completely revised versio
Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics
We discuss some basic properties of Lie group representations in rigged
Hilbert spaces. In particular, we show that a differentiable representation in
a rigged Hilbert space may be obtained as the projective limit of a family of
continuous representations in a nested scale of Hilbert spaces. We also
construct a couple of examples illustrative of the key features of group
representations in rigged Hilbert spaces. Finally, we establish a simple
criterion for the integrability of an operator Lie algebra in a rigged Hilbert
space
The density matrix in the de Broglie-Bohm approach
If the density matrix is treated as an objective description of individual
systems, it may become possible to attribute the same objective significance to
statistical mechanical properties, such as entropy or temperature, as to
properties such as mass or energy. It is shown that the de Broglie-Bohm
interpretation of quantum theory can be consistently applied to density
matrices as a description of individual systems. The resultant trajectories are
examined for the case of the delayed choice interferometer, for which Bell
appears to suggest that such an interpretation is not possible. Bell's argument
is shown to be based upon a different understanding of the density matrix to
that proposed here.Comment: 15 pages, 4 figure
Irreversible Quantum Mechanics in the Neutral K-System
The neutral Kaon system is used to test the quantum theory of resonance
scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with
complex Hamiltonian is obtained by truncating the complex basis vector
expansion of the exact theory in Rigged Hilbert space. This can be done for K_1
and K_2 as well as for K_S and K_L, depending upon whether one chooses the
(self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP.
As an unexpected curiosity one can show that the exact theory (without
truncation) predicts long-time 2 pion decays of the neutral Kaon system even if
the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include
Recoveries of Great Horned Owls Banded in Central Minnesota
Although great horned owls (Bubo virginianus) are often considered permanent residents, data from band returns have shown that movements by this species do occur. In banding activities conducted in central Minnesota from 1967 through 1983, 329 great horned owls were banded and 24 (7.3 percent) recoveries were reported. Twelve of the 24 recoveries (50.0 percent) were made 15 kilometers or more from where the individuals were banded. Five of these recoveries ( 41.7 percent) were to the southeast. Of 23 owls recovered dead, eight (34 .8 percent) were reported only as found dead, seven (30.4 percent) were found near highways or railroad tracks, and five (21.7 percent) were caught in traps. Difficulties in interpreting movements and causes of mortalities from information provided by band returns, and difficulties in determining whether great horned owl movements are due to juvenile dispersal or to declining prey populations, are discussed
Smearing effect due to the spread of a probe-particle on the Brownian motion near a perfectly reflecting boundary
Quantum fluctuations of electromagnetic vacuum are investigated in a
half-space bounded by a perfectly reflecting plate by introducing a probe
described by a charged wave-packet distribution in time-direction. The
wave-packet distribution of the probe enables one to investigate the smearing
effect upon the measured vacuum fluctuations caused by the quantum nature of
the probe particle. It is shown that the wave-packet spread of the probe
particle significantly influences the measured velocity dispersion of the
probe. In particular, the asymptotic late-time behavior of its -component, , for the wave-packet case is quite different from the test
point-particle case ( is the coordinate normal to the plate). The result for
the wave-packet is \sim 1/\t^2 in the late time (\t is the
measuring time), in stead of the reported late-time behavior for a point-particle probe. This result can be quite significant
for further investigations on the measurement of vacuum fluctuations.Comment: 8 page
Misleading signposts along the de Broglie-Bohm road to quantum mechanics
Eighty years after de Broglie's, and a little more than half a century after
Bohm's seminal papers, the de Broglie--Bohm theory (a.k.a. Bohmian mechanics),
which is presumably the simplest theory which explains the orthodox quantum
mechanics formalism, has reached an exemplary state of conceptual clarity and
mathematical integrity. No other theory of quantum mechanics comes even close.
Yet anyone curious enough to walk this road to quantum mechanics is soon being
confused by many misleading signposts that have been put up, and not just by
its detractors, but unfortunately enough also by some of its proponents.
This paper outlines a road map to help navigate ones way.Comment: Dedicated to Jeffrey Bub on occasion of his 65th birthday. Accepted
for publication in Foundations of Physics. A "slip of pen" in the
bibliography has been corrected -- thanks go to Oliver Passon for catching
it
Quantile Motion and Tunneling
The concepts of quantile position, trajectory, and velocity are defined. For
a tunneling quantum mechanical wave packet, it is proved that its quantile
position always stays behind that of a free wave packet with the same initial
parameters. In quantum mechanics the quantile trajectories are mathematically
identical to Bohm's trajectories. A generalization to three dimensions is
given.Comment: 13 pages, LaTeX, elsart, 3 ps figures, submitted to Phys. Lett.
The Mid-Infrared Emitting Dust Around AB Aur
Using the Keck I telescope, we have obtained 11.7 micron and 18.7 micron
images of the circumstellar dust emission from AB Aur, a Herbig Ae star. We
find that AB Aur is probably resolved at 18.7 micron with an angular diameter
of 1.2" at a surface brightness of 3.5 Jy/arcsec^2. Most of the dust mass
detected at millimeter wavelengths does not contribute to the 18.7 micron
emission, which is plausibly explained if the system possesses a relatively
cold, massive disk. We find that models with an optically thick, geometrically
thin disk, surrounded by an optically thin spherical envelope fit the data
somewhat better than flared disk models.Comment: ApJ in press, 4 color figure
Measuring ^{12}C(&alpha,&gamma)^{16}O from White Dwarf Asteroseismology
During helium burning in the core of a red giant, the relative rates of the
3&alpha and ^{12}C(&alpha,&gamma)^{16}O reactions largely determine the final
ratio of carbon to oxygen in the resulting white dwarf star. The uncertainty in
the 3&alpha reaction at stellar energies due to the extrapolation from
high-energy laboratory measurements is relatively small, but this is not the
case for the ^{12}C(&alpha,&gamma)^{16}O reaction. Recent advances in the
analysis of asteroseismological data on pulsating white dwarf stars now make it
possible to obtain precise measurements of the central ratio of carbon to
oxygen, providing a more direct way to measure the ^{12}C(&alpha,&gamma)^{16}O
reaction rate at stellar energies. We assess the systematic uncertainties of
this approach and quantify small shifts in the measured central oxygen
abundance originating from the observations and from model settings that are
kept fixed during the optimization. Using new calculations of white dwarf
internal chemical profiles, we find a rate for the ^{12}C(&alpha,&gamma)^{16}O
reaction that is significantly higher than most published values. The accuracy
of this method may improve as we modify some of the details of our description
of white dwarf interiors that were not accessible through previous
model-fitting methods.Comment: 8 pages, 4 figures, 3 tables, uses emulateapj5.sty, Accepted for
publication in the Astrophysical Journa
- …