8,306 research outputs found
Bound states of edge dislocations: The quantum dipole problem in two dimensions
We investigate bound state solutions of the 2D Schr\"odinger equation with a
dipole potential originating from the elastic effects of a single edge
dislocation. The knowledge of these states could be useful for understanding a
wide variety of physical systems, including superfluid behavior along
dislocations in solid He. We present a review of the results obtained by
previous workers together with an improved variational estimate of the ground
state energy. We then numerically solve the eigenvalue problem and calculate
the energy spectrum. In our dimensionless units, we find a ground state energy
of -0.139, which is lower than any previous estimate. We also make successful
contact with the behavior of the energy spectrum as derived from semiclassical
considerations.Comment: 6 pages, 3 figures, submitted to PR
Coupled-channels analysis of the O+Pb fusion barrier distribution
Analyses using simplified coupled-channels models have been unable to
describe the shape of the previously measured fusion barrier distribution for
the doubly magic O+Pb system. This problem was investigated by
re-measuring the fission excitation function for O+Pb with
improved accuracy and performing more exact coupled-channels calculations,
avoiding the constant-coupling and first-order coupling approximations often
used in simplified analyses. Couplings to the single- and 2-phonon states of
Pb, correctly taking into account the excitation energy and the phonon
character of these states, particle transfers, and the effects of varying the
diffuseness of the nuclear potential, were all explored. However, in contrast
to other recent analyses of precise fusion data, no satisfactory simultaneous
description of the shape of the experimental barrier distribution and the
fusion cross-sections for O+Pb was obtained.Comment: RevTex, 29 pages, 7 postscript figures, to appear in PR
High-Resolution Observations of Interstellar Ca I Absorption -- Implications for Depletions and Electron Densities in Diffuse Clouds
We present high-resolution (FWHM ~ 0.3-1.5 km/s) spectra of interstellar Ca I
absorption toward 30 Galactic stars. Comparisons of the column densities of Ca
I, Ca II, K I, and other species -- for individual components identified in the
line profiles and also when integrated over entire lines of sight -- yield
information on relative electron densities and depletions. There is no obvious
relationship between the ratio N(Ca I)/N(Ca II) [equal to n_e/(Gamma/alpha_r)
for photoionization equilibrium] and the fraction of hydrogen in molecular form
f(H2) (often taken to be indicative of the local density n_H). For a smaller
sample of sightlines for which the thermal pressure (n_H T) and local density
can be estimated via analysis of the C I fine-structure excitation, the average
electron density inferred from C, Na, and K (assuming photoionization
equilibrium) seems to be independent of n_H and n_H T. While the n_e obtained
from the ratio N(Ca I)/N(Ca II) is often significantly higher than the values
derived from other elements, the patterns of relative n_e derived from
different elements show both similarities and differences for different lines
of sight -- suggesting that additional processes besides photoionization and
radiative recombination commonly and significantly affect the ionization
balance of heavy elements in diffuse IS clouds. Such additional processes may
also contribute to the (apparently) larger than expected fractional ionizations
(n_e/n_H) found for some lines of sight with independent determinations of n_H.
In general, inclusion of ``grain-assisted'' recombination does reduce the
inferred n_e, but it does not reconcile the n_e estimated from different
elements. The depletion of calcium may have a much weaker dependence on density
than was suggested by earlier comparisons with CH and CN.Comment: aastex, 70 pages, accepted to ApJ
Space-Time Variation of Physical Constants and Relativistic Corrections in Atoms
Detection of high-redshift absorption in the optical spectra of quasars have
provided a powerful tool to measure spatial and temporal variations of physical
``constants'' in the Universe. It is demonstrated that high sensitivity to the
variation of the fine structure constant alpha can be obtained from a
comparison of the spectra of heavy and light atoms (or molecules). We have
performed calculations for the pair FeII and MgII for which accurate quasar and
laboratory spectra are available. A possibility of times enhanced
effects of the fundamental constants variation suitable for laboratory
measurements is also discussed.Comment: 8 pages; LaTeX; Submitted to Phys. Rev. Let
Dinosaur tracks from the Kilmaluag Formation (Bathonian, Middle Jurassic) of Score Bay, Isle of Skye, Scotland, UK
Tracks of a juvenile theropod dinosaur with footprint lengths of between 2 and 9 cm as well as adults of the same ichnospecies with footprints of about 15â25 cm in length were found in the Bathonian (Middle Jurassic) Kilmaluag Formation of Score Bay, northwestern Trotternish Peninsula, Isle of Skye, Scotland, UK. Two footprint sizes occur together on the same bedding plane in the central portion of Score Bay, both in situ and on loose blocks. Another horizon containing footprints above this was also identified. The footprints from the lowest horizon were produced in a desiccated silty mud that was covered with sand. A close association of both adults and juveniles with similar travel direction indicated by the footprints may suggest post-hatching care in theropod dinosaurs. Other footprints, produced on a rippled sandy substrate, have been found on the slightly higher bedding plane at this locality. Loose blocks found 130 m to the northeast in the central part of Score Bay have not been correlated with any in situ sediments, but were preserved in a similar manner to those from the higher bedding plane. These tracks represent the youngest dinosaur remains yet found in Scotland
Wigner Functions and Separability for Finite Systems
A discussion of discrete Wigner functions in phase space related to mutually
unbiased bases is presented. This approach requires mathematical assumptions
which limits it to systems with density matrices defined on complex Hilbert
spaces of dimension p^n where p is a prime number. With this limitation it is
possible to define a phase space and Wigner functions in close analogy to the
continuous case. That is, we use a phase space that is a direct sum of n
two-dimensional vector spaces each containing p^2 points. This is in contrast
to the more usual choice of a two-dimensional phase space containing p^(2n)
points. A useful aspect of this approach is that we can relate complete
separability of density matrices and their Wigner functions in a natural way.
We discuss this in detail for bipartite systems and present the generalization
to arbitrary numbers of subsystems when p is odd. Special attention is required
for two qubits (p=2) and our technique fails to establish the separability
property for more than two qubits.Comment: Some misprints have been corrected and a proof of the separability of
the A matrices has been adde
Separability and Fourier representations of density matrices
Using the finite Fourier transform, we introduce a generalization of
Pauli-spin matrices for -dimensional spaces, and the resulting set of
unitary matrices is a basis for matrices. If and H^{[ N]}=\bigotimes H^{% [ d_{k}]}, we give a
sufficient condition for separability of a density matrix relative to
the in terms of the norm of the spin coefficients of
Since the spin representation depends on the form of the tensor
product, the theory applies to both full and partial separability on a given
space % . It follows from this result that for a prescribed form of
separability, there is always a neighborhood of the normalized identity in
which every density matrix is separable. We also show that for every prime
and the generalized Werner density matrix is fully
separable if and only if
Quantum Knitting
We analyze the connections between the mathematical theory of knots and
quantum physics by addressing a number of algorithmic questions related to both
knots and braid groups.
Knots can be distinguished by means of `knot invariants', among which the
Jones polynomial plays a prominent role, since it can be associated with
observables in topological quantum field theory.
Although the problem of computing the Jones polynomial is intractable in the
framework of classical complexity theory, it has been recently recognized that
a quantum computer is capable of approximating it in an efficient way. The
quantum algorithms discussed here represent a breakthrough for quantum
computation, since approximating the Jones polynomial is actually a `universal
problem', namely the hardest problem that a quantum computer can efficiently
handle.Comment: 29 pages, 5 figures; to appear in Laser Journa
An efficient Fredholm method for calculation of highly excited states of billiards
A numerically efficient Fredholm formulation of the billiard problem is
presented. The standard solution in the framework of the boundary integral
method in terms of a search for roots of a secular determinant is reviewed
first. We next reformulate the singularity condition in terms of a flow in the
space of an auxiliary one-parameter family of eigenproblems and argue that the
eigenvalues and eigenfunctions are analytic functions within a certain domain.
Based on this analytic behavior we present a numerical algorithm to compute a
range of billiard eigenvalues and associated eigenvectors by only two
diagonalizations.Comment: 15 pages, 10 figures; included systematic study of accuracy with 2
new figures, movie to Fig. 4,
http://www.quantumchaos.de/Media/0703030media.av
Quasi-fission reactions as a probe of nuclear viscosity
Fission fragment mass and angular distributions were measured from the
^{64}Ni+^{197}Au reaction at 418 MeV and 383 MeV incident energy. A detailed
data analysis was performed, using the one-body dissipation theory implemented
in the code HICOL. The effect of the window and the wall friction on the
experimental observables was investigated. Friction stronger than one-body was
also considered. The mass and angular distributions were consistent with
one-body dissipation. An evaporation code DIFHEAT coupled to HICOL was
developed in order to predict reaction time scales required to describe
available data on pre-scission neutron multiplicities. The multiplicity data
were again consistent with one-body dissipation. The cross-sections for touch,
capture and quasi-fission were also obtained.Comment: 25 pages REVTeX, 3 tables, 13 figures, submitted to Phys. Rev
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