4,786 research outputs found
Exact Quantum Solutions of Extraordinary N-body Problems
The wave functions of Boson and Fermion gases are known even when the
particles have harmonic interactions. Here we generalise these results by
solving exactly the N-body Schrodinger equation for potentials V that can be
any function of the sum of the squares of the distances of the particles from
one another in 3 dimensions. For the harmonic case that function is linear in
r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) =
\zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2
M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the
solution is given in terms of the one or two body problem with potential U(r)
in 3 dimensions. The degeneracies of the levels are derived for distinguishable
particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter
involve significant combinatorial analysis which may have application to the
shell model of atomic nuclei. For large N the Fermionic ground state gives the
binding energy of a degenerate white dwarf star treated as a giant atom with an
N-body wave function. The N-body forces involved in these extraordinary N-body
problems are not the usual sums of two body interactions, but nor are forces
between quarks or molecules. Bose-Einstein condensation of particles in 3
dimensions interacting via these strange potentials can be treated by this
method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal
Societ
Scaling Study and Thermodynamic Properties of the cubic Helimagnet FeGe
The critical behavior of the cubic helimagnet FeGe was obtained from
isothermal magnetization data in very close vicinity of the ordering
temperature. A thorough and consistent scaling analysis of these data revealed
the critical exponents , , and . The
anomaly in the specific heat associated with the magnetic ordering can be well
described by the critical exponent . The values of these
exponents corroborate that the magnetic phase transition in FeGe belongs to the
isotropic 3D-Heisenberg universality class. The specific heat data are well
described by ab initio phonon calculations and confirm the localized character
of the magnetic moments.Comment: 10 pages, 8 figure
A measure of majorisation emerging from single-shot statistical mechanics
The use of the von Neumann entropy in formulating the laws of thermodynamics
has recently been challenged. It is associated with the average work whereas
the work guaranteed to be extracted in any single run of an experiment is the
more interesting quantity in general. We show that an expression that
quantifies majorisation determines the optimal guaranteed work. We argue it
should therefore be the central quantity of statistical mechanics, rather than
the von Neumann entropy. In the limit of many identical and independent
subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered
but in the non-equilbrium regime the optimal guaranteed work can be radically
different to the optimal average. Moreover our measure of majorisation governs
which evolutions can be realized via thermal interactions, whereas the
nondecrease of the von Neumann entropy is not sufficiently restrictive. Our
results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation,
same main results / added minor result on pure bipartite state entanglement
(appendix G) / near to published versio
Nonlocal Effects of Partial Measurements and Quantum Erasure
Partial measurement turns the initial superposition not into a definite
outcome but into a greater probability for it. The probability can approach
100%, yet the measurement can undergo complete quantum erasure. In the EPR
setting, we prove that i) every partial measurement nonlocally creates the same
partial change in the distant particle; and ii) every erasure inflicts the same
erasure on the distant particle's state. This enables an EPR experiment where
the nonlocal effect does not vanish after a single measurement but keeps
"traveling" back and forth between particles. We study an experiment in which
two distant particles are subjected to interferometry with a partial "which
path" measurement. Such a measurement causes a variable amount of correlation
between the particles. A new inequality is formulated for same-angle
polarizations, extending Bell's inequality for different angles. The resulting
nonlocality proof is highly visualizable, as it rests entirely on the
interference effect. Partial measurement also gives rise to a new form of
entanglement, where the particles manifest correlations of multiple
polarization directions. Another novelty in that the measurement to be erased
is fully observable, in contrast to prevailing erasure techniques where it can
never be observed. Some profound conceptual implications of our experiment are
briefly pointed out.Comment: To be published in Phys. Rev. A 63 (2001). 19 pages, 12 figures,
RevTeX 3.
Manifestation of impurity induced s_{+-} -> s_{++} transition: multiband model for dynamical response functions
We investigate effects of disorder on the density of states, the single
particle response function and optical conductivity in multiband
superconductors with s_{+-} symmetry of the order parameter, where s_{+-} ->
s_{++} transition may take place. In the vicinity of the transition the
superconductive gapless regime is realized. It manifests itself in anomalies in
the above mentioned properties. As a result, intrinsically phase-insensitive
experimental methods like ARPES, tunneling and terahertz spectroscopy may be
used for revealing of information about the underlying order parameter
symmetry.Comment: 14 pages, 6 figure
Signatures of Galaxy-Cluster Interactions: Spiral Galaxy Rotation Curve Asymmetry, Shape, and Extent
The environmental dependencies of the characteristics of spiral galaxy
rotation curves are studied in this work. We use our large, homogeneously
collected sample of 510 cluster spiral galaxy rotation curves to test the claim
that the shape of a galaxy's rotation curve strongly depends on its location
within the cluster, and thus presumably on the strength of the local
intracluster medium and on the frequency and strength of tidal interactions
with the cluster and cluster galaxies. Our data do not corroborate such a
scenario, consistent with the fact that Tully-Fisher residuals are independent
of galaxy location within the cluster; while the average late-type spiral
galaxy shows more rise in the outer parts of its rotation curve than does the
typical early-type spiral galaxy, there is no apparent trend for either subset
with cluster environment. We also investigate as a function of cluster
environment rotation curve asymmetry and the radial distribution of H II region
tracers within galactic disks. Mild trends with projected cluster-centric
distance are observed: (i) the (normalized) radial extent of optical line
emission averaged over all spiral galaxy types shows a 4%+/-2% increase per Mpc
of galaxy-cluster core separation, and (ii) rotation curve asymmetry falls by a
factor of two between the inner and outer cluster for early-type spirals (a
negligible decrease is found for late-type spirals). Such trends are consistent
with spiral disk perturbations or even the stripping of the diffuse, outermost
gaseous regions within the disks as galaxies pass through the dense cluster
cores.Comment: 17 pages; to appear in the April 2001 Astronomical Journa
The scaling of X-ray variability with luminosity in Ultra-luminous X-ray sources
We investigated the relationship between the X-ray variability amplitude and
X-ray luminosity for a sample of 14 bright Ultra-luminous X-ray sources (ULXs)
with XMM-Newton/EPIC data, and compare it with the well established similar
relationship for Active Galactic Nuclei (AGN). We computed the normalised
excess variance in the 2-10 keV light curves of these objects and their 2-10
keV band intrinsic luminosity. We also determined model
"variability-luminosity" relationships for AGN, under several assumptions
regarding their power-spectral shape. We compared these model predictions at
low luminosities with the ULX data. The variability amplitude of the ULXs is
significantly smaller than that expected from a simple extrapolation of the AGN
"variability-luminosity" relationship at low luminosities. We also find
evidence for an anti-correlation between the variability amplitude and L(2-10
keV) for ULXs. The shape of this relationship is consistent with the AGN data
but only if the ULXs data are shifted by four orders of magnitudes in
luminosity. Most (but not all) of the ULXs could be "scaled-down" version of
AGN if we assume that: i) their black hole mass and accretion rate are of the
order of ~(2.5-30)x 10E+03 Msolar and ~ 1-80 % of the Eddington limit, and ii)
their Power Spectral Density has a doubly broken power-law shape. This PDS
shape and accretion rate is consistent with Galactic black hole systems
operating in their so-called "low-hard" and "very-high" states.Comment: 10 pages, 5 figures, 2 tables, accepted for publication in A&
Assessment of fine scale population genetic diversity and regeneration in Congo basin logged forests
In the Congo Basin most of the light-demanding timber tree species display a deficit of natural regeneration which is a major handicap for sustainable production and certification. Whilst the majority of scientists investigate abiotic and biotic factors explaining that pattern, we hypothesize that tree population density or individual spatial isolation may also affect the tree fitness through inbreeding. In this study, we integrate ecological and genetic approaches to characterize the regeneration potential of a set of priority timber species by (i) estimating pollen dispersal distances at various tree population densities, and (ii) evaluating the impact of increasing spatial isolation on mating characteristics and tree fitness. The ultimate goal is the proposal of minimum population density that prevents inbreeding consequences.
Method
This ongoing study focuses on 10 timber species (Pericopsis elata, Milicia excelsa, Baillonella toxisperma, Entandrophragma cylindricum, E. utile, E. angolense, E. candollei, Afzelia bipindensis, Erythrophleum suaveloens, Terminalia superba). The data collection was carried out in the logging concession granted to Pallisco in Cameroon.
We established two 400-ha plots, where all individuals (DBH > 10 cm) of the target species were inventoried and mapped. A sample of leave or cambium was collected for each of these individuals, as well as for seedlings to characterize patterns of gene flow using genetic tools (nuclear microsatellites). Dispersal agents were identified by direct observations and camera traps. Germination success was characterized in nursery for seeds collected on trees under an increasing isolation gradient.
Results
Main dispersal agents (wind, bat, rodent) and predators (rodent) were identified for all the species. The gene flow and germination data is still being analyzed and the main results will be presented in the poster.
Conclusion
Our data will allow characterizing the reproductive biology of a set of important timber species from the Congo basin. These information will strengthen sustainable forest management and the application of certification by adjusting harvesting norms through the use of scientifically-relevant data. In particular, we will tentatively define a maximum distance to be maintained between two adults to allow a qualitative reproduction
The Duffin-Schaeffer Conjecture with extra divergence II
This paper takes a new step in the direction of proving the Duffin-Schaeffer
Conjecture for measures arbitrarily close to Lebesgue. The main result is that
under a mild `extra divergence' hypothesis, the conjecture is true.Comment: 7 page
Compensated electron and hole pockets in an underdoped high Tc superconductor
We report quantum oscillations in the underdoped high Tc YBCO over a wide
range in magnetic field 28<B<85 T corresponding to ~12 oscillations, enabling
the Fermi surface topology to be mapped to high resolution. As earlier reported
by Sebastian et al., we find a Fermi surface comprising multiple pockets, as
revealed by the additional distinct quantum oscillation frequencies and
harmonics reported in this work. We find the originally reported broad low
frequency Fourier peak at 535 T to be clearly resolved into three separate
peaks at 460 T, 532 T and 602 T. Our increased resolution and angle-resolved
measurements identify these frequencies to originate from two similarly sized
pockets with greatly contrasting degrees of interlayer corrugation. The
spectrally dominant frequency originates from a pocket (\alpha) that is almost
ideally two-dimensional in form. In contrast, the newly resolved weaker
adjacent spectral features originate from a deeply corrugated pocket (\gamma).
On comparison with band structure, the d-wave symmetry of the interlayer
dispersion locates the minimally corrugated \alpha pocket at the 'nodal' point
where holes are located in a translational symmetry-broken scenario, and the
significantly corrugated \gamma pocket at the 'antinodal' point in the
Brillouin zone, where electrons are located in a translational symmetry-broken
scenario. Translational symmetry breaking by an SDW is suggested from the
strong suppression of Zeeman splitting for the spectrally dominant pocket,
additional evidence for which is provided from the harmonics we resolve in the
present experiments. Given the similarity in \alpha and \gamma pocket sizes,
their opposite carrier type and the previous report of a diverging effective
mass, we discuss the possibility of a secondary Fermi surface instability at
low dopings of the excitonic insulator type, associated with the
metal-insulator QCP.Comment: Expanded abstract, added two new figures to establish the enhanced
resolution of the current measurements and provide further support for
earlier reported suppression of Zeeman splitting
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