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 $\beta=0.368$, $\gamma=1.382$, and $\delta=4.787$. The anomaly in the specific heat associated with the magnetic ordering can be well described by the critical exponent $\alpha=-0.133$. 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