10 research outputs found
Closed-orbit theory for spatial density oscillations
We briefly review a recently developed semiclassical theory for quantum
oscillations in the spatial (particle and kinetic energy) densities of finite
fermion systems and present some examples of its results. We then discuss the
inclusion of correlations (finite temperatures, pairing correlations) in the
semiclassical theory.Comment: LaTeX, 10pp., 2 figure
Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction
We investigate the many-body level density of gas of non-interacting
fermions. We determine its behavior as a function of the temperature and the
number of particles. As the temperature increases, and beyond the usual
Sommerfeld expansion that describes the degenerate gas behavior, corrections
due to a finite number of particles lead to Gumbel-like contributions. We
discuss connections with the partition problem in number theory, extreme value
statistics as well as differences with respect to the Bose gas.Comment: 5 pages, 1 figure, one figure added, accepted for publication in
Phys. Rev.
On the ground--state energy of finite Fermi systems
We study the ground--state shell correction energy of a fermionic gas in a
mean--field approximation.
Considering the particular case of 3D harmonic trapping potentials, we show
the rich variety of different behaviors (erratic, regular, supershells) that
appear when the number--theoretic properties of the frequency ratios are
varied. For self--bound systems, where the shape of the trapping potential is
determined by energy minimization, we obtain accurate analytic formulas for the
deformation and the shell correction energy as a function of the particle
number . Special attention is devoted to the average of the shell correction
energy. We explain why in self--bound systems it is a decreasing (and negative)
function of .Comment: 10 pages, 5 figures, 2 table
Level density of a Fermi gas: average growth and fluctuations
We compute the level density of a two--component Fermi gas as a function of
the number of particles, angular momentum and excitation energy. The result
includes smooth low--energy corrections to the leading Bethe term (connected to
a generalization of the partition problem and Hardy--Ramanujan formula) plus
oscillatory corrections that describe shell effects. When applied to nuclear
level densities, the theory provides a unified formulation valid from
low--lying states up to levels entering the continuum. The comparison with
experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur
Closed orbits and spatial density oscillations in the circular billiard
We present a case study for the semiclassical calculation of the oscillations
in the particle and kinetic-energy densities for the two-dimensional circular
billiard. For this system, we can give a complete classification of all closed
periodic and non-periodic orbits. We discuss their bifurcations under variation
of the starting point r and derive analytical expressions for their properties
such as actions, stability determinants, momentum mismatches and Morse indices.
We present semiclassical calculations of the spatial density oscillations using
a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev.
Lett. 100 200408], employing standard uniform approximations from perturbation
and bifurcation theory, and test the convergence of the closed-orbit sum.Comment: LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final
version (v3) to be published in J. Phys.
Level density of a Fermi gas: average growth and fluctuations
4 pages, 1 figureWe compute the level density of a two--component Fermi gas as a function of the number of particles, angular momentum and excitation energy. The result includes smooth low--energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy--Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low--lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results
Closed-orbit theory of spatial density oscillations in finite fermion systems
We investigate the particle and kinetic-energy densities for non-interacting fermions confined in a local potential. Using Gutzwiller's semi-classical Green function, we describe the oscillating parts of the densities in terms of closed non-periodic classical orbits. We derive universal relations between the oscillating parts of the densities for potentials with spherical symmetry in arbitrary dimensions, and a ``local virial theorem'' valid also for arbitrary non-integrable potentials. We give simple analytical formulae for the density oscillations in a one-dimensional potential
Transcriptome database resource and gene expression atlas for the rose
International audienceBackground: For centuries roses have been selected based on a number of traits. Little information exists on the genetic and molecular basis that contributes to these traits, mainly because information on expressed genes for this economically important ornamental plant is scarce. Results: Here, we used a combination of Illumina and 454 sequencing technologies to generate information on Rosa sp. transcripts using RNA from various tissues and in response to biotic and abiotic stresses. A total of 80714 transcript clusters were identified and 76611 peptides have been predicted among which 20997 have been clustered into 13900 protein families. BLASTp hits in closely related Rosaceae species revealed that about half of the predicted peptides in the strawberry and peach genomes have orthologs in Rosa dataset. Digital expression was obtained using RNA samples from organs at different development stages and under different stress conditions. qPCR validated the digital expression data for a selection of 23 genes with high or low expression levels. Comparative gene expression analyses between the different tissues and organs allowed the identification of clusters that are highly enriched in given tissues or under particular conditions, demonstrating the usefulness of the digital gene expression analysis. A web interface ROSAseq was created that allows data interrogation by BLAST, subsequent analysis of DNA clusters and access to thorough transcript annotation including best BLAST matches on Fragaria vesca, Prunus persica and Arabidopsis. The rose peptides dataset was used to create the ROSAcyc resource pathway database that allows access to the putative genes and enzymatic pathways. Conclusions: The study provides useful information on Rosa expressed genes, with thorough annotation and an overview of expression patterns for transcripts with good accuracy