Time evolution of non-Hermitian Hamiltonian systems

We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in addition in some cases also invariant under PT-symmetry. In particular, for the harmonic oscillator perturbed by a cubic non-Hermitian term, we evaluate explicitly various transition amplitudes, for the situation when these systems are exposed to a monochromatic linearly polarized electric field.Comment: 25 pages Latex, 1 eps figure, references adde

Attosecond electron thermalization by laser-driven electron recollision in atoms

Nonsequential multiple ionization of atoms in intense laser fields is initiated by a recollision between an electron, freed by tunneling, and its parent ion. Following recollision, the initial electron shares its energy with several bound electrons. We use a classical model based on rapid electron thermalization to interpret recent experiments. For neon, good agreement with the available data is obtained with an upper bound of 460 attoseconds for the thermalization time.Comment: 5 pages revtex and 4 figures (eps files

An exactly solvable quantum-lattice model with a tunable degree of nonlocality

An array of N subsequent Laguerre polynomials is interpreted as an eigenvector of a non-Hermitian tridiagonal Hamiltonian $H$ with real spectrum or, better said, of an exactly solvable N-site-lattice cryptohermitian Hamiltonian whose spectrum is known as equal to the set of zeros of the N-th Laguerre polynomial. The two key problems (viz., the one of the ambiguity and the one of the closed-form construction of all of the eligible inner products which make $H$ Hermitian in the respective {\em ad hoc} Hilbert spaces) are discussed. Then, for illustration, the first four simplest, $k-$parametric definitions of inner products with $k=0,k=1,k=2$ and $k=3$ are explicitly displayed. In mathematical terms these alternative inner products may be perceived as alternative Hermitian conjugations of the initial N-plet of Laguerre polynomials. In physical terms the parameter $k$ may be interpreted as a measure of the "smearing of the lattice coordinates" in the model.Comment: 35 p

Integrative mapping analysis of chicken microchromosome 16 organization

<p>Abstract</p> <p>Background</p> <p>The chicken karyotype is composed of 39 chromosome pairs, of which 9 still remain totally absent from the current genome sequence assembly, despite international efforts towards complete coverage. Some others are only very partially sequenced, amongst which microchromosome 16 (GGA16), particularly under-represented, with only 433 kb assembled for a full estimated size of 9 to 11 Mb. Besides the obvious need of full genome coverage with genetic markers for QTL (Quantitative Trait Loci) mapping and major genes identification studies, there is a major interest in the detailed study of this chromosome because it carries the two genetically independent <it>MHC </it>complexes <it>B </it>and <it>Y</it>. In addition, GGA16 carries the ribosomal RNA (<it>rRNA</it>) genes cluster, also known as the <it>NOR </it>(nucleolus organizer region). The purpose of the present study is to construct and present high resolution integrated maps of GGA16 to refine its organization and improve its coverage with genetic markers.</p> <p>Results</p> <p>We developed 79 STS (Sequence Tagged Site) markers to build a physical RH (radiation hybrid) map and 34 genetic markers to extend the genetic map of GGA16. We screened a BAC (Bacterial Artificial Chromosome) library with markers for the <it>MHC-B</it>, <it>MHC-Y </it>and <it>rRNA </it>complexes. Selected clones were used to perform high resolution FISH (Fluorescent <it>In Situ </it>Hybridization) mapping on giant meiotic lampbrush chromosomes, allowing meiotic mapping in addition to the confirmation of the order of the three clusters along the chromosome. A region with high recombination rates and containing PO41 repeated elements separates the two <it>MHC </it>complexes.</p> <p>Conclusions</p> <p>The three complementary mapping strategies used refine greatly our knowledge of chicken microchromosome 16 organisation. The characterisation of the recombination hotspots separating the two <it>MHC </it>complexes demonstrates the presence of PO41 repetitive sequences both in tandem and inverted orientation. However, this region still needs to be studied in more detail.</p

Avian W and mammalian Y chromosomes convergently retained dosage-sensitive regulators

After birds diverged from mammals, different ancestral autosomes evolved into sex chromosomes in each lineage. In birds, females are ZW and males are ZZ, but in mammals females are XX and males are XY. We sequenced the chicken W chromosome, compared its gene content with our reconstruction of the ancestral autosomes, and followed the evolutionary trajectory of ancestral W-linked genes across birds. Avian W chromosomes evolved in parallel with mammalian Y chromosomes, preserving ancestral genes through selection to maintain the dosage of broadly expressed regulators of key cellular processes. We propose that, like the human Y chromosome, the chicken W chromosome is essential for embryonic viability of the heterogametic sex. Unlike other sequenced sex chromosomes, the chicken W chromosome did not acquire and amplify genes specifically expressed in reproductive tissues. We speculate that the pressures that drive the acquisition of reproduction-related genes on sex chromosomes may be specific to the male germ line

An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher’s alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between ∼40,000 and ∼53,000, i.e. at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of ∼19,000–25,000 tree species. Continental Africa is relatively depauperate with a minimum of ∼4,500–6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa