Spherical-box approach for resonances in presence of Coulomb interaction

The spherical-box approach is extended to calculate the resonance parameters and the real part of the wave function for single particle resonances in a potential containing the long-range Coulomb interaction. A model potential is taken to demonstrate the ability and accuracy of this approach. The calculated resonance parameters are compared with available results from other methods. It is shown that in the presence of the Coulomb interaction, the spherical-box approach works well for not so broad resonances. In particular, for very narrow resonances, the present method gives resonance parameters in a very high precision.Comment: 10 pages, 5 EPS figures; to be published in J. Phys.

Conceptual Foundations for a Service-oriented Knowledge and Learning Architecture: Supporting Content, Process and Ontology Maturing

Abstract: The knowledge maturing model views learning activities as embedded into, interwoven with, and even indistinguishable from everyday work processes. Learning is understood as an inherently social and collaborative activity. The Knowledge Maturing Process Model structures this process into five phases: expressing ideas, distributing in communities, formalizing, ad-hoc learning and standardization. It is applicable not only for content but also to process knowledge and semantics. In the MATURE IP two toolsets will be develop that support the maturing process: a personal learning environment and an organisation learning environment integrating the levels of individuals, communities and organisation. The development is guided by the SER theory of seeding, evolutionary growth and reseeding and is based on generally applicable maturing services

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

Pseudo-time Schroedinger equation with absorbing potential for quantum scattering calculations

The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time correlation function. An efficient formula for Green's function matrix elements is also derived. Since the exact propagation up to time 2t can be done with only t real matrix-vector products, this gives an unprecedently efficient scheme for accurate calculations of quantum spectra for possibly very large systems.Comment: 9 page

Delta-Function Potential with a Complex Coupling

We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at E=-z^2/4. For \Re(z)<0, H has an eigenvalue at E=-z^2/4. For the case that \Re(z)>0, H has a real, positive, continuous spectrum that is free from spectral singularities. For this latter case, we construct an associated biorthonormal system and use it to perform a perturbative calculation of a positive-definite inner product that renders H self-adjoint. This allows us to address the intriguing question of the nonlocal aspects of the equivalent Hermitian Hamiltonian for the system. In particular, we compute the energy expectation values for various Gaussian wave packets to show that the non-Hermiticity effect diminishes rapidly outside an effective interaction region.Comment: Published version, 14 pages, 2 figure

The dynamical Green's function and an exact optical potential for electron-molecule scattering including nuclear dynamics

We derive a rigorous optical potential for electron-molecule scattering including the effects of nuclear dynamics by extending the common many-body Green's function approach to optical potentials beyond the fixed-nuclei limit for molecular targets. Our formalism treats the projectile electron and the nuclear motion of the target molecule on the same footing whereby the dynamical optical potential rigorously accounts for the complex many-body nature of the scattering target. One central result of the present work is that the common fixed-nuclei optical potential is a valid adiabatic approximation to the dynamical optical potential even when projectile and nuclear motion are (nonadiabatically) coupled as long as the scattering energy is well below the electronic excitation thresholds of the target. For extremely low projectile velocities, however, when the cross sections are most sensitive to the scattering potential, we expect the influences of the nuclear dynamics on the optical potential to become relevant. For these cases, a systematic way to improve the adiabatic approximation to the dynamical optical potential is presented that yields non-local operators with respect to the nuclear coordinates.Comment: 22 pages, no figures, accepted for publ., Phys. Rev.

Fifteen species in one: deciphering the Brachionus plicatilis species complex (Rotifera, Monogononta) through DNA taxonomy

Understanding patterns and processes in biological diversity is a critical task given current and rapid environmental change. Such knowledge is even more essential when the taxa under consideration are important ecological and evolutionary models. One of these cases is the monogonont rotifer cryptic species complex Brachionus plicatilis, which is by far the most extensively studied group of rotifers, is widely used in aquaculture, and is known to host a large amount of unresolved diversity. Here we collate a dataset of previously available and newly generated sequences of COI and ITS1 for 1273 isolates of the B. plicatilis complex and apply three approaches in DNA taxonomy (i.e. ABGD, PTP, and GMYC) to identify and provide support for the existence of 15 species within the complex. We used these results to explore phylogenetic signal in morphometric and ecological traits, and to understand correlation among the traits using phylogenetic comparative models. Our results support niche conservatism for some traits (e.g. body length) and phylogenetic plasticity for others (e.g. genome size)

Sex Differences in the Brain: A Whole Body Perspective

Most writing on sexual differentiation of the mammalian brain (including our own) considers just two organs: the gonads and the brain. This perspective, which leaves out all other body parts, misleads us in several ways. First, there is accumulating evidence that all organs are sexually differentiated, and that sex differences in peripheral organs affect the brain. We demonstrate this by reviewing examples involving sex differences in muscles, adipose tissue, the liver, immune system, gut, kidneys, bladder, and placenta that affect the nervous system and behavior. The second consequence of ignoring other organs when considering neural sex differences is that we are likely to miss the fact that some brain sex differences develop to compensate for differences in the internal environment (i.e., because male and female brains operate in different bodies, sex differences are required to make output/function more similar in the two sexes). We also consider evidence that sex differences in sensory systems cause male and female brains to perceive different information about the world; the two sexes are also perceived by the world differently and therefore exposed to differences in experience via treatment by others. Although the topic of sex differences in the brain is often seen as much more emotionally charged than studies of sex differences in other organs, the dichotomy is largely false. By putting the brain firmly back in the body, sex differences in the brain are predictable and can be more completely understood

Characteristics of Early-Onset vs Late-Onset Colorectal Cancer: A Review.

The incidence of early-onset colorectal cancer (younger than 50 years) is rising globally, the reasons for which are unclear. It appears to represent a unique disease process with different clinical, pathological, and molecular characteristics compared with late-onset colorectal cancer. Data on oncological outcomes are limited, and sensitivity to conventional neoadjuvant and adjuvant therapy regimens appear to be unknown. The purpose of this review is to summarize the available literature on early-onset colorectal cancer. Within the next decade, it is estimated that 1 in 10 colon cancers and 1 in 4 rectal cancers will be diagnosed in adults younger than 50 years. Potential risk factors include a Westernized diet, obesity, antibiotic usage, and alterations in the gut microbiome. Although genetic predisposition plays a role, most cases are sporadic. The full spectrum of germline and somatic sequence variations implicated remains unknown. Younger patients typically present with descending colonic or rectal cancer, advanced disease stage, and unfavorable histopathological features. Despite being more likely to receive neoadjuvant and adjuvant therapy, patients with early-onset disease demonstrate comparable oncological outcomes with their older counterparts. The clinicopathological features, underlying molecular profiles, and drivers of early-onset colorectal cancer differ from those of late-onset disease. Standardized, age-specific preventive, screening, diagnostic, and therapeutic strategies are required to optimize outcomes

Synthesis and Cathodoluminescence of Undoped and Cr^3^+-Doped Sodium Titanate Nanotubes and Nanoribbons

We report on the synthesis of Cr^3^+-doped sodium titanate nanotubes and nanoribbons by a hydrothermal method. The presence of dopant ions in these nanostructures was confirmed by high angle annular dark field scanning transmission electron microscopy in combination with electron energy loss spectroscopy measurements. Luminescence properties of undoped and Cr^3^+-doped sodium titanate nanotubes and nanoribbons were investigated by cathodoluminescence in the scanning electron microscope. A broad visible band in the range 1.7−2.7 eV is observed in these nanostructures. Such emission is similar to that observed in bulk anatase TiO_2 and titanate powders, and is related to TiO_6 octahedra, which is a common feature to all the samples investigated. Near-infrared emission, sometimes attributed to Ti^3^+ interstitials, is observed in bulk powders but is absent in the titanate nanotubes and nanoribbons. Incorporation of Cr^3^+ between the titanate layers of the nanostructures is revealed by the characteristic intraionic emission line at 1.791 eV. Sodium titanate nanoribbons appear to be an effective host for optically active Cr^3^+ ions, as compared with nanotubes or bulk powder