Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media

The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

Unveiling the morphology of buried In(Ga)As nanostructures by selective wet chemical etching: From quantum dots to quantum rings

The three-dimensional morphology of In(Ga)As nanostructures embedded in a GaAs matrix is investigated by combining atomic force microscopy and removal of the GaAs cap layer by selective wet etching. This method is used to investigate how the morphology of In(Ga)As quantum dots changes upon GaAs capping and subsequent in situ etching with AsBr3. A wave function calculation based on the experimentally determined morphologies suggests that quantum dots transform into quantum rings during in situ etching. (c) 2007 American Institute of Physics.

Additions and corrections to “Terminal coalgebras in well-founded set theory”

This note is to correct certain mistaken impressions of the author's that were in the original paper, “Terminal coalgebras in well-founded set theory”, which appeared in Theoretical Computer Science 114 (1993) 299–315.

Why does relativity allow quantum tunnelling to 'take no time'?

In quantum tunnelling, what appears to be an infinitely fast barrier traversal can be explained in terms of an Aharonov-like weak measurement of the tunnelling time, in which the role of the pointer is played by the particle's own coordinate. A relativistic wave packet is shown to be reshaped through a series of subluminal shifts which together produce an anomalous 'superluminal' result.

Passing quantum correlations to qubits using any two-mode state

We draw an explicit connection between the statistical properties of an entangled two-mode continuous variable (CV) resource and the amount of entanglement that can be dynamically transferred to a pair of noninteracting two-level systems. More specifically, we rigorously reformulate entanglement-transfer process by making use of covariance matrix formalism. When the resource state is Gaussian, our method makes the approach to the transfer of quantum correlations much more flexible than in previously considered schemes and allows the straightforward inclusion of the effects of noise affecting the CV system. Moreover, the proposed method reveals that the use of de-Gaussified two-mode states is almost never advantageous for transferring entanglement with respect to the full Gaussian picture, despite the entanglement in the non-Gaussian resource can be much larger than in its Gaussian counterpart. We can thus conclude that the entanglement-transfer map overthrows the

On the required shape corrections to the local density and generalized gradient approximations to the Kohn-Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

It is well known that shape corrections have to be applied to the local-density (LDA) and generalized gradient (GGA) approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential (BP-GRAC) and the statistical averaging of (model) orbital potentials (SAOP), versus LDA and GGA potentials, in molecular response calculations of the static average polarizability alpha, the Cauchy coefficient S-4, and the static average hyperpolarizability beta. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr (BLYP), and Becke-Perdew (BP) characteristically underestimate contributions to alpha and S-4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N-2 molecule shows, that both SAOP and BP-GRAC yield reliable energies omega(i) and oscillator strengths f(i) of individual excitations, so that they reproduce well the spectral structure of alpha and S-4.(C) 2002 American Institute of Physics.

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Shape corrections to the standard approximate Kohn-Sham exchange-correlation (xc) potentials are considered with the aim to improve the excitation energies (especially for higher excitations) calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection (GRAC) of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends (LB) are seamlessly connected to the (shifted) xc potential of Becke and Perdew (BP) with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N-2, CO, CH2O, C2H4, C5NH5, C6H6, Li-2, Na-2, K-2. The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of (model) orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, which in quite a few cases approach the benchmark accuracy of 0.1 eV for the electronic spectra. Based on these results, the potential BP-GRAC-LB is proposed for molecular response calculations, which is a smooth potential and a genuine "local" density functional with an analytical representation. (C) 2001 American Institute of Physics.

True navigation in birds: from quantum physics to global migration

Birds are capable of true navigation, the ability to return to a known goal from a place they have never visited before. This is demonstrated most spectacularly during the vast migratory journeys made by these animals year after year, often between continents and occasionally global in nature. However, it remains one of the great unanswered questions in science, despite more than 50 years of research in this field. Nevertheless, the study of true navigation in birds has made significant advances in the previous 20 years, in part thanks to the integration of many disciplines outside its root in behavioural biology, to address questions of neurobiology, molecular aspects, and the physics of sensory systems and environmental cues involved in bird navigation, often involving quantum physics. However, true navigation remains a controversial field, with many conflicting and confusing results making interpretation difficult, particularly for those outside or new to the field. Unlike many general texts on migration, which avoid discussion of these issues, this review will present these conflicting findings and assess the state of the field of true navigation during bird migration.

Full characterization of the quantum linear-zigzag transition in atomic chains

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. Based on the emergent symmetry Z2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. An extensive Density Matrix Renormalization Group analysis is performed, resulting in an high-precision evaluation of the critical exponents and of the central charge of the system, confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. Quantum corrections to the classical phase diagram are computed, and the range of experimental parameters where quantum effects play a role is provided. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.