On the concepts of radial and angular kinetic energies

We consider a general central-field system in D dimensions and show that the division of the kinetic energy into radial and angular parts proceeds differently in the wavefunction picture and the Weyl-Wigner phase-space picture. Thus, the radial and angular kinetic energies are different quantities in the two pictures, containing different physical information, but the relation between them is well defined. We discuss this relation and illustrate its nature by examples referring to a free particle and to a ground-state hydrogen atom.Comment: 10 pages, 2 figures, accepted by Phys. Rev.

Extreme points of the set of density matrices with positive partial transpose

We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for finding such extreme points and illustrate this by some examples.Comment: 4 pages, 2 figure

Hydrogen atom in phase space. The Kirkwood-Rihaczek representation

We present a phase-space representation of the hydrogen atom using the Kirkwood-Rikaczek distribution function. This distribution allows us to obtain analytical results, which is quite unique because an exact analytical form of the Wigner functions corresponding to the atom states is not known. We show how the Kirkwood-Rihaczek distribution reflects properties of the hydrogen atom wave functions in position and momentum representations.Comment: 5 pages (and 5 figures

Segregation, precipitation, and \alpha-\alpha' phase separation in Fe-Cr alloys: a multi-scale modelling approach

Segregation, precipitation, and phase separation in Fe-Cr systems is investigated. Monte Carlo simulations using semiempirical interatomic potential, first-principles total energy calculations, and experimental spectroscopy are used. In order to obtain a general picture of the relation of the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and interface regions several complementary methods has to be used. Using Exact Muffin-Tin Orbitals method the effective chemical potential as a function of Cr content (0-15 at.% Cr) is calculated for a surface, second atomic layer and bulk. At ~10 at.% Cr in the alloy the reversal of the driving force of a Cr atom to occupy either bulk or surface sites is obtained. The Cr containing surfaces are expected when the Cr content exceeds ~10 at.%. The second atomic layer forms about 0.3 eV barrier for the migration of Cr atoms between bulk and surface atomic layer. To get information on Fe-Cr in larger scales we use semiempirical methods. Using combined Monte Carlo molecular dynamics simulations, based on semiempirical potential, the precipitation of Cr into isolated pockets in bulk Fe-Cr and the upper limit of the solubility of Cr into Fe layers in Fe/Cr layer system is studied. The theoretical predictions are tested using spectroscopic measurements. Hard X-ray photoelectron spectroscopy and Auger electron spectroscopy investigations were carried out to explore Cr segregation and precipitation in Fe/Cr double layer and Fe_0.95Cr_0.05 and Fe_0.85Cr_0.15 alloys. Initial oxidation of Fe-Cr was investigated experimentally at 10^-8 Torr pressure of the spectrometers showing intense Cr_2O_3 signal. Cr segregation and the formation of Cr rich precipitates were traced by analysing the experimental spectral intensities with respect to annealing time, Cr content, and kinetic energy of the exited electron.Comment: 16 pages, 14 figures, 52 reference

Differential gaze behavior towards sexually preferred and non-preferred human figures

The gaze pattern associated with image exploration is a sensitive index of our attention, motivation and preference. To examine whether an individual’s gaze behavior can reflect his/her sexual interest, we compared gaze patterns of young heterosexual men and women (M = 19.94 years, SD = 1.05) while viewing photos of plain-clothed male and female figures aged from birth to sixty years old. Our analysis revealed a clear gender difference in viewing sexually preferred figure images. Men displayed a distinctive gaze pattern only when viewing twenty-year-old female images, with more fixations and longer viewing time dedicated to the upper body and waist-hip region. Women also directed more attention at the upper body on female images in comparison to male images, but this difference was not age-specific. Analysis of local image salience revealed that observers’ eye-scanning strategies could not be accounted for by low-level processes, such as analyzing local image contrast and structure, but were associated with attractiveness judgments. The results suggest that the difference in cognitive processing of sexually preferred and non-preferred figures can be manifested in gaze patterns associated with figure viewing. Thus, eye-tracking holds promise as a potential sensitive measure for sexual preference, particularly in men

Measuring responses of harbour seals to potential aversive acoustic mitigation signals using controlled exposure behavioural response studies

This work was funded by Scottish Government's Marine Mammal Scientific Support Research Programme MMSS/001/11 and UK's Natural Environment Research Council (NERC), and Department for Environment Food and Rural Affairs (NE/J004251/1) and NERC (National Capability SMRU1001).1.  Some anthropogenic activities pose acute risks for marine species. For example, pile driving could damage the hearing of marine mammals while underwater explosions can also result in physical damage or death. Effective mitigation is required to reduce these risks, but the exclusion zones specified in regulations can extend over hundreds or thousands of metres and seals pose particular problems because they are difficult to detect at sea. 2.  Aversive sound mitigation aims to exclude animals from high‐risk areas before dangerous activities take place by broadcasting specific acoustic signals. Field research is needed to identify signals that might be effective in eliciting short‐term avoidance by marine species such as harbour seals (Phoca vitulina). A series of controlled‐exposure experiments (CEEs) were undertaken to measure seal movements in response to acoustic deterrent devices (ADD) and predator calls, and to assess the effectiveness of candidate signals for aversive sound mitigation. 3.  Seals were fitted with UHF/GPS transmitters providing continuous high‐resolution tracks and real‐time transmissions of their locations. A tracking/playback vessel located seals at sea and transmitted either ADD signals or orca (Orcinus orca) calls over a range of distances while seals were foraging or moving between sites. Behaviour before, during and after exposure was analysed to assess responses. 4.  One‐hundred and ten CEEs were assessed as being of at least ‘adequate’ quality. Of the 71 adequate trials with the Lofitech ADD, all 38 at ranges of <1 km (predicted received level 134.6 dB RMS re 1 μPa) elicited a response. The maximum response range was 3123 m (predicted RL: 111 dB RMS re 1 μPa). However, the responses observed did not always result in substantial movements away from the source, especially for seals that were travelling at the time of the exposures. More work is needed to better understand how exposure risks would be reduced in different scenarios. 5.  The mean net speed of horizontal movements for seals responding to aversive sounds (1.15 m s−1) was only 7% higher than their mean travel speed. 6.  Responses to broadcasts of orca calls were highly variable. 7.  The results suggest that signals similar to those generated by a Lofitech ADD could be used to reduce risks to harbour seals from pile driving and underwater explosions in coastal waters. More work will be needed to develop systems that match the requirements of industry and regulators and to explore whether these results can be generalized to offshore waters and to other phocids.PostprintPeer reviewe

Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations

In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and Kohatsu-Higa (2003). Efficient path-generation algorithms, such as Linear Transformation and Principal Component Analysis, exhibit a high computational cost in a market with time-dependent volatilities. We present a new and fast Cholesky algorithm for block matrices that makes the Linear Transformation even more convenient. Moreover, we propose a new-path generation technique based on a Kronecker Product Approximation. This construction returns the same accuracy of the Linear Transformation used for the computation of the deltas and the prices in the case of correlated asset returns while requiring a lower computational time. All these techniques can be easily employed for stochastic volatility models based on the mixture of multi-dimensional dynamics introduced by Brigo et al. (2004).Comment: 16 page

A New Non-Perturbative Approach to Quantum Theory in Curved Spacetime Using the Wigner Function

A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been proposed, and does not imply any approximations. It is a completely exact equation, fully equivalent to the Heisenberg equations of motion. The approach makes different approximation schemes possible, e.g. it is possible to perform a systematic calculation of the quantum effects order by order. An iterative scheme for this is also proposed. The method is illustrated with some simple examples and applications. A calculation of the trace of the renormalised energy-momentum tensor is done, and the conformal anomaly is thereby related to non-conservation of a current in d=2 dimensions and a relationship between a vector and an axial-vector current in d=4 dimensions. The corresponding ``hydrodynamic equations'' governing the evolution of macroscopic quantities are derived by taking appropriate moments. The emphasis is put on the spin-1/2 case, but it is shown how to extend to arbitrary spins. Gravity is treated first in the Palatini formalism, which is not very tractable, and then more successfully in the Ashtekar formalism, where the constraints lead to infinite order differential equations for the Wigner functions.Comment: LaTeX2e (uses amssymb), 36 page

Measurement of Spin Correlation Parameters ANN_{NN}, ASS_{SS}, and A_SL{SL} at 2.1 GeV in Proton-Proton Elastic Scattering

At the Cooler Synchrotron COSY/J\"ulich spin correlation parameters in elastic proton-proton (pp) scattering have been measured with a 2.11 GeV polarized proton beam and a polarized hydrogen atomic beam target. We report results for A$_{NN}$, A$_{SS}$, and A_${SL}$ for c.m. scattering angles between 30$^o$ and 90$^o$. Our data on A$_{SS}$ -- the first measurement of this observable above 800 MeV -- clearly disagrees with predictions of available of pp scattering phase shift solutions while A$_{NN}$ and A_${SL}$ are reproduced reasonably well. We show that in the direct reconstruction of the scattering amplitudes from the body of available pp elastic scattering data at 2.1 GeV the number of possible solutions is considerably reduced.Comment: 4 pages, 4 figure