Wigner quasi-probability distribution for the infinite square well: energy eigenstates and time-dependent wave packets

We calculate the Wigner quasi-probability distribution for position and momentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite well potential, using both x- and p-space stationary-state solutions, as well as visualizing the results. We then evaluate the time-dependent Wigner distribution, P_W(x,p;t), for Gaussian wave packet solutions of this system, illustrating both the short-term semi-classical time dependence, as well as longer-term revival and fractional revival behavior and the structure during the collapsed state. This tool provides an excellent way of demonstrating the patterns of highly correlated Schrodinger-cat-like `mini-packets' which appear at fractional multiples of the exact revival time.Comment: 45 pages, 16 embedded, low-resolution .eps figures (higher resolution, publication quality figures are available from the authors); submitted to American Journal of Physic

Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects

We demonstrate that polarization-sensitive optical coherence tomography (PS-OCT) is suitable to map the stress distribution within materials in a contactless and non-destructive way. In contrast to transmission photoelasticity measurements the samples do not have to be transparent but can be of scattering nature. Denoising and analysis of fringe patterns in single PS-OCT retardation images are demonstrated to deliver the basis for a quantitative whole-field evaluation of the internal stress state of samples under investigation.Comment: 10 pages, 6 figures; Copyright: Blackwell Publishing Ltd 2008; The definitive version is available at: www.blackwell-synergy.co

Comment on 'Tumour antigen expression in hepatocellular carcinoma in a low-endemic western area'

We comment on the recent study by Sideras et al (2015) that combines tissue microarrays (TMAs) and immunohistochemistry to investigate the expression pattern of 15 antigens belonging to different categories, including cancer-testis antigens and oncofetal proteins in hepatocellular carcinoma (HCC). Because current therapies for HCC are far from ideal (Ilan, 2014) and immunotherapy has been suggested as a potential therapeutic option, the Authors aimed at identifying a panel of biologically relevant tumour antigens with broad expression in a western European population of HCC patients and specific expression in the tumour tissue with no, or little, expression in surrounding non- tumoral tissue (Sideras et al., 2015)

Bose-Einstein condensates on tilted lattices: coherent, chaotic and subdiffusive dynamics

The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation. If the static field is varied the system shows a plethora of dynamical phenomena. In the strong field limit we demonstrate the existence of (almost) non-spreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so called quantum carpets). With decreasing field, the dynamics becomes irregular, however, still confined in configuration space. For even weaker fields we find sub-diffusive dynamics with a wave-packet width spreading as $t^{1/4}$.Comment: 4 pages, 5 figure

Exact results for `bouncing' Gaussian wave packets

We consider time-dependent Gaussian wave packet solutions of the Schrodinger equation (with arbitrary initial central position, x_0, and momentum, p_0, for an otherwise free-particle, but with an infinite wall at x=0, so-called bouncing wave packets. We show how difference or mirror solutions of the form psi(x,t)-psi(-x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate _t explicitly which illustrates how the free-particle kinetic (and hence total) energy is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, _t, and momentum, _t, and their relation to the impulsive force during the `collision' with the wall. Finally, the x_0,p_0 --> 0 limit is shown to reduce to a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands on the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form.Comment: 14 pages, 1 embedded .eps figur

Superrevivals in the quantum dynamics of a particle confined in a finite square well potential

We examine the revival features in wave packet dynamics of a particle confined in a finite square well potential. The possibility of tunneling modifies the revival pattern as compared to an infinite square well potential. We study the dependence of the revival times on the depth of the square well and predict the existence of superrevivals. The nature of these superrevivals is compared with similar features seen in the dynamics of wavepackets in an anharmonic oscillator potential.Comment: 8 pages in Latex two-column format with 5 figures (eps). To appear in Physical Review

Self-interference of a single Bose-Einstein condensate due to boundary effects

A simple model wavefunction, consisting of a linear combination of two free-particle Gaussians, describes many of the observed features seen in the interactions of two isolated Bose-Einstein condensates as they expand, overlap, and interfere. We show that a simple extension of this idea can be used to predict the qualitative time-development of a single expanding BEC condensate produced near an infinite wall boundary, giving similar interference phenomena. We also briefly discuss other possible time-dependent behaviors of single BEC condensates in restricted geometries,such as wave packet revivals.Comment: 8 pages, no figures, to appear in Physica Script

Late-preterm birth, maternal symptomatology, and infant negativity

The present study examined infant negativity and maternal symptomatology by term status in a predominately low-income, rural sample of 132 infants (66 late-preterm) and their mothers. Late-preterm and term infants were group-matched by race, income, and maternal age. Maternal depression and anxiety symptoms were measured with the Brief Symptom Inventory 18 (BSI-18) when infants were 2 and 6 months of age. Also at 6 months, infant negativity was assessed by global observer ratings, maternal ratings, and microanalytic behavioral coding of fear and frustration. Results indicate that after controlling for infant age, late-preterm status predicted higher ratings of infant negativity by mothers, but not by global observers or microanalytic coding, despite a positive association in negativity across the three measures. Further, mothers of late-preterm infants reported more elevated and chronic co-morbid symptoms of depression and anxiety, which in turn, was related to concurrent maternal ratings of their infant’s negativity. Mothers response to late-preterm birth and partiality in the assessment of their infant’s temperament is discussed

Unravelling quantum carpets: a travelling wave approach

Quantum carpets are generic spacetime patterns formed in the probability distributions P(x,t) of one-dimensional quantum particles, first discovered in 1995. For the case of an infinite square well potential, these patterns are shown to have a detailed quantitative explanation in terms of a travelling-wave decomposition of P(x,t). Each wave directly yields the time-averaged structure of P(x,t) along the (quantised)spacetime direction in which the wave propagates. The decomposition leads to new predictions of locations, widths depths and shapes of carpet structures, and results are also applicable to light diffracted by a periodic grating and to the quantum rotator. A simple connection between the waves and the Wigner function of the initial state of the particle is demonstrated, and some results for more general potentials are given.Comment: Latex, 26 pages + 6 figures, submitted to J. Phys. A (connections with prior literature clarified