Quantum chaos in nanoelectromechanical systems

We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems (NEMS) and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate's surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian Orthogonal Ensemble (GOE) or the Gaussian Unitary Ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.Comment: 14 pages, two column

Casimir force between integrable and chaotic pistons

We have computed numerically the Casimir force between two identical pistons inside a very long cylinder, considering different shapes for the pistons. The pistons can be considered as quantum billiards, whose spectrum determines the vacuum force. The smooth part of the spectrum fixes the force at short distances, and depends only on geometric quantities like the area or perimeter of the piston. However, correcting terms to the force, coming from the oscillating part of the spectrum which is related to the classical dynamics of the billiard, are qualitatively different for classically integrable or chaotic systems. We have performed a detailed numerical analysis of the corresponding Casimir force for pistons with regular and chaotic classical dynamics. For a family of stadium billiards, we have found that the correcting part of the Casimir force presents a sudden change in the transition from regular to chaotic geometries.Comment: 13 pages, 10 figure

Anomalous quantum chaotic behavior in nanoelectromechanical structures

It is predicted that for sufficiently strong electron-phonon coupling an anomalous quantum chaotic behavior develops in certain types of suspended electro-mechanical nanostructures, here comprised by a thin cylindrical quantum dot (billiard) on a suspended rectangular dielectric plate. The deformation potential and piezoelectric interactions are considered. As a result of the electron-phonon coupling between the two systems the spectral statistics of the electro-mechanic eigenenergies exhibit an anomalous behavior. If the center of the quantum dot is located at one of the symmetry axes of the rectangular plate, the energy level distributions correspond to the Gaussian Orthogonal Ensemble (GOE), otherwise they belong to the Gaussian Unitary Ensemble (GUE), even though the system is time-reversal invariant.Comment: 4 pages, pdf forma

Quantity and quality of empathic responding by autistic and non-autistic adolescent girls and boys

Empathy evokes support for the person in distress, and thus strengthening social cohesion. The question is to what extent empathic reactions can be observed in autistic adolescents and autistic girls in particular, since there is evidence that they have better social skills than boys, which might hinder their recognition as autistic. We examined 193 adolescents (autistic/non-autistic boys/girls) during an in vivo task in which the experimenter hurt herself. In line with our predictions, no group or gender differences appeared related to their attention for the event; yet autistic girls and boys showed less visible emotional arousal, indicative of less affective empathy. Autistic girls and boys reacted by comforting the experimenter equally often as their non-autistic peers, but autistic boys seemed to address the problem more often than any other group; while girls (autistic and non-autistic) more often addressed the emotion of the person in need. Our findings highlight that empathic behaviour – to some extent – seems similar between autistic and non-autistic boys and girls. However, differences exist, in terms of expressed emotional arousal and gender-specific comforting styles. Autistic girls’ higher levels of emotion-focused comforting could be explained by well-developed social skills, camouflaging, or emotional investment in relationships with others

A new test specimen for the determination of the field of view of small-area X-ray photoelectron spectrometers

Small-area/spot photoelectron spectroscopy (SAXPS) is a powerful tool for the investigation of small surface features like microstructures of electronic devices, sensors or other functional surfaces, and so forth. For evaluating the quality of such microstructures, it is often crucial to know whether a small signal in a spectrum is an unwanted contamination of the field of view (FoV), defined by the instrument settings, or it originated from outside. To address this issue, the d80/20 parameter of a line scan across a chemical edge is often used. However, the typical d80/20 parameter does not give information on contributions from the long tails of the X-ray beam intensity distribution or the electron-optical system as defined by apertures. In the VAMAS TWA2 A22 project “Applying planar, patterned, multi-metallic samples to assess the impact of analysis area in surface-chemical analysis,” new test specimen was developed and tested. The here presented testing material consists of a silicon wafer substrate with an Au-film and embedded Cr circular and square spots with decreasing dimensions from 200 μm down to 5 μm. The spot sizes are traceable to the length unit due to size measurements with a metrological SEM. For the evaluation of the FoV, we determined the Au4f intensities measured with the center of the FoV aligned with the center of the spot and normalized to the Au4f intensity determined on the Au-film. With this test specimen, it was possible to characterize, as an example, the FoV of a Kratos AXIS Ultra DLD XPS instrument

Summary of ISO/TC 201 International Standard ISO 18516:2019 Surface chemical analysis—Determination of lateral resolution and sharpness in beam-based methods with a range from nanometres to micrometres and its implementation for imaging laboratory X-ray photoelectron spectrometers (XPS)

ISO 18516:2019 Surface chemical analysis—Determination of lateral resolution and sharpness in beam-based methods with a range from nanometres to micrometres revises ISO 18516:2006 Surface chemical analysis—Auger electron spectroscopy and X-ray photoelectron spectroscopy—Determination of lateral resolution. It implements three different methods delivering parameters useful to express the lateral resolution: (1) the straight edge method, (2) the narrow line method and (3) the grating method. The theoretical background of these methods is introduced in ISO/TR 19319:2013 Surface chemical analysis—Fundamental approaches to determination of lateral resolution and sharpness in beam-based methods. The revised International Standard ISO 18516 delivers standardized procedures for the determination of the (1) effective lateral resolution by imaging of square-wave gratings, the (2) lateral resolution expressed as the parameter D12–88 characterizing the steepness of the sigmoidal edge spread function (ESF) determined by imaging a straight edge and (3) the lateral resolution expressed as the full width of half maximum of the line spread function (LSF), wLSF, determined by imaging a narrow line. The last method also delivers information on the shape of the LSF, which characterizes an individual imaging instrument. Finally, the implementation of all three standardized methods in the field of imaging laboratory X-ray photoelectron spectroscopy (XPS) is shortly presented. This part of the letter is based on the use of a new test sample developed at ETH Zurich, Switzerland. This test sample displays a micrometre scaled pattern motivated by the resolving power of recent imaging XPS instruments

Semiclassical coherent state propagator for systems with spin

We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin-orbit interactions and the Jaynes-Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit. As special cases we consider separable systems, the limit of very large spins and the case of spin 1/2.Comment: 19 pages, no figure

Effects of comorbidity on Tourette's tic severity and quality of life

Objective The aim of this study is to gain more insight in the differential contributions of anxiety, depression and obsessive-compulsive (OC) symptom severity to quality of life (QoL) and tic severity in adults with Tourette Disorder (TD). Methods Self-reported OC symptom, anxiety and depression severity measures were used to investigate their predictive value on QoL and Tic severity in adult TD patients (N = 187), using correlation, regression, and mediation analyses. Results Tic severity has no effect on QoL. Depression severity directly reduces QoL, whereas anxiety and OC symptom severity have an indirect effect on QoL, mediated by depression severity. OC symptom severity directly affects tic severity, whereas depression and anxiety severity do not have a direct effect on tic or OC severity. Finally, anxiety severity indirectly impacts tic severity, with OC symptom severity functioning as a mediator. Conclusion In line with and extending previous studies, these findings indicate that OC symptom severity directly influences tic symptom severity whereas depression severity directly influences QoL in TD. Results imply that to improve QoL in TD patients, treatment should primarily focus on diminishing OC and depressive symptom severity rather than focusing on tic reduction

Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

Casimir force on amplifying bodies

Based on a unified approach to macroscopic QED that allows for the inclusion of amplification in a limited space and frequency range, we study the Casimir force as a Lorentz force on an arbitrary partially amplifying system of linearly locally responding (isotropic) magnetoelectric bodies. We demonstrate that the force on a weakly polarisable/magnetisable amplifying object in the presence of a purely absorbing environment can be expressed as a sum over the Casimir--Polder forces on the excited atoms inside the body. As an example, the resonant force between a plate consisting of a dilute gas of excited atoms and a perfect mirror is calculated