Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation

We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations where other criteria, such as the energy gap criterion or the extent of population transfer, fail. We further propose to estimate this quantum fidelity efficiently with a generalization of the dephasing representation to multiple surfaces. Two variants of the multiple-surface dephasing representation (MSDR) are introduced, in which the nuclei are propagated either with the fewest-switches surface hopping (FSSH) or with the locally mean field dynamics (LMFD). The LMFD can be interpreted as the Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used previously in the nonadiabatic semiclassical initial value representation. In addition to propagating an ensemble of classical trajectories, the MSDR requires evaluating nonadiabatic couplings and solving the Schr\"{o}dinger (or more generally, the quantum Liouville-von Neumann) equation for a single discrete degree of freedom. The MSDR can be also used to measure the importance of other terms present in the molecular Hamiltonian, such as diabatic couplings, spin-orbit couplings, or couplings to external fields, and to evaluate the accuracy of quantum dynamics with an approximate nonadiabatic Hamiltonian. The method is tested on three model problems introduced by Tully, on a two-surface model of dissociation of NaI, and a three-surface model including spin-orbit interactions. An example is presented that demonstrates the importance of often-neglected second-order nonadiabatic couplings.Comment: 14 pages, 4 figures, submitted to J. Chem. Phy

Conditional Regressive Random Forest Stereo-based Hand Depth Recovery

This paper introduces Conditional Regressive Random Forest (CRRF), a novel method that combines a closed-form Conditional Random Field (CRF), using learned weights, and a Regressive Random Forest (RRF) that employs adaptively selected expert trees. CRRF is used to estimate a depth image of hand given stereo RGB inputs. CRRF uses a novel superpixel-based regression framework that takes advantage of the smoothness of the hand’s depth surface. A RRF unary term adaptively selects different stereo-matching measures as it implicitly determines matching pixels in a coarse-to-fine manner. CRRF also includes a pair-wise term that encourages smoothness between similar adjacent superpixels. Experimental results show that CRRF can produce high quality depth maps, even using an inexpensive RGB stereo camera and produces state-of-the-art results for hand depth estimation

Quantized Census for Stereoscopic Image Matching

Current depth capturing devices show serious drawbacks in certain applications, for example ego-centric depth recovery: they are cumbersome, have a high power requirement, and do not portray high resolution at near distance. Stereo-matching techniques are a suitable alternative, but whilst the idea behind these techniques is simple it is well known that recovery of an accurate disparity map by stereo-matching requires overcoming three main problems: occluded regions causing absence of corresponding pixels; existence of noise in the image capturing sensor and inconsistent color and brightness in the captured images. We propose a modified version of the Census-Hamming cost function which allows more robust matching with an emphasis on improving performance under radiometric variations of the input images

Data-driven Recovery of Hand Depth using Conditional Regressive Random Forest on Stereo Images

Hand pose is emerging as an important interface for human-computer interaction. This paper presents a data-driven method to estimate a high-quality depth map of a hand from a stereoscopic camera input by introducing a novel superpixel based regression framework that takes advantage of the smoothness of the depth surface of the hand. To this end, we introduce Conditional Regressive Random Forest (CRRF), a method that combines a Conditional Random Field (CRF) and a Regressive Random Forest (RRF) to model the mapping from a stereo RGB image pair to a depth image. The RRF provides a unary term that adaptively selects different stereo-matching measures as it implicitly determines matching pixels in a coarse-to-fine manner. While the RRF makes depth prediction for each super-pixel independently, the CRF unifies the prediction of depth by modeling pair-wise interactions between adjacent superpixels. Experimental results show that CRRF can generate a depth image more accurately than the leading contemporary techniques using an inexpensive stereo camera

The quality of different types of child care at 10 and 18 months. A comparison between types and factors related to quality.

The quality of care offered in four different types of non-parental child care to 307 infants at 10 months old and 331 infants at 18 months old was compared and factors associated with higher quality were identified. Observed quality was lowest in nurseries at each age point, except that at 18 months they offered more learning activities. There were few differences in the observed quality of care by child-minders, grandparents and nannies, although grandparents had somewhat lower safety and health scores and offered children fewer activities. Cost was largely unrelated to quality of care except in child-minding, where higher cost was associated with higher quality. Observed ratios of children to adults had a significant impact on quality of nursery care; the more infants or toddlers each adult had to care for, the lower the quality of the care she gave them. Mothers' overall satisfaction with their child's care was positively associated with its quality for home-based care but not for nursery settings

Hand Pose Estimation Using Deep Stereovision and Markov-chain Monte Carlo

Hand pose is emerging as an important interface for human-computer interaction. The problem of hand pose estimation from passive stereo inputs has received less attention in the literature compared to active depth sensors. This paper seeks to address this gap by presenting a datadriven method to estimate a hand pose from a stereoscopic camera input, by introducing a stochastic approach to propose potential depth solutions to the observed stereo capture and evaluate these proposals using two convolutional neural networks (CNNs). The first CNN, configured in a Siamese network architecture, evaluates how consistent the proposed depth solution is to the observed stereo capture. The second CNN estimates a hand pose given the proposed depth. Unlike sequential approaches that reconstruct pose from a known depth, our method jointly optimizes the hand pose and depth estimation through Markov-chain Monte Carlo (MCMC) sampling. This way, pose estimation can correct for errors in depth estimation, and vice versa. Experimental results using an inexpensive stereo camera show that the proposed system more accurately measures pose better than competing methods

Degenerate Landau-Zener model: Exact analytical solution

The exact analytical solution of the degenerate Landau-Zener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the Morris-Shore transformation, which reduces the fully coupled system to a set of independent nondegenerate two-state systems and a set of decoupled states. Due to the divergence of the phase of the off-diagonal element of the propagator in the original Landau-Zener model, not all transition probabilities exist for infinite time duration. In general, apart from some special cases, only the transition probabilities between states within the same degenerate set exist, but not between states of different sets. An illustration is presented for the transition between the magnetic sublevels of two atomic levels with total angular momenta J=2 and 1

State-to-State Differential and Relative Integral Cross Sections for Rotationally Inelastic Scattering of H2O by Hydrogen

State-to-state differential cross sections (DCSs) for rotationally inelastic scattering of H2O by H2 have been measured at 71.2 meV (574 cm-1) and 44.8 meV (361 cm-1) collision energy using crossed molecular beams combined with velocity map imaging. A molecular beam containing variable compositions of the (J = 0, 1, 2) rotational states of hydrogen collides with a molecular beam of argon seeded with water vapor that is cooled by supersonic expansion to its lowest para or ortho rotational levels (JKaKc= 000 and 101, respectively). Angular speed distributions of fully specified rotationally excited final states are obtained using velocity map imaging. Relative integral cross sections are obtained by integrating the DCSs taken with the same experimental conditions. Experimental state-specific DCSs are compared with predictions from fully quantum scattering calculations on the most complete H2O-H2 potential energy surface. Comparison of relative total cross sections and state-specific DCSs show excellent agreement with theory in almost all detailsComment: 46 page

Counterintuitive transitions between crossing energy levels

We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the tilted energy is coupled to the other two states in a chainwise linkage pattern with constant couplings of finite duration. The probability for a counterintuitive transition is found to increase with the square of the coupling and decrease with the squares of the interaction duration, the energy splitting between the parallel energies, and the tilt (chirp) rate. Physical examples of this model can be found in coherent atomic excitation and optical shielding in cold atomic collisions

Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field

The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck’s constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution