We study the analytically solvable Ising model of a single qubit system coupled to a spin bath. The purpose of this study is to analyze and elucidate the performance of Markovian and non-Markovian master equations describing the dynamics of the system qubit, in comparison to the exact solution. We find that the time-convolutionless master equation performs particularly well up to fourth order in the system-bath coupling constant, in comparison to the Nakajima-Zwanzig master equation. Markovian approaches fare poorly due to the infinite bath correlation time in this model. A recently proposed post-Markovian master equation performs comparably to the time-convolutionless master equation for a properly chosen memory kernel, and outperforms all the approximation methods considered here at long times. Our findings shed light on the applicability of master equations to the description of reduced system dynamics in the presence of spin-baths.

The Abel transform is a mathematical operation that transforms a cylindrically symmetric three-dimensional (3D) object into its two-dimensional (2D) projection. The inverse Abel transform reconstructs the 3D object from the 2D projection. Abel transforms have wide application across numerous fields of science, especially chemical physics, astronomy, and the study of laser-plasma plumes. Consequently, many numerical methods for the Abel transform have been developed, which makes it challenging to select the ideal method for a specific application. In this work eight transform methods have been incorporated into a single, open-source Python software package (PyAbel) to provide a direct comparison of the capabilities, advantages, and relative computational efficiency of each transform method. Most of the tested methods provide similar, high-quality results. However, the computational efficiency varies across several orders of magnitude. By optimizing the algorithms, we find that some transform methods are sufficiently fast to transform 1-megapixel images at more than 100 frames per second on a desktop personal computer. In addition, we demonstrate the transform of gigapixel images. a) danhickstein@gmail.com, Questions and comments regarding PyAbel may be posted to: http://github.com/PyAbel/PyAbel

The dissociation of the hydroxymethyl radical, CH(2)OH, and its isotopolog, CD(2)OH, following excitation in the 4ν(1) region (OH stretch overtone, near 13,600 cm(-1)) was studied using sliced velocity map imaging. A new vibrational band near 13,660 cm(-1) arising from interaction with the antisymmetric CH stretch was discovered for CH(2)OH. In CD(2)OH dissociation, D atom products (correlated with CHDO) were detected, providing the first experimental evidence of isomerization in the CH(2)OH ↔ CH(3)O (CD(2)OH ↔ CHD(2)O) system. Analysis of the H (D) fragment kinetic energy distributions shows that the rovibrational state distributions in the formaldehyde cofragments are different for the OH bond fission and isomerization pathways. Isomerization is responsible for 10%-30% of dissociation events in all studied cases, and its contribution depends on the excited vibrational level of the radical. Accurate dissociation energies were determined: D(0)(CH(2)OH → CH(2)O + H) = 10,160 ± 70 cm(-1), D(0)(CD(2)OH → CD(2)O + H) = 10,135 ± 70 cm(-1), D(0)(CD(2)OH → CHDO + D) = 10,760 ± 60 cm(-1).

Experimental observations of D fragments from the predissociation of rovibrationally excited partially deuterated 2-hydroxyethyl radicals, CD(2)CD(2)OH, are reported, and possible dissociation channels are analyzed by theory. The radicals are produced by photolysis of 2-bromoethanol at 202-215 nm, and some of them have sufficient internal energy to predissociate. D fragments are detected by 1 + 1' REMPI and their TOF distributions are determined. They can be associated with vinyl alcohol and/or acetaldehyde cofragments. From analysis of the maximum velocities and kinetic energies of the observed D fragments it is concluded that they originate from the decomposition of CD(2)CD(2)OH, but the experimental resolution is insufficient to distinguish between the two possible channels leading to D products. Theoretical analysis and RRKM calculations of microcanonical dissociation rates and branching ratios for the range of available excess energies (up to 5000-8000 cm(-1) above the OH + C(2)D(4) threshold) indicate that the D-producing channels are minor (about 1%) compared to the predominant OH + C(2)D(4) channel, and the branching ratio for D production is more favorable when the reactant radicals have low rotational energy. The vinyl alcohol channel is strongly favored over the acetaldehyde channel at all excess energies, except near the threshold of these channels.

Time-sliced velocity map imaging (SVMI), a high-resolution method for measuring kinetic energy distributions of products in scattering and photodissociation reactions, is challenging to implement for atomic hydrogen products. We describe an ion optics design aimed at achieving SVMI of H fragments in a broad range of kinetic energies (KE), from a fraction of an electronvolt to a few electronvolts. In order to enable consistently thin slicing for any imaged KE range, an additional electrostatic lens is introduced in the drift region for radial magnification control without affecting temporal stretching of the ion cloud. Time slices of ∼5 ns out of a cloud stretched to ⩾50 ns are used. An accelerator region with variable dimensions (using multiple electrodes) is employed for better optimization of radial and temporal space focusing characteristics at each magnification level. The implemented system was successfully tested by recording images of H fragments from the photodissociation of HBr, H2S, and the CH2OH radical, with kinetic energies ranging from <0.4 eV to >3 eV. It demonstrated KE resolution ≲1%-2%, similar to that obtained in traditional velocity map imaging followed by reconstruction, and to KE resolution achieved previously in SVMI of heavier products. We expect it to perform just as well up to at least 6 eV of kinetic energy. The tests showed that numerical simulations of the electric fields and ion trajectories in the system, used for optimization of the design and operating parameters, provide an accurate and reliable description of all aspects of system performance. This offers the advantage of selecting the best operating conditions in each measurement without the need for additional calibration experiments.