Functional integral for non-Lagrangian systems

A novel functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The new approach, which we call "stringy quantization," is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force $-\kappa[\dot{q}]^A$. Results for $A = 1$ are compared with those obtained in the approaches by Caldirola-Kanai, Bateman and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.Comment: 14 pages, 7 figures, corrected typo

Theory of spin-orbit coupling in bilayer graphene

Theory of spin-orbit coupling in bilayer graphene is presented. The electronic band structure of the AB bilayer in the presence of spin-orbit coupling and a transverse electric field is calculated from first-principles using the linearized augmented plane wave method implemented in the WIEN2k code. The first-principles results around the K points are fitted to a tight-binding model. The main conclusion is that the spin-orbit effects in bilayer graphene derive essentially from the single-layer spin-orbit coupling which comes almost solely from the d orbitals. The intrinsic spin-orbit splitting (anticrossing) around the K points is about 24\mu eV for the low-energy valence and conduction bands, which are closest to the Fermi level, similarly as in the single layer graphene. An applied transverse electric field breaks space inversion symmetry and leads to an extrinsic (also called Bychkov-Rashba) spin-orbit splitting. This splitting is usually linearly proportional to the electric field. The peculiarity of graphene bilayer is that the low-energy bands remain split by 24\mu eV independently of the applied external field. The electric field, instead, opens a semiconducting band gap separating these low-energy bands. The remaining two high-energy bands are spin-split in proportion to the electric field; the proportionality coefficient is given by the second intrinsic spin-orbit coupling, whose value is 20\mu eV. All the band-structure effects and their spin splittings can be explained by our tight-binding model, in which the spin-orbit Hamiltonian is derived from symmetry considerations. The magnitudes of intra- and interlayer couplings---their values are similar to the single-layer graphene ones---are determined by fitting to first-principles results.Comment: 16 pages, 13 figures, 5 tables, typos corrected, published versio

Handling and analysis of ices in cryostats and glove boxes in view of cometary samples

Comet nucleus sample return mission and other return missions from planets and satellites need equipment for handling and analysis of icy samples at low temperatures under vacuum or protective gas. Two methods are reported which were developed for analysis of small icy samples and which are modified for larger samples in cometary matter simulation experiments (KOSI). A conventional optical cryostat system was modified to allow for transport of samples at 5 K, ion beam irradiation, and measurement in an off-line optical spectrophotometer. The new system consists of a removable window plug containing nozzles for condensation of water and volatiles onto a cold finger. This plug can be removed in a vacuum system, changed against another plug (e.g., with other windows (IR, VIS, VUV) or other nozzles). While open, the samples can be treated under vacuum with cooling by manipulators (cut, removal, sample taking, irradiation with light, photons, or ions). After bringing the plug back, the samples can be moved to another site of analysis. For handling the 30 cm diameter mineral-ice samples from the KOSI experiments an 80x80x80 cm glove box made out of plexiglass was used. The samples were kept in a liquid nitrogen bath, which was filled from the outside. A stream a dry N2 and evaporating gas from the bath purified the glove box from impurity gases and, in particular, H2O, which otherwise would condense onto the samples

Invariant variational principle for Hamiltonian mechanics

It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some 1-form $\gamma$, such that $\omega= d \gamma$, which is not unique and does not even generally exist in a global sense.Comment: final version; to appear in J.Phys.A; 17 pages, 2 figure

Berry's phase in noncommutative spaces

We introduce the perturbative aspects of noncommutative quantum mechanics. Then we study the Berry's phase in the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics which depend on the parameter of space/space noncommtativity.Comment: 7 pages, no figur

The Pauli equation with complex boundary conditions

We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.Comment: 16 pages, 4 figure

Fatty acid distribution and polymorphism in solid lipid particles of milkfat and long chain omega-3 fatty acids

Saturated fatty acid-containing lipids, such as milkfat, may protect long chain polyunsaturated fatty acids in fish oil when blended together into solid lipid particles (SLPs). One of the main challenges of SLPs is structural polymorphism, which can lead to expulsion of the protected component during prolonged storage. To investigate this phenomenon, the change in thermal and crystalline behaviours, and fatty acid distribution, were analysed in SLPs of fish oil and milkfat during storage at different temperatures for up to 28 days. X-ray diffraction analysis showed changes in molten and crystalline states occurred even at –22 °C. Room temperature (21 °C) storage led to more than 45% molten state but SLPs retained their initial shape. Confocal Raman Spectroscopy of the SLPs showed the distribution of fatty acids was not uniform, with 10 μm outermost layer of predominantly saturated fatty acids likely responsible for the intact SLP shape and stability of the core

Reliability, Validity, and User-Experience of Remote Unsupervised Computerized Neuropsychological Assessments in Community-Living 55- to 75-Year-Olds

Background: Self-administered computerized neuropsychological assessments (CNAs) provide lower cost, more accessible alternatives to traditional in-person assessments but lack critical information on psychometrics and subjective experience of older adults in remote testing environments. Objective: We used an online brief battery of computerized tasks selected from the Cogstate Brief Battery (CBB) and Cambridge Brain Sciences (CBS) to 1) determine test-retest reliability in an unsupervised setting; 2) examine convergent validity with a comprehensive 'gold standard' paper-and-pencil neuropsychological test battery administered in-person; and 3) explore user-experience of remote computerized testing and individual tests. Methods: Fifty-two participants (mean age 65.8±5.7 years) completed CBB and CBS tests on their own computer, unsupervised from home, on three occasions, and visited a research center for an in-person paper-and-pencil assessment. They also completed a user-experience questionnaire. Results: Test-retest reliabilities varied for individual measures (ICCs = 0.20 to 0.83). Global cognition composites showed excellent reliability (ICCs > 0.8 over 1-month follow-up). A strong relationship between a combination of CNA measures and paper-and-pencil battery was found (canonical correlation R = 0.87, p = 0.04). Most tests were rated as enjoyable with easy-to-understand instructions. Ratings of general experience with online testing were mostly favorable; few had difficulty concentrating (17%) or using the computer for tasks (10%), although over one-third experienced performance anxiety (38%). Conclusion: A combined brief online battery selected from two CNAs demonstrated robust psychometric standards for reliability (global composite), and convergent validity with a gold standard battery, and mostly good usability and acceptability in the remote testing environment