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

Quantization of Equations of Motion

The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential). A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail.

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

Changing Employment Relations and Governance in the International Auto Industry

In recent years, considerable debate has surrounded the issue of whether a fundamental transformation of employment relations is underway in both the industrialised and industrialising countries. Comparative studies at the national or macro-level of employment relations have been conducted within both an OECD group of countries (see Locke et al 1995) and newly industrialising economies (see Verma et al 1995). To these have been added complementary studies at the industry-level: in steel, telecommunications, banking and automobile manufacturing. These studies have adopted a broader similar analytical framework that focus on five sets of employment practices or issues, as follows: (1) the way work is organised (2) the process of skills acquisition and development (3) the structures and processes of pay and compensation (4) staffing and employment security arrangements (5) enterprise governance and labour-management relations issues. The analytical framework adopted for these studies argues that employment practices are shaped by features of the external environment and the choices of firms, unions and governments, as well as by the broader institutional context at the industry and firm levels. The issue of enterprise governance occupies an ambiguous position in that it may be viewed both as a feature of the external environment (especially where governments have legislated for certain arrangements) as well as an element in employment relations practice

Noncommutative Lagrange Mechanics

It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within noncommutative quantum theories. Newton-Lagrange noncommutative equations of motion are formulated and their properties are analyzed from the pure geometrical point of view. It is argued that the dynamical quintessence of the system consists in its kinetic energy (Riemannian metric) specifying Riemann-Levi-Civita connection and thus the inertia geodesics of the free motion. Throughout the paper, ''noncommutativity'' is considered as an internal geometric structure of the configuration space, which can not be ''observed'' per se. Manifestation of the noncommutative phenomena is mediated by the interaction of the system with noncommutative background under the consideration. The simplest model of the interaction (minimal coupling) is proposed and it is shown that guiding affine connection is modified by the quadratic analog of the Lorentz electromagnetic force (contortion term)

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

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

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

Is intraindividual reaction time variability an independent cognitive predictor of mortality in old age? Findings from the Sydney Memory and Ageing Study

Intraindividual variability of reaction time (IIVRT), a proposed cognitive marker of neurobiological disturbance, increases in old age, and has been associated with dementia and mortality. The extent to which IIVRT is an independent predictor of mortality, however, is unclear. This study investigated the association of IIVRT and all-cause mortality while accounting for cognitive level, incident dementia and biomedical risk factors in 861 participants aged 70–90 from the Sydney Memory and Ageing Study. Participants completed two computerised reaction time (RT) tasks (76 trials in total) at baseline, and comprehensive medical and neuropsychological assessments every 2 years. Composite RT measures were derived from the two tasks—the mean RT and the IIVRT measure computed from the intraindividual standard deviation of the RTs (with age and time-on-task effects partialled out). Consensus dementia diagnoses were made by an expert panel of clinicians using clinical criteria, and mortality data were obtained from a state registry. Cox proportional hazards models estimated the association of IIVRT and mean RT with survival time over 8 years during which 191 (22.2%) participants died. Greater IIVRT but not mean RT significantly predicted survival time after adjusting for age, sex, global cognition score, cardiovascular risk index and apolipoprotein ɛ4 status. After excluding incident dementia cases, the association of IIVRT with mortality changed very little. Our findings suggest that greater IIVRT uniquely predicts shorter time to death and that lower global cognition and prodromal dementia in older individuals do not explain this relationship