From Lagrangian to Quantum Mechanics with Symmetries

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of Physics: Conference Series, (2012

On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain

A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical application we show that periodic kink solutions (kink chains) of the double sine-Gordon model can be described in a canonical form in terms of generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table

Modular Solutions to Equations of Generalized Halphen Type

Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus zero and have $q$--series with integral coefficients. Rational maps relating these functions are derived, implying subgroup relations between their automorphism groups, as well as symmetrization maps relating the associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.

Who is really at risk? Identifying risk factors for subthreshold and full syndrome eating disorders in a high-risk sample

BACKGROUND: Numerous longitudinal studies have identified risk factors for the onset of most eating disorders (EDs). Identifying women at highest risk within a high-risk sample would allow for focusing of preventive resources and also suggests different etiologies. METHOD: A longitudinal cohort study over 3 years in a high-risk sample of 236 college-age women randomized to the control group of a prevention trial for EDs. Potential risk factors and interactions between risk factors were assessed using the methods developed previously. Main outcome measures were time to onset of a subthreshold or full ED. RESULTS: At the 3-year follow-up, 11.2% of participants had developed a full or partial ED. Seven of 88 potential risk factors could be classified as independent risk factors, seven as proxies, and two as overlapping factors. Critical comments about eating from teacher/coach/siblings and a history of depression were the most potent risk factors. The incidence for participants with either or both of these risk factors was 34.8% (16/46) compared to 4.2% (6/144) for participants without these risk factors, with a sensitivity of 0.75 and a specificity of 0.82. CONCLUSIONS: Targeting preventive interventions at women with high weight and shape concerns, a history of critical comments about eating weight and shape, and a history of depression may reduce the risk for EDs

Little groups of irreps of O(3), SO(3), and the infinite axial subgroups

Little groups are enumerated for the irreps and their components in any basis of O(3) and SO(3) up to rank 9, and for all irreps of C$_{\infty}$, C$_{\infty h}$, C$_{\infty v}$, D$_{\infty}$ and D$_{\infty h}$. The results are obtained by a new chain criterion, which distinguishes massive (rotationally inequivalent) irrep basis functions and allows for multiple branching paths, and are verified by inspection. These results are relevant to the determination of the symmetry of a material from its linear and nonlinear optical properties and to the choices of order parameters for symmetry breaking in liquid crystals.Comment: 28 pages and 3 figure

A characterization of Dirac morphisms

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.Comment: 18 pages; restricted to the even-dimensional cas

Structural changes in lower ionosphere wind trends at midlatitudes

Long-term variability of the mesosphere/lower thermosphere (lower E region ionosphere) since 1970 has been analyzed using wind data series obtained at Collm (52° N, 15° E) using the LF drift method and at Obninsk (55° N, 37° E) applying VHF meteor radar. Applying piecewise linear trend analysis with a priori unknown number and positions of breakpoints shows that trend models with breakpoints are generally to be preferred against straight lines. There is a strong indication for a change of trends in wind parameters around 1975–1980. Similar changes are also found in the lower atmosphere, e.g., in tropospheric temperatures. This indicates a coupling between atmospheric layers at time scales of decades

Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. For strong coupling (of the order N^2), the system synchronises, in the sense that all oscillators assume almost the same position in their respective local potential most of the time. In a previous paper, we showed that the transition from strong to weak coupling involves a sequence of symmetry-breaking bifurcations of the system's stationary configurations, and analysed in particular the behaviour for coupling intensities slightly below the synchronisation threshold, for arbitrary N. Here we describe the behaviour for any positive coupling intensity \gamma of order N^2, provided the particle number N is sufficiently large (as a function of \gamma/N^2). In particular, we determine the transition time between synchronised states, as well as the shape of the "critical droplet", to leading order in 1/N. Our techniques involve the control of the exact number of periodic orbits of a near-integrable twist map, allowing us to give a detailed description of the system's potential landscape, in which the metastable behaviour is encoded

Poisson Structures for Aristotelian Model of Three Body Motion

We present explicitly Poisson structures, for both time-dependent and time-independent Hamiltonians, of a dynamical system with three degrees of freedom introduced and studied by Calogero et al [2005]. For the time-independent case, new constant of motion includes all parameters of the system. This extends the result of Calogero et al [2009] for semi-symmetrical motion. We also discuss the case of three bodies two of which are not interacting with each other but are coupled with the interaction of third one