Generalized Hamilton-Jacobi equations for nonholonomic dynamics

Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the action is actually minimized (not just extremized)

Calculation of isotope shifts and relativistic shifts in CI, CII, CIII and CIV

We present an accurate ab initio method of calculating isotope shifts and relativistic shifts in atomic spectra. We test the method on neutral carbon and three carbon ions. The relativistic shift of carbon lines may allow them to be included in analyses of quasar absorption spectra that seek to measure possible variations in the fine structure constant, alpha, over the lifetime of the Universe. Carbon isotope shifts can be used to measure isotope abundances in gas clouds: isotope abundances are potentially an important source of systematic error in the alpha-variation studies. These abundances are also needed to study nuclear reactions in stars and supernovae, and test models of chemical evolution of the Universe

Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances

We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be satisfied. Correspondingly, phenomena of scattering on a resonance and capture into a resonance happen in the system. These phenomena lead to destruction of adiabatic invariance and to unlimited acceleration of the particle.Comment: 20 pages. Presented on School-Conference "Mathematics and Physics of Billiard-Like Systems" (Ubatuba, 2011). Accepted to Chao

Using Molecules to Measure Nuclear Spin-Dependent Parity Violation

Nuclear spin-dependent parity violation arises from weak interactions between electrons and nucleons, and from nuclear anapole moments. We outline a method to measure such effects, using a Stark-interference technique to determine the mixing between opposite-parity rotational/hyperfine levels of ground-state molecules. The technique is applicable to nuclei over a wide range of atomic number, in diatomic species that are theoretically tractable for interpretation. This should provide data on anapole moments of many nuclei, and on previously unmeasured neutral weak couplings

Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes

In [arXiv:hep-th/0611083] we announced the complete integrability of geodesic motion in the general higher-dimensional rotating black-hole spacetimes. In the present paper we prove all the necessary steps leading to this conclusion. In particular, we demonstrate the independence of the constants of motion and the fact that they Poisson commute. The relation to a different set of constants of motion constructed in [arXiv:hep-th/0612029] is also briefly discussed.Comment: 8 pages, no figure

Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes

We explicitly exhibit n-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n = [(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.Comment: 4 pages. We have now found that the geodesic motion is not just integrable, but completely integrabl

The Bose-Einstein correlation function C2(Q)C_2(Q) from a Quantum Field Theory point of view

We show that a recently proposed derivation of Bose-Einstein correlations (BEC) by means of a specific version of thermal Quantum Field Theory (QFT), supplemented by operator-field evolution of the Langevin type, allows for a deeper understanding of the possible coherent behaviour of the emitting source and a clear identification of the origin of the observed shape of the BEC function $C_2(Q)$. Previous conjectures in this matter obtained by other approaches are confirmed and have received complementary explanation.Comment: Some misprints corrected. To be publishe in Phys. Rev.

Some forgotten features of the Bose Einstein Correlations

Notwithstanding the visible maturity of the subject of Bose-Einstein Correlations (BEC), as witnessed nowadays, we would like to bring to ones attention two points, which apparently did not received attention they deserve: the problem of the choice of the form of $C_2(Q)$ correlation function when effects of partial coherence of the hadronizing source are to be included and the feasibility to model effects of Bose-Einstein statistics, in particular the BEC, by direct numerical simulations.Comment: Talk delivered by G.Wilk at the International Workshop {\it Relativistic Nuclear Physics: from Nuclotron to LHC energies}, Kiev, June 18-22, 2007, Ukraine; misprints correcte

Optics of spin-noise-induced gyrotropy of asymmetric microcavity

The optical gyrotropy noise of a high-finesse semiconductor Bragg microcavity with an embedded quantum well (QW) is studied at different detunings of the photon mode and the QW exciton resonances. A strong suppression of the noise magnitude for the photon mode frequencies lying above exciton resonances is found. We show that such a critical behavior of the observed optical noise power is specific of asymmetric Fabry-Perot resonators. As follows from our analysis, at a certain level of intracavity loss, the reflectivity of the asymmetric resonator vanishes, while the polarimetric sensitivity to the gyrotropy changes dramatically when moving across the critical point. The results of model calculations are in a good agreement with our experimental data on the spin noise in a single-quantum-well microcavity and are confirmed also by the spectra of the photo-induced Kerr rotation in the pump-probe experiments.Comment: 6 pages, 5 figure