Time-resolved Stark effect in rapidly varying fields

The cycle-averaged ac Stark effect associated with the ^[ A _]2Σ⁺v^′=2?^[ X _]2Π1/2v^′=0 two-photon absorption of NO at intensities between 7.7 and 15.2 TW cm^-2 has been characterized in real time through a synergic combination of bichromatic laser experiments and quantum-dynamics calculations. Measurements of the fluorescence emitted by the Rydberg ^[ A _]2Σ⁺v^′=2 level as a function of time between Stark and probe components of a bichromatic field exhibit a characteristic evolution in temporal peak structure with Stark-field intensity, which is interpreted in terms of a time-dependent Floquet analysis of the laser–matter interaction. The experimental observations are consistent with a dynamic Stark shift of Δε_s(ω₁,ω₂)≤0.23 eV of the optical transition at these intensities. Received: 18 January 2002 / Revised version: 6 March 2002 / Published online: 24 April 2002     

Spin-flavor oscillations of neutrinos in rapidly varying external fields

Spin-flavor oscillations of neutrinos in rapidly varying external fields are studied. A method for describing neutrino oscillations in arbitrary rapidly varying external fields is developed. An effective Hamiltonian that describes the evolution of the averaged neutrino wave function is obtained. Neutrino oscillations in rapidly varying magnetic fields are considered on the basis of the general formalism developed in this study. Neutrino transitions in a superposition of a constant and a rotating (in space) magnetic field that are transverse with respect to the neutrino velocity are studied. The probabilities of transitions in spin-flavor oscillations of neutrinos in the magnetic fields of the Sun are estimated. Numerical solutions to the Schrödinger equation for the Hamiltonian that describes neutrino interaction with a constant and a rotating (in space) magnetic field are given. It is shown that the approximate analytic formula obtained in the present study for the probability of neutrino transitions is consistent with the respective numerical solution to the evolution equation at high frequencies of the rotating magnetic fields.     

Asymptotic analysis of deterministic and stochastic equations with rapidly varying components

The asymptotic character of deterministic and stochastic equations whose solutions have a rapidly varying component is studied. Of particular interest is the class of problems for which the limiting behavior can be described in a contracted and simplified framework.     

A mobile computerized laser radar system for observing rapidly varying meteorological phenomena

A high repetition, mobile laser radar system with a computerized real-time data acquisition and display system is described. Signal-to-noise levels of the system are compared with theoretical values, and it is found that they are affected by the shot noise in the system. An example of a stack plume observation is also presented to show the performance of the system.     

利用取帧技术在气轨上验证变力做功

在气垫导轨上研究了滑块在变力作用下的运动规律.利用质量较为均匀的细铁链的下落改变作用在滑块上的力,利用摄像机记录随铁链下落滑块的运动过程,通过取帧技术获得滑块运动的位移、速度和时间关系.     

Canonical connections of Finsler metrics and Finslerian connections on Riemannian metrics

A concept of canonical connection of a Finsler metric is developed. Connections that are compatible with Finsler metrics are compared with the canonical connection itself. They are also compared with the corresponding Cartan connection. A necessary and sufficient condition on metric Finsler connections is given for the metric to be Riemannian. This study unearths different ways in which Finsler geometry could be used to generalize the theory of general relativity.     

The Einstein action of Riemannian metrics and its relation to quantum gravity and thermodynamics

The Einstein action evaluated on Riemannian metrics is investigated. It is neither bounded below or above and its critical points are saddle points. This probably means that the functional integral will not converge, and is related to the negative specific heat of self gravitating systems and the breakdown of the validity of the canonical ensemble. The contribution from Wheeler's foam-like structures is shown to have the correct sign for convergence and to contribute positively to the free energy.     

Quasi-Einstein metrics on hypersurface families

We construct quasi-Einstein metrics on some hypersurface families. The hypersurfaces are circle bundles over the product of Fano, Kähler–Einstein manifolds. The quasi-Einstein metrics are related to various gradient Kähler–Ricci solitons constructed by Dancer and Wang and some Hermitian, non-Kähler, Einstein metrics constructed by Wang and Wang on the same manifolds.     

Some observations on degenerate metrics

There are some polynomial formulations of Einstein's equations in which the metric is allowed to become degenerate. We examine some known exact solutions to see whether they may be smoothly joined to solutions with degenerate metrics. If one uses a lapse function which is a spatial scalar, this is very easy. If the lapse function has a small and negative tensor density weight, the joining together may take place across the horizons in the Schwarzschild and Kerr solutions. For large and negative weights, we have been unable to find any examples.     

Dragged metrics

We show that the path of any accelerated body in an arbitrary spacetime geometry $g_{\mu \nu }$ can be described as a geodesic in a dragged metric $\hat{q}_{\mu \nu }$ that depends only on the background metric and on the motion of the body. Such procedure allows the interpretation of all kinds of non-gravitational force as modifications of the spacetime metric. This method of effective elimination of the forces by changing the metric of the substratum can be understood as a generalization of the d’Alembert principle applied to all relativistic processes.     

Gravity on Finite Groups

Gravity theories are constructed on finite groups G. A self-consistent review of the differential calculi on finite G is given, with some new developments. The example of a bicovariant differential calculus on the nonabelian finite group S ₃ is treated in detail, and used to build a gravity-like field theory on S ₃. Received: 11 November 1999 / Accepted: 11 December 2000     

Gravity on a multifractal

Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of these models of Nature. Thus motivated, we entertain the idea that spacetime is a multifractal with integer dimension 4 at large scales, while it is two-dimensional in the ultraviolet. Consequences for particle physics, gravity and cosmology are discussed.     

Generalized Vaidya metrics

We investigate criteria under which one may construct the energy tensor of a null radiation field from an algebraically special vacuum metric. The field bears the same relationship to the original metric as does Vaidya's to Schwarzschild's. As an example we generate a class of null radiation fields from a class of vacuum metrics without symmetry discovered by Robinson and Robinson.Supported in part by the National Science Foundation (GP-8868, GP-20033, and GU-1598), Air Force Office of Scientific Research under Grant AF-AFOSR-903-67 and by the National Aeronautics and Space Administration under NASA Grant No. NGL 44-004-001.     

Optically pumped quantum M X magnetometers: Digital measurement of the M X resonance frequency in a rapidly varying field

A new way of digitally constructing a phase-locked loop for an optically pumped quantum M _X magnetometer is suggested. It provides a high accuracy and speed of magnetic resonance frequency tracking in a rapidly varying field.     

Charged Tomimatsu-Sato metrics

We show that the solutions of Einstein-Maxwell field equations can be constructed from the Tomimatsu-Sato solutions of Einstein's field equations for empty space simply by inspection when δ has integral values.     

Self-dual metrics on non-simply connected 4-manifolds

We construct self-dual (SD) but not locally conformally flat (LCF) metrics on families of non-simply connected 4-manifolds with small signature. We construct various sequences with bounded or unbounded Betti numbers and Euler characteristic. These metrics have negative scalar curvature. As an application, this is used to address Remark 4.79 of [1].