Gravitational effects of rotating masses

A gyroscope in orbit about a central rotating mass undergoes relativistic nutational oscillations in addition to the well-known precessional motions. The amplitude of the oscillation is proportional to the angular momentum of the rotating mass and its period is the Fokker period of geodetic precession. The amplitude is maximum for a polar orbit and vanishes if the orbit is equatorial. This nodding effect is due to a small divisor phenomenon involving the Fokker frequency, and its existence implies that the applicability of the post-Newtonian approximation of general relativity is limited in time. The dynamical significance of the new effect for the relative motion of neighboring test masses in the field of a rotating mass as well as for the restricted three-body problem in general relativity is investigated and the possibility of its detection is briefly discussed.     

Relativistic precession of a gyroscope. I. Circular orbits

The relativistic precession of the rotation axis of a spherical gyroscope is treated in the framework of monadic specification of the frame of reference. It is found that the precession in the comoving frame compensates the rotation of the frame of reference itself. An exact expression is derived for the angular velocity of precession for motion of a gyroscope in circular epiequatorial orbits in the Kerr field. The results are compared with the approximate expression obtained by Schiff. Numerical examples are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 64–68, March, 1981.     

Gravitomagnetic influence on gyroscopes and on the lunar orbit

Gravitomagnetism--a motional coupling of matter analogous to the Lorentz force in electromagnetism--has observable consequences for any scenario involving differing mass currents. Examples include gyroscopes located near a rotating massive body and the interaction of two orbiting bodies. In the former case, the resulting precession of the gyroscope is often called "frame dragging" and is the principal measurement sought by the Gravity Probe-B experiment. The latter case is realized in the Earth-Moon system, and the effect has in fact been confirmed via lunar laser ranging to approximately 0.1% accuracy--better than the anticipated accuracy of the Gravity-Probe-B result. This Letter shows the connection between these seemingly disparate phenomena by employing the same gravitomagnetic term in the equation of motion to obtain both gyroscopic precession and modification of the lunar orbit.     

Gyroscope precession frequency analysis of a five-dimensional charged rotating Kaluza-Klein black hole

We study the spin precession frequency of a test gyroscope attached to a stationary observer in the five-dimensional rotating Kaluza-Klein black hole(RKKBH). We derive the conditions under which the test gyroscope moves along a timelike trajectory in this geometry, and the regions where the spin precession frequency diverges. The magnitude of the gyroscope precession frequency around the KK black hole diverges at two spatial locations outside the event horizon. However, in the static case, the behavior of the Lense-Thirring frequency of a gyroscope around the KK black hole is similar to the ordinary Schwarzschild black hole. Since a rotating Kaluza-Klein black hole is a generalization of the Kerr-Newman black hole, we present two mass-independent schemes to distinguish these two spacetimes.     

Oscillations of a spin in a circular orbit in the schwarzschild and Lense-Thirring metrics

A gyroscope in motion along a circular geodesic line oscillates with respect to a reference body because of the variability of the inclination of its orbit. Due to precession of the spin vector, these oscillations have the appearance of beats whose frequency is close to that of the orbital motion, and whose amplitude changes with a large period, so that the amplitude increases linearly during a long time. This phenomenon can be detected using symmetrical oscillations of gyroscopes with opposite spin vectors in an orbit around the Earth, or by observing the evolution of a planet orbit in the solar system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 68–70, November, 1982.The author is thankful to Yu. S. Vladimirov and N. V. Mitskevich for their discussion of the results.     

Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar <Superscript>3</Superscript>He

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid ³He, experimentally observed in uniaxial aerogel ³He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.     

Manifestation of dynamic chaos in spin-spin relaxation processes in a solid

The results of several experiments on the dynamics of paramagnetic spin systems are analyzed on the basis of the theory developed here. It is shown that the asymptotic expressions for time correlation functions of various (high) orders are mutually similar and have a characteristic form [18], which probably indicates the “forgetting” of the initial conditions due to the development of Lyapunov instability in the dynamic system. The existence of exponential functions with close exponents, which describe the damping of correlations in the experimental observation of signals from free NMR precession and their buildup in experiments on multiquantum NMR, are manifestations of this instability because the Lyapunov exponents exist in pairs. The results suggest the development of “deterministic chaos” in the systems under investigation.     

Magnetic relaxation in superfluid<Superscript>3</Superscript>He-B at very low temperatures

Main properties of the spin supercurrents and coherent precession of magnetization in the superfluid³He-B in hydrodynamic regime seem to be very well understood now. But recently surprisingly new unpredicted phenomena such as, for example, “catastrophic” relaxation, persistent spin precession, very strong magnetic relaxation, etc., have been observed in³He-B at ultralow temperatures in so-called non-hydrodynamic regime using both pulse and cw-NMR techniques. This paper deals with some of these new phenomena (a “linear term” in magnetic relaxation and a reduction of magnetization of coherent precession with magnetic field gradient) observed by cw-NMR technique, compares these results with new effects found by pulse NMR and speculates about the nature of these new phenomena.     

Precession of a gyroscope on the ground and the existence of magnetic-type gravitation

Using the Maxwell-type linearized Einstein equation, a measurable effect on the precession of a gyroscope on the surface of the earth is predicted. These experiments will test general relativity and magnetic-type gravitation in particular.     

Two-magnon relaxation reversal in ferrite spheres

The reversal of two-magnon relaxation associated with linear scattering of oscillations of uniform magnetization precession from sample nonuniformities is studied theoretically and experimentally in ferrite spheres of yttrium iron garnet (YIG). Relaxation reversal is performed by parametric phase conjugation of dipole-exchange spin waves formed as a result of scattering of uniform precession from inhomogeneities. As a result of two-magnon backward scattering of dipole-exchange spin waves with a certain time delay, magnetization oscillations are renewed with an amplitude that could exceed the initial amplitude of uniform precession. The relaxation reversal is due to crystallographic anisotropy of the sample and is manifested most strongly when a YIG sphere is magnetized along the intermediate axis [110]. Experiments were carried out on YIG spheres of diameter 0.65–1.05 mm for a parallel pumping frequency ω _p /2π ≈ 9.4 GHz, which is about twice the uniform precession frequency. The maximal delay time for the restored signal of uniform precession was about 2 μs, while the maximal amplitude exceeded the initial uniform precession amplitude by a factor of about 5. The “latent” relaxation parameters of ferrites, e.g., the natural ferromagnetic resonance linewidth associated with many-particle processes and the linewidth associated with two-magnon scattering at bulk nonuniformities, are determined experimentally.     

Hybrid Atomic–Optical Quantum Gyrometry

JETP Letters - A “hybrid” atomic–optical scheme of an interferometer–gyroscope has been proposed and investigated. It is based on the ring configuration of a...     

General Treatment of Orbiting GyroscopePrecession

We review the derivation of the metric for a spinning body of any shape andcomposition using linearized general relativity theory (LGRT), and also obtainthe same metric using a transformation argument. The latter derivation makes itclear that the linearized metric contains only the Eddington and parameters,so no new parameter is involved in frame-dragging or Lense—Thirring effects.We then calculate the precession of an orbiting gyroscope in a general weakgravitational field described by a Newtonian potential (the gravitoelectric field)and a vector potential (the gravitomagnetic field). Next we make a multipoleanalysis of the potentials and the precession equations, giving all of these interms of the spherical harmonics moments of the density distribution. The analysisis not limited to an axially symmetric source, although the Earth, which is themain application, is very nearly axisymmetric. Finally, we analyze the precessionin regard to the Gravity Probe B (GP-B) experiment, and find that the effect ofthe Earth's quadrupole moment (J ₂) on the geodetic precession is large enoughto be measured by GP-B (a previously known result), but the effect on theLense—Thirring precession is somewhat beyond the expected GP-B accuracy.     

LaTiO3(110)薄膜分子束外延生长的精确控制和表面截止层的研究

LaTiO₃ 是一种典型的强关联电子材料, 其(110) 薄膜为通过晶格对称性、应变等的设计调控外延结构的物理性质提供了新的机会. 本文研究了SrTiO₃(110) 衬底表面金属La 和Ti 沉积所引起的微观结构变化, 进而利用电子衍射信号对分子束外延薄膜生长表面阳离子浓度的灵敏响应, 发展了原位、实时、精确控制金属蒸发源沉积速率的方法, 实现了高质量LaTiO₃(110) 薄膜的生长和对阳离子化学配比的精确控制. 由于LaTiO₃中Ti³⁺ 3d 电子的库仑排斥作用, 氧原子层截止的(110) 表面更容易实现极性补偿, 因此生长得到的薄膜表面暴露出单一类型的氧截止面.     

The photoelectron spectra of anti- and syn-[2.2](2,6)-azulenophanes

The He(Iα) photoelectron spectra of the title compounds are almost superposable, as predicted on the basis of a simple LCMO model which takes account of the “through-space” and “through-bond” interactions between the two azulene moieties. This observation, i.e., that the interaction of the two “layers” (decks) of the azulenophane molecule is independent of their relative orientation, may seem surprising in view of the fact that azulene is a polar molecule. However, the observed result indicates once more that azulene is essentially a perturbed [10]annulene rather than a “strongly” non-alternant hydrocarbon, a conclusion which had already been reached by the analysis of other spectroscopic properties of this molecule.     

Superfluid gyroscope with cold atomic gases

A trapped Bose-Einstein condensed atomic gas containing a quantized vortex is predicted to exhibit precession after a sudden rotation of the confining potential. The equations describing the motion of the condensate are derived and the effects of superfluidity explicitly pointed out. The dependence of the precession frequency on the relevant parameters of the problem is discussed. The proposed gyroscope is well suited to explore rotational effects at the level of single quanta of circulation.     

Non-Langevin high-temperature magnetization of nanoparticles in a weak magnetic field

Experimental evidence and theoretical substantiation are presented for the asymptotic behavior of high-temperature magnetization of an ensemble of nanoparticles in a weak magnetic field, which was predicted earlier and which differs qualitatively from the “Langevin” limit for ideal superparamagnetic particles. It is shown that the physical reason for the new asymptotic behavior is the temperature-independent “positive” tilt of the uniform magnetization vector at local energy minima in the direction of the field; this asymptotic behavior is associated with the nonstandard thermodynamics of single-domain particles, which depends on the ratio of characteristic frequencies of regular precession and random diffusion of this vector. An alternative approach is proposed for describing the magnetic dynamics of an ensemble of nanoparticles in a magnetic field, and the precession orbits of the magnetization vector are considered as stochastic states of each particle, whereas each state is characterized by the trajectory-averaged value of magnetization.     

Parametric instability in uniform spin precession in superfluid 3He-B

In order to explain the “catastrophic spin relaxation” observed in superfluid ³He-B, the stability of spatially uniform spin precession in this liquid relative to the parametric excitation of spin waves has been analyzed. It is shown that uniform spin precession becomes unstable at low temperatures (Suhl instability). At zero temperature, the growth increments are determined for all spin wave branches. The temperature at which the transition from stable spin precession to instability takes place is estimated.     

Gyro precession and mach's principle

The precession of a gyroscope is calculated in a nonrelativistic theory due to Harbour which satisfies Mach's principle. It is shown that the theory predicts both the geodetic and motional precession of general relativity to within factors of order 1. The significance of the gyro experiment is discussed from the point of view of metric theories of gravity and this is contrasted with its significance from the point of view of Mach's principle.     

The gravitational interaction: Spin,rotation, and quantum effects-a review

Previous work on spin, rotation, and quantum effects in gravitation is surveyed, with particular emphasis on the gravitational two-body interaction, both for elementary particles and for macroscopic bodies. Applications considered include (a) the precession of a gyroscope, (b) rotational effects on the equations of motion for the orbit, (c) binary systems, particularly the binary pulsar PSR 1913+16, and (d) the prospects of measuring spin-orbit and spin-spin forces in the laboratory. In addition, we discuss quantum effects that arise in the interaction between elementary particles. In particular, we point out the potentially decisive role of these forces in high-density matter, with emphasis on the fact that repulsive forces arise that may prevent gravitational collapse. All of the above considerations are within the framework of Einstein's theory of general relativity, albeit extended to treat spin-dependent and quantum forces. Finally, we consider the additional quantum terms that are present if one works with a generalization of Einstein's theory, the Einstein-Cartan-Sciama-Kibble theory of gravitation, in which the spin of matter, as well as its mass, plays a dynamical role.     

Shell structure and orbit bifurcations in finite fermion systems

We first give an overview of the shell-correction method which was developed by V.M. Strutinsky as a practicable and efficient approximation to the general self-consistent theory of finite fermion systems suggested by A.B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M.C. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the “periodic orbit theory”. We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called “superdeformed” energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).