High-frequency QPOs as a problem in physics: non-linear resonance

The presence of a kHz frequency in LMXBs has been expected from scaling laws, by analogy with the QPO phenomenon in HMXB X-ray pulsars. Interpretation of the two kHz frequencies, observed in accreting neutron stars, in terms of non-linear resonance in strong-field gravity led to the prediction of twin QPOs in black hole systems, in a definite frequency ratio (such as 2/3). The imprint of a subharmonic of the 401 Hz rotation rate in the frequencies of the QPOs detected in the accreting millisecond pulsar is at once a signature of non-linear resonance and of coupling between accretion disk modes and the neutron star spin.Comment: presented at X-ray Timing 2003: Rossi and Beyond, Boston, November 200

A non-linear resonance model for the black hole and neutron star QPOs: theory supported by observations

Kilohertz Quasi-Periodic Oscillations (QPOs) have been detected in many accreting X-ray binaries. It has been suggested that the highest QPO frequencies observed in the modulation of the X-ray flux reflect a non-linear resonance between two modes of accreting disk oscillation. This hypothesis implies certain very general predictions, several of which have been borne out by observations. Some of these follow from properties of non-linear oscillators, while the others are specific to oscillations of fluid in strong gravity. A 3:2 resonant ratio of frequencies can be clearly recognized in the black-hole as well as in the neutron-star QPO data.Comment: 8 pages, 8 figures, to appear in Proceedings of the Albert Einstein Century International Conferenc

Epicyclic oscillations of fluid bodies Paper II. Strong gravity

Fluids in external gravity may oscillate with frequencies characteristic of the epicyclic motions of test particles. We explicitly demonstrate that global oscillations of a slender, perfect fluid torus around a Kerr black hole admit incompressible vertical and radial epicyclic modes. Our results may be directly relevant to one of the most puzzling astrophysical phenomena -- high (hundreds of hertz) frequency quasiperiodic oscillations (QPOs) detected in X-ray fluxes from several black hole sources. Such QPOs are pairs of stable frequencies in the 3/2 ratio. It seems that they originate a few gravitational radii away from the black hole and thus observations of them have the potential to become an accurate probe of super-strong gravity.Comment: submitted to Classical and Quantum Gravit

Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ions

One-electron 3+1 and 2+1 Dirac equations are used to calculate the motion of a relativistic electron in a vacuum in the presence of an external magnetic field. First, calculations are carried on an operator level and exact analytical results are obtained for the electron trajectories which contain both intraband frequency components, identified as the cyclotron motion, as well as interband frequency components, identified as the trembling motion (Zitterbewegung, ZB). Next, time-dependent Heisenberg operators are used for the same problem to compute average values of electron position and velocity employing Gaussian wave packets. It is shown that the presence of a magnetic field and the resulting quantization of the energy spectrum has pronounced effects on the electron Zitterbewegung: it introduces intraband frequency components into the motion, influences all the frequencies and makes the motion stationary (not decaying in time) in case of the 2+1 Dirac equation. Finally, simulations of the 2+1 Dirac equation and the resulting electron ZB in the presence of a magnetic field are proposed and described employing trapped ions and laser excitations. Using simulation parameters achieved in recent experiments of Gerritsma and coworkers we show that the effects of the simulated magnetic field on ZB are considerable and can certainly be observed.Comment: 19 pages, 9 figures, published versio

No observational proof of the black-hole event-horizon

Recently, several ways of obtaining observational proof of the existence of black-hole horizons have been proposed. We argue here that such proof is fundamentally impossible: observations can provide arguments, sometimes very strong ones, in favour of the existence of the event horizon, but they cannot prove it. This applies also to future observations, which will trace very accurately the details of the spacetime metric of a body suspected of being a black hole.Comment: 4 pages, no figures, submitted to A&A Letter

Epicyclic orbital oscillations in Newton's and Einstein's dynamics

We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical geometry of Schwarzschild's spacetime. For this reason, rather unexpectedly, Newton's formulae for Kepler's problem, in the case of nearly circular motion in a static, spherically spherical gravitational potential accurately describe strong field general relativistic effects, in particular vanishing of the radial epicyclic frequency at the marginally stable orbit.Comment: 8 page

One-dimensional semirelativity for electrons in carbon nanotubes

It is shown that the band structure of single-wall semiconducting carbon nanotubes (CNT) is analogous to relativistic description of electrons in vacuum, with the maximum velocity $u$= $10^8$cm/s replacing the light velocity. One-dimensional semirelativistic kinematics and dynamics of electrons in CNT is formulated. Two-band k.p Hamiltonian is employed to demonstrate that electrons in CNT experience a Zitterbewegung (trembling motion) in absence of external fields. This Zitterbewegung should be observable much more easily in CNT than its analogue for free relativistic electrons in vacuum.Comment: 4 pages no figure