Plasmons in topological insulator cylindrical nanowires

We present a theoretical analysis of Dirac magneto-plasmons in topological insulator nanowires. We discuss a cylindrical geometry where Berry phase effects induce the opening of a gap at the neutrality point. By taking into account surface electron wave functions introduced in previous papers and within the random phase approximation, we provide an analytical form of the dynamic structure factor. Dispersions and spectral weights of Dirac plasmons are studied with varying the radius of the cylinder, the surface doping, and the strength of an external magnetic field. We show that, at zero surface doping, inter-band damped plasmon-like excitations form at the surface and survive at low electron surface dopings ($\sim 10^{10} cm^{-2}$). Then, we point out that the plasmon excitations are sensitive to the Berry phase gap closure when an external magnetic field close to half quantum flux is introduced. Indeed, a well-defined magneto-plasmon peak is observed at lower energies upon the application of the magnetic field. Finally, the increase of the surface doping induces a crossover from damped inter-band to sharp intra-band magneto-plasmons which, as expected for large radii and dopings ($\sim 10^{12} cm^{-2}$), approach the proper limit of a two-dimensional surface.Comment: 18 pages, 11 figures, 2 Appendice

The Lense-Thirring effect in the Jovian system of the Galilean satellites and its measurability

In this paper we investigate the possibility of measuring the post-Newtonian general relativistic gravitomagnetic Lense-Thirring effect in the Jovian system of its Galilean satellites Io, Europa, Ganymede and Callisto in view of recent developments in processing and modelling their optical observations spanning a large time interval (125 years). The present day best observations have an accuracy between several kilometers to few tens of kilometers, which is just the order of magnitude of the Lense-Thirring shifts of the orbits of the Galilean satellites over almost a century. From a comparison between analytical development and numerical integration it turns out that, unfortunately, most of the secular component of the gravitomagnetic signature is removed in the process of fitting the initial conditions. Indeed, an estimation of the magnitude of the Lense-Thirring effect in the ephemerides residuals is given; the resulting residuals have a maximum magnitude of 20 meters only (over 125 years).Comment: Latex, 10 pages, 4 tables, 3 figures, 27 references. Invited paper for a Special Issue of Int. J. Mod. Phys. D on the Lense-Thirring effect, D. Grumiller edito

On the perspectives of testing the Dvali-Gabadadze-Porrati gravity model with the outer planets of the Solar System

The multidimensional braneworld gravity model by Dvali, Gabadadze and Porrati was primarily put forth to explain the observed acceleration of the expansion of the Universe without resorting to dark energy. One of the most intriguing features of such a model is that it also predicts small effects on the orbital motion of test particles which could be tested in such a way that local measurements at Solar System scales would allow to get information on the global properties of the Universe. Lue and Starkman derived a secular extra-perihelion \omega precession of 5\times 10^-4 arcseconds per century, while Iorio showed that the mean longitude \lambda is affected by a secular precession of about 10^-3 arcseconds per century. Such effects depend only on the eccentricities e of the orbits via second-order terms: they are, instead, independent of their semimajor axes a. Up to now, the observational efforts focused on the dynamics of the inner planets of the Solar System whose orbits are the best known via radar ranging. Since the competing Newtonian and Einsteinian effects like the precessions due to the solar quadrupole mass moment J2, the gravitoelectric and gravitomagnetic part of the equations of motion reduce with increasing distances, it would be possible to argue that an analysis of the orbital dynamics of the outer planets of the Solar System, with particular emphasis on Saturn because of the ongoing Cassini mission with its precision ranging instrumentation, could be helpful in evidencing the predicted new features of motion. In this note we investigate this possibility in view of the latest results in the planetary ephemeris field. Unfortunately, the current level of accuracy rules out this appealing possibility and it appears unlikely that Cassini and GAIA will ameliorate the situation.Comment: LaTex, 22 pages, 2 tables, 10 figures, 27 references. Reference [17] added, reference [26] updated, caption of figures changed, small change in section 1.

Will the recently approved LARES mission be able to measure the Lense-Thirring effect at 1%?

After the approval by the Italian Space Agency of the LARES satellite, which should be launched at the end of 2009 with a VEGA rocket and whose claimed goal is a about 1% measurement of the general relativistic gravitomagnetic Lense-Thirring effect in the gravitational field of the spinning Earth, it is of the utmost importance to reliably assess the total realistic accuracy that can be reached by such a mission. The observable is a linear combination of the nodes of the existing LAGEOS and LAGEOS II satellites and of LARES able to cancel out the impact of the first two even zonal harmonic coefficients of the multipolar expansion of the classical part of the terrestrial gravitational potential representing a major source of systematic error. While LAGEOS and LAGEOS II fly at altitudes of about 6000 km, LARES will be placed at an altitude of 1450 km. Thus, it will be sensitive to much more even zonals than LAGEOS and LAGEOS II. Their corrupting impact \delta\mu has been evaluated by using the standard Kaula's approach up to degree L=70 along with the sigmas of the covariance matrices of eight different global gravity solutions (EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, JEM01-RL03B, ITG-Grace02s, ITG-Grace03, EGM2008) obtained by five institutions (GFZ, CSR, JPL, IGG, NGA) with different techniques from long data sets of the dedicated GRACE mission. It turns out \delta\mu about 100-1000% of the Lense-Thirring effect. An improvement of 2-3 orders of magnitude in the determination of the high degree even zonals would be required to constrain the bias to about 1-10%.Comment: Latex, 15 pages, 1 table, no figures. Final version matching the published one in General Relativity and Gravitation (GRG

On the twin paradox in static spacetimes: I. Schwarzschild metric

Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.Comment: 18 pages, paper accepted for publication in Gen. Rel. Gra

A uniform treatment of the orbital effects due to a violation of the Strong Equivalence Principle in the gravitational Stark-like limit

We analytically work out several effects which a violation of the Strong Equivalence Principle (SEP) induces on the orbital motion of a binary system constituted of self-gravitating bodies immersed in a constant and uniform external field. We do not restrict to the small eccentricity limit. Moreover, we do not select any specific spatial orientation of the external polarizing field. We explicitly calculate the SEP-induced mean rates of change of all the osculating Keplerian orbital elements of the binary, the perturbation of the projection of the binary orbit onto the line-of-sight, the shift of the radial velocity, and the range and range-rate signatures and as well. We find that the ratio of the SEP precessions of the node and the inclination of the binary depends only on and the pericenter of the binary itself, being independent on both the magnitude and the orientation of the polarizing field, and on the semimajor axis, the eccentricity and the node of the binary. Our results, which do not depend on any particular SEP-violating theoretical scheme, can be applied to quite general astronomical and astrophysical scenarios. They can be used to better interpret present and future SEP experiments, especially when several theoretical SEP mechanisms may be involved, and to suitably design new dedicated tests.Comment: LaTex2e, 14 pages, no figures, no tables, 42 references. To appear in Classical and Quantum Gravity (CQG

LAGEOS-type Satellites in Critical Supplementary Orbit Configuration and the Lense-Thirring Effect Detection

In this paper we analyze quantitatively the concept of LAGEOS--type satellites in critical supplementary orbit configuration (CSOC) which has proven capable of yielding various observables for many tests of General Relativity in the terrestrial gravitational field, with particular emphasis on the measurement of the Lense--Thirring effect.Comment: LaTex2e, 20 pages, 7 Tables, 6 Figures. Changes in Introduction, Conclusions, reference added, accepted for publication in Classical and Quantum Gravit

On the Clock Paradox in the case of circular motion of the moving clock

In this paper we deal analytically with a version of the so called clock paradox in which the moving clock performs a circular motion of constant radius. The rest clock is denoted as (1), the rotating clock is (2), the inertial frame in which (1) is at rest and (2) moves is I and, finally, the accelerated frame in which (2) is at rest and (1) rotates is A. By using the General Theory of Relativity in order to describe the motion of (1) as seen in A we will show the following features. I) A differential aging between (1) and (2) occurs at their reunion and it has an absolute character, i.e. the proper time interval measured by a given clock is the same both in I and in A. II) From a quantitative point of view, the magnitude of the differential aging between (1) and (2) does depend on the kind of rotational motion performed by A. Indeed, if it is uniform there is no any tangential force in the direction of motion of (2) but only normal to it. In this case, the proper time interval reckoned by (2) does depend only on its constant velocity v=romega. On the contrary, if the rotational motion is uniformly accelerated, i.e. a constant force acts tangentially along the direction of motion, the proper time intervals $do depend$ on the angular acceleration alpha. III) Finally, in regard to the sign of the aging, the moving clock (2) measures always a $shorter$ interval of proper time with respect to (1).Comment: LaTex2e, 9 pages, no figures, no tables. It is the follow-on of the paper physics/040503

On the effects of the Dvali-Gabadadze-Porrati braneworld gravity on the orbital motion of a test particle

In this paper we explicitly work out the secular perturbations induced on all the Keplerian orbital elements of a test body to order O(e^2) in the eccentricity e by the weak-field long-range modifications of the usual Newton-Einstein gravity due to the Dvali-Gabadadze-Porrati (DGP) braneworld model. The Gauss perturbative scheme is used. It turns out that the argument of pericentre and the mean anomaly are affected by secular rates which are independent of the semimajor axis of the orbit of the test particle. The first nonvaishing eccentricity-dependent corrections are of order O(e^2). For circular orbits the Lue-Starkman (LS) effect on the pericentre is obtained. Some observational consequences are discussed for the Solar System planetary mean longitudes lambda which would undergo a 1.2\cdot 10^-3 arcseconds per century braneworld secular precession. According to recent data analysis over 92 years for the EPM2004 ephemerides, the 1-sigma formal accuracy in determining the Martian mean longitude amounts to 3\cdot 10^-3 milliarcseconds, while the braneworld effect over the same time span would be 1.159 milliarcseconds. The major limiting factor is the 2.6\cdot 10^-3 arcseconds per century systematic error due to the mismodelling in the Keplerian mean motion of Mars. A suitable linear combination of the mean longitudes of Mars and Venus may overcome this problem. The formal, 1-sigma obtainable observational accuracy would be \sim 7%. The systematic error due to the present-day uncertainties in the solar quadrupole mass moment, the Keplerian mean motions, the general relativistic Schwarzschild field and the asteroid ring would amount to some tens of percent.Comment: LaTex2e, 23 pages, 5 tables, 1 figure, 37 references. Second-order corrections in eccentricity explicitly added. Typos corrected. References update