Ground state of a large number of particles on a frozen topography

Problems consisting in finding the ground state of particles interacting with a given potential constrained to move on a particular geometry are surprisingly difficult. Explicit solutions have been found for small numbers of particles by the use of numerical methods in some particular cases such as particles on a sphere and to a much lesser extent on a torus. In this paper we propose a general solution to the problem in the opposite limit of a very large number of particles M by expressing the energy as an expansion in M whose coefficients can be minimized by a geometrical ansatz. The solution is remarkably universal with respect to the geometry and the interaction potential. Explicit solutions for the sphere and the torus are provided. The paper concludes with several predictions that could be verified by further theoretical or numerical work.Comment: 9 pages, 9 figures, LaTeX fil

Crystalline Order on a Sphere and the Generalized Thomson Problem

We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree with simulations of long range power law interactions of the form 1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain boundaries is studied in the context of tilted crystalline order and the generality of our approach is illustrated with new results for square tilings on the sphere.Comment: 4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference typo fixe

Current Flow and Pair Creation at Low Altitude in Rotation Powered Pulsars' Force-Free Magnetospheres: Space-Charge Limited Flow

(shortened) We report the results of an investigation of particle acceleration and electron-positron plasma generation at low altitude in the polar magnetic flux tubes of Rotation Powered Pulsars, when the stellar surface is free to emit whatever charges and currents are demanded by the force-free magnetosphere. We observe novel behavior. a) When the current density is less than the Goldreich-Julian (GJ) value (0<j/j_{GJ}<1), space charge limited acceleration of the current carrying beam is mild, with the full GJ charge density being comprised of the charge density of the beam, co-existing with a cloud of electrically trapped particles with the same sign of charge as the beam. The voltage drops are on the order of mc^2/e, and pair creation is absent. b) When the current density exceeds the GJ value (j/j_{GJ}>1), the system develops high voltage drops, causing emission of gamma rays and intense bursts of pair creation. The bursts exhibit limit cycle behavior, with characteristic time scales somewhat longer than the relativistic fly-by time over distances comparable to the polar cap diameter (microseconds). c) In return current regions, where j/j_{GJ}<0, the system develops similar bursts of pair creation. In cases b) and c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady, finding that such steady flows can occupy only a small fraction of the current density parameter space of the force-free magnetospheric model. The generic polar flow dynamics and pair creation is strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage as a function of the applied current.Comment: 35 pages, 29 figures. Accepted for publication in MNRAS. Added new appendix, several minor changes in the tex

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure

Limits on models of the ultrahigh energy cosmic rays based on topological defects

An erratum exists for this article. Please see the description link below for details.Using the propagation of ultrahigh energy nucleons, photons, and electrons in the universal radiation backgrounds, we obtain limits on the luminosity of topological defect scenarios for the origin of the highest energy cosmic rays. The limits are set as a function of the mass of the X particles emitted by the cosmic strings or other defects, the cosmological evolution of the topological defects, and the strength of the extragalactic magnetic fields. The existing data on the cosmic ray spectrum and on the isotropic 100 MeV gamma-ray background limit significantly the parameter space in which topological defects can generate the flux of the highest energy cosmic rays, and rule out models with the standard X-particle mass of 10¹⁶GeV and higher.R. J. Protheroe and Todor Stane

Corrections to flat-space particle dynamics arising from space granularity

The construction of effective Hamiltonians describing corrections to flat space particle dynamics arising from the granularity of space at very short distances is discussed in the framework of an heuristic approach to the semiclassical limit of loop quantum gravity. After some general motivation of the subject, a brief non-specialist introduction to the basic tools employed in the loop approach is presented. The heuristical semiclassical limit is subsequently defined and the application to the case of photons and spin 1/2 fermions is described. The resulting modified Maxwell and Dirac Hamiltonians, leading in particular to Planck scale corrections in the energy-momentum relations, are presented. Alternative interpretations of the results and their limitations, together with other approaches are briefly discussed along the text. Three topics related to the above methods are reviewed: (1) The determination of bounds to the Lorentz violating parameters in the fermionic sector, obtained from clock comparison experiments.(2) The calculation of radiative corrections in preferred frames associated to space granularity in the framework of a Yukawa model for the interactions and (3) The calculation of synchrotron radiation in the framework of the Myers-Pospelov effective theories describing Lorentz invariance violations, as well as a generalized approach to radiation in Planck scale modified electrodynamics. The above exploratory results show that quantum gravity phenomenology provides observational guidance in the construction of quantum gravity theories and opens up the possibility of probing Planck scale physics.Comment: 49 pages, 6 figures and 4 tables. Extended version of the talk given at the 339-th WE-Heraeus-Seminar: Special Relativity, will it survive the next 100 years?, Potsdam, february 200

Asymptotic conditions of motion for radiating charged particles

Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein- Infeld-Hoffmann (EIH) surface integral method. While superficially similar to the Abraham-Lorentz and Lorentz-Dirac (ALD) equations of motion, these conditions differ from them in several fundamental ways. They are not equations of motion in the usual sense but rather a set of conditions which these motions must obey in the asymptotic future of an initial value surface. In addition to being asymptotic, these conditions of motion are approximate and apply, as do the original EIH equations, only to slowly moving systems. Also, they do not admit the run- away solutions of these other equations. As in the original EIH work, they are integrability conditions gotten from integrating the empty-space (i.e., source free) Einstein-Maxwell equations of general relativity over closed two-surfaces surrounding the sources of the fields governed by these equations. No additional ad hoc assumptions, such as the form of a force law or the introduction of inertial reaction terms, needed to derive the ALD equations are required for this purpose. Nor is there a need for any of the infinite mass renormalizations that are required in deriving these other equations.Comment: 15 page

Radiation in Lorentz violating electrodynamics

Synchrotron radiation is analyzed in the classical effective Lorentz invariance violating model of Myers-Pospelov. Within the full far-field approximation we compute the electric and magnetic fields, the angular distribution of the power spectrum and the total emitted power in the m-th harmonic, as well as the polarization. We find the appearance of rather unexpected and large amplifying factors, which go together with the otherwise negligible naive expansion parameter. This opens up the possibility of further exploring Lorentz invariance violations by synchrotron radiation measurements in astrophysical sources where these amplifying factors are important.Comment: Presented at the Second Mexican Meeting on Theoretical and Experimental Physics, El Colegio Nacional, Mexico City, 6-10 September 200

Quantum optical dipole radiation fields

We introduce quantum optical dipole radiation fields defined in terms of photon creation and annihilation operators. These fields are identified through their spatial dependence, as the components of the total fields that survive infinitely far from the dipole source. We use these radiation fields to perturbatively evaluate the electromagnetic radiated energy-flux of the excited dipole. Our results indicate that the standard interpretation of a bare atom surrounded by a localised virtual photon cloud, is difficult to sustain, because the radiated energy-flux surviving infinitely far from the source contains virtual contributions. It follows that there is a clear distinction to be made between a radiative photon defined in terms of the radiation fields and a real photon, whose identification depends on whether or not a given process conserves the free energy. This free energy is represented by the difference between the total dipole-field Hamiltonian and its interaction component

The nature of the highest energy cosmic rays

Ultra high energy gamma rays produce electron--positron pairs in interactions on the geomagnetic field. The pair electrons suffer magnetic bremsstrahlung and the energy of the primary gamma ray is shared by a bunch of lower energy secondaries. These processes reflect the structure of the geomagnetic field and cause experimentally observable effects. The study of these effects with future giant air shower arrays can identify the nature of the highest energy cosmic rays as either gamma-rays or nuclei.Comment: 15 pages of RevTeX plus 6 postscript figures, tarred, gzipped and uuencoded. Subm. to Physical Review