Tag Archives: Classical Physics

Non-equilibrium statistical field theory for classical particles: Initially correlated canonical ensembles [CL]

Posted on by

http://arxiv.org/abs/1411.0806


Building upon the recent pioneering work by Mazenko and Das and Mazenko, we develop the generating functional for an initially correlated canonical ensemble of classical microscopic particles obeying Hamiltonian dynamics. Our primary target is cosmic structure formation, where initial Gaussian correlations in phase space are believed to be set by inflation. Despite this specific motivation, our results may be useful for wider classes of applications in different fields of physics where the non-equilibrium statistics of correlated classical particle ensembles is to be studied. We give an exact expression for the generating functional and work out two approximations with linear and quadratic initial momentum correlations in detail. Cumulants of the density or other collective fields can be immediately derived from our results once the initial correlations have been defined.

Read this paper on arXiv…

M. Bartelmann, F. Fabis, D. Berg, et. al.
Wed, 5 Nov 14
42/61

Comments: 13 pages, no figures

Trajectories of point particles in cosmology and the Zel'dovich approximation [CL]

Posted on by

http://arxiv.org/abs/1411.0805


Using a Green’s function approach, we compare the trajectories of classical Hamiltonian point particles in an expanding space-time to the effectively inertial trajectories in the Zel’dovich approximation. It is shown that the effective gravitational potential accelerating the particles relative to the Zel’dovich trajectories vanishes exactly initially as a consequence of the continuity equation, and acts only during a short, early period. The Green’s function approach suggests an iterative scheme for improving the Zel’dovich trajectories, which can be analytically solved. We construct these trajectories explicitly and show how they interpolate between the Zel’dovich and the exact trajectories. The effective gravitational potential acting on the improved trajectories is substantially smaller at late times than the potential acting on the exact trajectories. The results may be useful for Lagrangian perturbation theory and for numerical simulations.

Read this paper on arXiv…

M. Bartelmann
Wed, 5 Nov 14
44/61

Comments: 7 pages, 3 figures

Newtonian wormholes [CL]

Posted on by

http://arxiv.org/abs/1409.3231


A wormhole solution in Newtonian gravitation, enhanced through an equation relating the Ricci scalar to the mass density, is presented. The wormhole inhabits a spherically symmetric curved space, with one throat and two asymptotically flat regions. Particle dynamics in this geometry is studied, and the three distinct dynamical radii, namely, the geodesic, circumferential, and curvature radii, appear naturally in the study of circular motion. Generic motion is also analysed. A limiting case, although inconclusive, suggests the possibility of having a Newtonian black hole in a region of finite (nonzero) size.

Read this paper on arXiv…

J. Lemos and P. Luz
Fri, 12 Sep 14
25/61

Comments: 28 pages, 5 figures. Accepted for publication in General Relativity and Gravitation

A fully relativistic radial fall [CL]

Posted on by

http://arxiv.org/abs/1407.5391


Radial fall has historically played a momentous role. It is one of the most classical problems, the solutions of which represent the level of understanding of gravitation in a given epoch. A {\it gedankenexperiment} in a modern frame is given by a small body, like a compact star or a solar mass black hole, captured by a supermassive black hole. The mass of the small body itself and the emission of gravitational radiation cause the departure from the geodesic path due to the back-action, that is the self-force. For radial fall, as any other non-adiabatic motion, the instantaneous identity of the radiated energy and the loss of orbital energy cannot be imposed and provide the perturbed trajectory. In the first part of this letter, we present the effects due to the self-force computed on the geodesic trajectory in the background field. Compared to the latter trajectory, in the Regge-Wheeler, harmonic and all others smoothly related gauges, a far observer concludes that the self-force pushes inward (not outward) the falling body, with a strength proportional to the mass of the small body for a given large mass; further, the same observer notes an higher value of the maximal coordinate velocity, this value being reached earlier on during infall. In the second part of this letter, we implement a self-consistent approach for which the trajectory is iteratively corrected by the self-force, this time computed on osculating geodesics. Finally, we compare the motion driven by the self-force without and with self-consistent orbital evolution. Subtle differences are noticeable, even if self-force effects have hardly the time to accumulate in such a short orbit.

Read this paper on arXiv…

A. Spallicci and P. Ritter
Tue, 22 Jul 14
31/45

Comments: To appear in Int. J. Geom. Meth. Mod. Phys

Skewon field and cosmic wave propagation [CL]

Posted on by

http://arxiv.org/abs/1312.3056


For the study of the gravitational coupling of electromagnetism and the equivalence principle, we have used the spacetime constitutive tensor density {chi}ijkl, and discovered the nonmetric (axion) part (A){chi}ijkl (equal to {phi}eijkl) of {chi}ijkl worthy investigation. Since we have used Lagrangian formalism, {chi}ijkl is effectively symmetric under the interchange of index pairs, ij and kl, and has 21 independent degrees of freedom. Hehl, Obukhov and Rubilar have started from charge-flux formalism to study electromagnetism, discovered the antisymmetric part (Sk){chi}ijkl (15 degrees of freedom) of {chi}ijkl under the interchange of index pairs ij and kl worthy investigation, and called it skewon field. In this paper, we study the propagation of the Hehl-Obukhov-Rubilar skewon field in weak gravity field/dilute matter or with weak violation of the Einstein Equivalence Principle (EEP), and further classify it into Type I and Type II skewons. From the dispersion relation we show that no dissipation/no amplification condition implies that the additional skewon field must be of Type II. For Type I skewon field, the dissipation/amplification is proportional to the frequency and the CMB spectrum would deviate from Planck spectrum. From the high precision agreement of the CMB spectrum to 2.755 K Planck spectrum, we constrain the Type I cosmic skewon field (SkI){chi}ijkl to less than a few x 10-35. The skewon part of constitutive tensor constructed from asymmetric metric is of Type II, hence is allowed. This study may also find applications in macroscopic electrodynamics in the case of laser pumped medium or dissipative medium.

Read this paper on arXiv…

Thu, 12 Dec 13
49/54