Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes

We study the topological signature of euclidean isometries in pair separations histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing the noise of individual PSH's using mean pair separations histograms we show how to distinguish between topological and statistical spikes. We report results of simulations that evince that topological spikes are not enough to distinguish between manifolds with the same set of Clifford translations in their covering groups, and that they are not the only signature of topology in PSH's corresponding to euclidean small universes. We also show how to evince the topological signature due to non-translational isometries.Comment: 15 pages, 5 figures, LaTeX2e; Added 2 references and inserted clarifying details. To appear in Phys. Lett. A (2000) in the present for

Vacuum friction on a rotating pair of atoms

Zero-point quantum fluctuations of the electromagnetic vacuum create the widely known London-van der Waals attractive force between two atoms. Recently, there was a revived interest in the interaction of rotating matter with the quantum vacuum. Here, we consider a rotating pair of atoms maintained by London van der Waals forces and calculate the frictional torque they experience due to zero-point radiation. Using a semi-classical framework derived from the Fluctuation Dissipation Theorem, we take into account the full electrostatic coupling between induced dipoles. Considering the case of zero temperature only, we find a braking torque proportional to the angular velocity and to the third power of the fine structure constant. Although very small compared to London van der Waals attraction, the torque is strong enough to induce the formation of dimers in binary collisions. This new friction phenomenon at the atomic level should induce a paradigm change in the explanation of irreversibility.Comment: 18 pages, 2 figures, to be published in PRL main text pp. 1 to 8, figures p. 9-10, Supplemental Material pp. 11 to 1

Distinguishing Marks of Simply-connected Universes

A statistical quantity suitable for distinguishing simply-connected Robertson-Walker (RW) universes is introduced, and its explicit expressions for the three possible classes of simply-connected RW universes with an uniform distribution of matter are determined. Graphs of the distinguishing mark for each class of RW universes are presented and analyzed.There sprout from our results an improvement on the procedure to extract the topological signature of multiply-connected RW universes, and a refined understanding of that topological signature of these universes studied in previous works.Comment: 13 pages, 4 figures, LaTeX2e. To appear in Int. J. Mod. Phys. D (2000

The exit-time problem for a Markov jump process

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.Comment: 15 pages, 7 figure

Can We See the Shape of the Universe?

This is a written version of a talk given at the Fifth Friedmann Seminar on recent work in Observational Cosmic Topology done in partial collaboration with Armando Bernui. We address three relevant questions related to the search for the size and shape of our Universe: (i) How do the actual observation of multiple images of certain cosmic objects, e.g. galaxy clusters, constrain the possible models for the shape of our Universe?, (ii) What kind of predictions can be done once a pair of cosmic objects have been identified to be topological images related by a translation?, and (iii) Is it possible to determine if two regions of space are topologically identified, even when distortions on the distributions of cosmic sources due to observational limitations are not negligible? We give examples answering the first two questions using the suggestion of Roukema and Edge that the clusters RXJ 1347.5-1145 and CL 09104+4109 might be topological images of the Coma cluster. For the third question, we suggest a method based on the analysis of PSH's noise correlations which seems to give a positive answer.Comment: 6 pages, latex2e, contribution to the 5th Alexander Friedmann Seminar on Gravitation and Cosmology, to appear in Int. J. Mod. Phys. A (2002). Macros: ws-ijmpa.cl

Wave function statistics at the symplectic 2D Anderson transition: bulk properties

The wavefunction statistics at the Anderson transition in a 2d disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents ($\alpha_0{=}2.172\pm 0.002, \tau_2{=}1.642\pm 0.004$), we report three qualitative results: (i) the anomalous dimensions are invariant under $q\to (1-q)$ which is in agreement with a recent analytical prediction and supports the universality hypothesis. (ii) The multifractal spectrum is not parabolic and therefore differs from behavior suspected, e.g., for (integer) quantum Hall transitions in a fundamental way. (iii) The critical fixed point satisfies conformal invariance.Comment: 4 pages, 3 figure