Complexity, action, and black holes

Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the "Wheeler-DeWitt" patch). We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are the fastest computers in nature.Comment: 55+14 pages, many figures. v2: (so many) typos fixed, references adde

Lectures on Holographic Space Time

Summary of three talks on the Holographic Space Time models of early universe cosmology, particle physics, and the asymptotically de Sitter final state of our universe.Comment: LaTex2e. 32 page

Are black holes over-produced during preheating?

We provide a simple but robust argument that primordial black hole (PBH) production generically does {\em not} exceed astrophysical bounds during the resonant preheating phase after inflation. This conclusion is supported by fully nonlinear lattice simulations of various models in two and three dimensions which include rescattering but neglect metric perturbations. We examine the degree to which preheating amplifies density perturbations at the Hubble scale and show that at the end of the parametric resonance, power spectra are universal, with no memory of the power spectrum at the end of inflation. In addition we show how the probability distribution of density perturbations changes from exponential on very small scales to Gaussian when smoothed over the Hubble scale -- the crucial length for studies of primordial black hole formation -- hence justifying the standard assumption of Gaussianity.Comment: 12 pages, 8 figures, revtex, added references for section

Phenomenology of a Pseudo-Scalar Inflaton: Naturally Large Nongaussianity

Many controlled realizations of chaotic inflation employ pseudo-scalar axions. Pseudo-scalars \phi are naturally coupled to gauge fields through c \phi F \tilde{F}. In the presence of this coupling, gauge field quanta are copiously produced by the rolling inflaton. The produced gauge quanta, in turn, source inflaton fluctuations via inverse decay. These new cosmological perturbations add incoherently with the "vacuum" perturbations, and are highly nongaussian. This provides a natural mechanism to generate large nongaussianity in single or multi field slow-roll inflation. The resulting phenomenological signatures are highly distinctive: large nongaussianity of (nearly) equilateral shape, in addition to detectably large values of both the scalar spectral tilt and tensor-to-scalar ratio (both being typical of large field inflation). The WMAP bound on nongaussianity implies that the coupling, c, of the pseudo-scalar inflaton to any gauge field must be smaller than about 10^{2} M_p^{-1}.Comment: 45 pages, 7 figure

Understanding Galaxy Formation and Evolution

The old dream of integrating into one the study of micro and macrocosmos is now a reality. Cosmology, astrophysics, and particle physics intersect in a scenario (but still not a theory) of cosmic structure formation and evolution called Lambda Cold Dark Matter (LCDM) model. This scenario emerged mainly to explain the origin of galaxies. In these lecture notes, I first present a review of the main galaxy properties, highlighting the questions that any theory of galaxy formation should explain. Then, the cosmological framework and the main aspects of primordial perturbation generation and evolution are pedagogically detached. Next, I focus on the ``dark side'' of galaxy formation, presenting a review on LCDM halo assembling and properties, and on the main candidates for non-baryonic dark matter. It is shown how the nature of elemental particles can influence on the features of galaxies and their systems. Finally, the complex processes of baryon dissipation inside the non-linearly evolving CDM halos, formation of disks and spheroids, and transformation of gas into stars are briefly described, remarking on the possibility of a few driving factors and parameters able to explain the main body of galaxy properties. A summary and a discussion of some of the issues and open problems of the LCDM paradigm are given in the final part of these notes.Comment: 50 pages, 10 low-resolution figures (for normal-resolution, DOWNLOAD THE PAPER (PDF, 1.9 Mb) FROM http://www.astroscu.unam.mx/~avila/avila.pdf). Lectures given at the IV Mexican School of Astrophysics, July 18-25, 2005 (submitted to the Editors on March 15, 2006

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Energy level dynamics across the many-body localization transition

The level dynamics across the many body localization transition is examined for XXZ-spin model with a random magnetic field. We compare different scenaria of parameter dependent motion in the system and consider measures such as level velocities, curvatures as well as their fidelity susceptibilities. Studying the ergodic phase of the model we find that the level dynamics does not reveal the commonly believed universal behavior after rescaling the curvatures by the level velocity variance. At the same time, distributions of level curvatures and fidelity susceptibilities coincide with properly rescaled distributions for Gaussian Orthogonal Ensemble of random matrices. Profound differences exists depending on way the level dynamics is imposed in the many-body localized phase of the model in which the level dynamics can be understood with the help of local integrals of motion.Comment: version close to that accepted in PR