Harnessing the Bethe Free Energy

Gibbs measures induced by random factor graphs play a prominent role in computer science, combinatorics and physics. A key problem is to calculate the typical value of the partition function. According to the "replica symmetric cavity method", a heuristic that rests on non-rigorous considerations from statistical mechanics, in many cases this problem can be tackled by way of maximising a functional called the "Bethe free energy". In this paper we prove that the Bethe free energy upper-bounds the partition function in a broad class of models. Additionally, we provide a sufficient condition for this upper bound to be tight

Proton Stopping Power of Different Density Profile Plasmas

In this work, the stopping power of a partially ionized plasma is analyzed by means of free electron stopping and bound electron stopping. For the first one, the RPA dielectric function is used, and for the latter one, an interpolation of high and low projectile velocity formulas is used. The dynamical energy loss of an ion beam inside a plasma is estimated by using an iterative scheme of calculation. The Abel inversion is also applied when we have a plasma with radial symmetry. Finally, we compare our methods with two kind of plasmas. In the first one, we estimate the energy loss in a plasma created by a laser prepulse, whose density is approximated by a piecewise function. For the latter one, a radial electron density is supposed and the stopping is obtained as function of radius from the calculated lateral points. In both cases, the dependence with the density profile is observed.Comment: 5 pages, 7 figure

Belief Propagation on replica symmetric random factor graph models

According to physics predictions, the free energy of random factor graph models that satisfy a certain "static replica symmetry" condition can be calculated via the Belief Propagation message passing scheme [Krzakala et al., PNAS 2007]. Here we prove this conjecture for two general classes of random factor graph models, namely Poisson random factor graphs and random regular factor graphs. Specifically, we show that the messages constructed just as in the case of acyclic factor graphs asymptotically satisfy the Belief Propagation equations and that the free energy density is given by the Bethe free energy formula

Galactic-scale macro-engineering: Looking for signs of other intelligent species, as an exercise in hope for our own

If we consider Big History as simply 'our' example of the process of cosmic evolution playing out, then we can seek to broaden our view of our possible fate as a species by asking questions about what paths or trajectories other species' own versions of Big History might take or have taken. This paper explores the broad outlines of possible scenarios for the evolution of long-lived intelligent engineering species---scenarios which might have been part of another species' own Big History story, or which may yet lie ahead in our own distant future. A sufficiently long-lived engineering-oriented species may decide to undertake a program of macro-engineering projects that might eventually lead to a re-engineered galaxy so altered that its artificiality may be detectable from Earth. We consider activities that lead ultimately to a galactic structure consisting of a central inner core surrounded by a more distant ring of stars separated by a relatively sparser 'gap', where star systems and stellar materials may have been removed, 'lifted' or turned into Dyson Spheres. When one looks to the sky, one finds that such galaxies do indeed exist---including the beautiful ringed galaxy known as 'Hoag's Object' (PGC 54559) in the constellation Serpens. This leads us to pose the question: Is Hoag's Object an example of galaxy-scale macro-engineering? And this suggests a program of possible observational activities and theoretical explorations, several of which are presented here, that could be carried out in order to begin to investigate this beguiling question.Comment: 17 pages. Published in: Teaching and Researching Big History: Exploring a New Scholarly Field; L. Grinin, D. Baker, E. Quaedackers and A. Korotayev (eds). Uchitel Publ House, Volgograd, Russia, 2014, Chapter 14, pp. 283-304. ISBN: 978-5-7057-4027-

Longitudinal hydrodynamics from event-by-event Landau initial conditions

We investigate three-dimensional ideal hydrodynamic evolution, with Landau initial conditions, incorporating event-by-event variation with many events and transverse density inhomogeneities. We show that the transition to boost-invariant flow occurs too late for realistic setups, with corrections of \order{20-30\%} expected at freezeout for most scenarios. Moreover, the deviation from boost-invariance is correlated with both transverse flow and elliptic flow, with the more highly transversely flowing regions also showing the most violation of boost invariance. Therefore, if longitudinal flow is not fully developed at the early stages of heavy ion collisions, hydrodynamics where boost-invariance holds at mid-rapidity is inadequate to extract transport coefficients of the quark-gluon plasma. We conclude by arguing that developing experimental probes of boost invariance is necessary, and suggest some promising directions in this regard.Comment: Accepted for publication, Phys.Rev.

Polytope of Correct (Linear Programming) Decoding and Low-Weight Pseudo-Codewords

We analyze Linear Programming (LP) decoding of graphical binary codes operating over soft-output, symmetric and log-concave channels. We show that the error-surface, separating domain of the correct decoding from domain of the erroneous decoding, is a polytope. We formulate the problem of finding the lowest-weight pseudo-codeword as a non-convex optimization (maximization of a convex function) over a polytope, with the cost function defined by the channel and the polytope defined by the structure of the code. This formulation suggests new provably convergent heuristics for finding the lowest weight pseudo-codewords improving in quality upon previously discussed. The algorithm performance is tested on the example of the Tanner [155, 64, 20] code over the Additive White Gaussian Noise (AWGN) channel.Comment: 6 pages, 2 figures, accepted for IEEE ISIT 201

Nonlinear photocurrents in two-dimensional systems based on graphene and boron nitride

DC photoelectrical currents can be generated purely as a non-linear effect in uniform media lacking inversion symmetry without the need for a material junction or bias voltages to drive it, in what is termed photogalvanic effect. These currents are strongly dependent on the polarization state of the radiation, as well as on topological properties of the underlying Fermi surface such as its Berry curvature. In order to study the intrinsic photogalvanic response of gapped graphene (GG), biased bilayer graphene (BBG), and hexagonal boron nitride (hBN), we compute the non-linear current using a perturbative expansion of the density matrix. This allows a microscopic description of the quadratic response to an electromagnetic field in these materials, which we analyze as a function of temperature and electron density. We find that the intrinsic response is robust across these systems and allows for currents in the range of pA cm/W to nA cm/W. At the independent-particle level, the response of hBN-based structures is significant only in the ultra-violet due to their sizeable band-gap. However, when Coulomb interactions are accounted for by explicit solution of the Bethe-Salpeter equation, we find that the photoconductivity is strongly modified by transitions involving exciton levels in the gap region, whose spectral weight dominates in the overall frequency range. Biased bilayers and gapped monolayers of graphene have a strong photoconductivity in the visible and infrared window, allowing for photocurrent densities of several nA cm/W. We further show that the richer electronic dispersion of BBG at low energies and the ability to change its band-gap on demand allows a higher tunability of the photocurrent, including not only its magnitude but also, and significantly, its polarity.Comment: Updating with published version and respective references; 14 pages, 11 figure