Random Access over Multi-Packet Reception Channels: A Mean-Field Approach

Thesis (Ph.D.)--University of Washington, 2016-06

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Field theory model for dark matter and dark energy in interaction

We propose a field theory model for dark energy and dark matter in interaction. Comparing the classical solutions of the field equations with the observations of the CMB shift parameter, baryonic acoustic oscillations, lookback time, and the Gold supernovae sample, we observe a possible interaction between dark sectors with energy decay from dark energy into dark matter. The observed interaction provides an alleviation to the coincidence problem.

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Entanglement of Low-Energy Excitations in Conformal Field Theory

In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.

A(2)((2)) parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A(2)((2))/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A(2)((2)) parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two. (C) 2002 Published by Elsevier Science B.V.

gl(2 vertical bar 2) current superalgebra and non-unitary conformal field theory

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2\2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented. (C) 2003 Elsevier B.V. All rights reserved.

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it, can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures. (C). 2004 American Institute of Physics.

Evolution of reputation in networks: A mean field game approach

This work models the competitive behaviour of individuals who maximize their own utility managing their network of connections with other individuals. Utility is taken as a synonym of reputation in this model. Each agent has to decide between two variables: the quality of connections and the number of connections. Hence, the reputation of an individual is a function of the number and the quality of connections within the network. On the other hand, individuals incur in a cost when they improve their network of contacts. The initial value of the quality and number of connections of each individual is distributed according to an initial (given) distribution. The competition occurs over continuous time and among a continuum of agents. A mean field game approach is adopted to solve the model, leading to an optimal trajectory for the number and quality of connections for each individual.

Quantum field theory approach to the optical conductivity of strained and deformed graphene

The computation of the optical conductivity of strained and deformed graphene is discussed within the framework of quantum field theory in curved spaces. The analytical solutions of the Dirac equation in an arbitrary static background geometry for one dimensional periodic deformations are computed, together with the corresponding Dirac propagator. Analytical expressions are given for the optical conductivity of strained and deformed graphene associated with both intra and interbrand transitions. The special case of small deformations is discussed and the result compared to the prediction of the tight-binding model.

Modeling premartensitic effects in Ni2MnGa: A mean-field and Monte Carlo simulation study

ic first-order transition line ending in a critical point. This critical point is responsible for the existence of large premartensitic fluctuations which manifest as broad peaks in the specific heat, not always associated with a true phase transition. The main conclusion is that premartensitic effects result from the interplay between the softness of the anomalous phonon driving the modulation and the magnetoelastic coupling. In particular, the premartensitic transition occurs when such coupling is strong enough to freeze the involved mode phonon. The implication of the results in relation to the available experimental data is discussed.

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.