Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Perturbations on domain walls and strings: A covariant theory

A covariant formalism is developed for describing perturbations on vacuum domain walls and strings. The treatment applies to arbitrary domain walls in (N+1)-dimensional flat spacetime, including the case of bubbles of a true vacuum nucleating in a false vacuum. Straight strings and planar walls in de Sitter space, as well as closed strings and walls nucleating during inflation, are also considered. Perturbations are represented by a scalar field defined on the unperturbed wall or string world sheet. In a number of interesting cases, this field has a tachyonic mass and a nonminimal coupling to the world-sheet curvature.

Black holes from nucleating strings

We evaluate the probability that a loop of string that has spontaneously nucleated during inflation will form a black hole upon collapse, after the end of inflation. We then use the observational bounds on the density of primordial black holes to put constraints on the parameters of the model. Combining these constraints with current upper limits on the expansion rate during inflation, we conclude that the density of black holes formed from nucleating strings is too low to be observed. Also, constraints on domain wall nucleation and monopole pair production during inflation are briefly discussed.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

Classical anisotropies in models of open inflation

In the simplest model of open inflation there are two inflaton fields decoupled from each other. One of them, the tunneling field, produces a first stage of inflation which prepares the ground for the nucleation of a highly symmetric bubble. The other, a free field, drives a second period of slow-roll inflation inside the bubble. However, the second field also evolves during the first stage of inflation, which to some extent breaks the needed symmetry. We show that this generates large supercurvature anisotropies which, together with the results of Tanaka and Sasaki, rule out this class of simple models (unless, of course, Omega0 is sufficiently close to 1). The problem does not arise in modified models where the second field does not evolve in the first stage of inflation.

Correlations between black holes formed in cosmic string breaking

An analysis of cosmic string breaking with the formation of black holes attached to the ends reveals a remarkable feature: the black holes can be correlated or uncorrelated. We find that, as a consequence, the number-of-states enhancement factor in the action governing the formation of uncorrelated black holes is twice the one for a correlated pair. We argue that when an uncorrelated pair forms at the ends of the string, the physics involved is more analogous to thermal nucleation than to particle-antiparticle creation. Also, we analyze the process of intercommuting strings induced by black hole annihilation and merging. Finally, we discuss the consequences for grand unified strings. The process whereby uncorrelated black holes are formed yields a rate which significantly improves over those previously considered, but still not enough to modify string cosmology. 1995 The American Physical Society.

Dissipation, noise and vacuum decay in quantum field theory

We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long- and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function describing the state of long-wavelength modes, and thereby to a finite activation rate even at zero temperature. This effect can make a substantial contribution to the total decay rate.

Microstates of a neutral black hole in M theory

We consider vacuum solutions in M theory of the form of a five-dimensional Kaluza-Klein black hole cross T6. In a certain limit, these include the five-dimensional neutral rotating black hole (cross T6). From a type-IIA standpoint, these solutions carry D0 and D6 charges. We show that there is a simple D-brane description which precisely reproduces the Hawking-Bekenstein entropy in the extremal limit, even though supersymmetry is completely broken.

Self-dynamic structure factor of dense liquids: Theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnstrm and Sjgren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Financial crisis: theory and practice

In the last 50 years, we have had approximately 40 events with characteristics related to financial crisis. The most severe crisis was in 1929, when the financial markets plummet and the US gross domestic product decline in more than 30 percent. Recently some years ago, a new crisis developed in the United States, but instantly caused consequences and effects in the rest of the world.This new economic and financial crisis has increased the interest and motivation for the academic community, professors and researchers, to understand the causes and effects of the crisis, to learn from it. This is the one of the main reasons for the compilation of this book, which begins with a meeting of a group of IAFI researchers from the University of Barcelona, where researchers form Mexico and Spain, explain causes and consequences of the crisis of 2007.For that reason, we believed this set of chapters related to methodologies, applications and theories, would conveniently explained the characteristics and events of the past and future financial crisisThis book consists in 3 main sections, the first one called "State of the Art and current situation", the second named "Econometric applications to estimate crisis time periods" , and the third one "Solutions to diminish the effects of the crisis". The first section explains the current point of view of many research papers related to financial crisis, it has 2 chapters. In the first one, it describe and analyzes the models that historically have been used to explain financial crisis, furthermore, it proposes to used alternative methodologies such as Fuzzy Cognitive Maps. On the other hand , Chapter 2 , explains the characteristics and details of the 2007 crisis from the US perspective and its comparison to 1929 crisis, presenting some effects in Mexico and Latin America.The second section presents two econometric applications to estimate possible crisis periods. For this matter, Chapter 3, studies 3 Latin-American countries: Argentina, Brazil and Peru in the 1994 crisis and estimates the multifractal characteristics to identify financial and economic distress.Chapter 4 explains the crisis situations in Argentina (2001), Mexico (1994) and the recent one in the United States (2007) and its effects in other countries through a financial series methodology related to the stock market.The last section shows an alternative to prevent the effects of the crisis. The first chapter explains the financial stability effects through the financial system regulation and some globalization standards. Chapter 6, study the benefits of the Investor activism and a way to protect personal and national wealth to face the financial crisis risks.

Extrapolation theory for the real interpolation method

We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega