Multiple scattering formalism for correlated systems: A KKR+DMFT approach

We present a charge and self-energy self-consistent computational scheme for correlated systems based on the Korringa-Kohn-Rostoker (KKR) multiple scattering theory with the many-body effects described by the means of dynamical mean field theory (DMFT). The corresponding local multi-orbital and energy dependent self-energy is included into the set of radial differential equations for the single-site wave functions. The KKR Green's function is written in terms of the multiple scattering path operator, the later one being evaluated using the single-site solution for the $t$-matrix that in turn is determined by the wave functions. An appealing feature of this approach is that it allows to consider local quantum and disorder fluctuations on the same footing. Within the Coherent Potential Approximation (CPA) the correlated atoms are placed into a combined effective medium determined by the dynamical mean field theory (DMFT) self-consistency condition. Results of corresponding calculations for pure Fe, Ni and Fe$_{x}$Ni$_{1-x}$ alloys are presented.Comment: 25 pages, 5 fig. acepted PR

Anthropic prediction in a large toy landscape

The successful anthropic prediction of the cosmological constant depends crucially on the assumption of a flat prior distribution. However, previous calculations in simplified landscape models showed that the prior distribution is staggered, suggesting a conflict with anthropic predictions. Here we analytically calculate the full distribution, including the prior and anthropic selection effects, in a toy landscape model with a realistic number of vacua, $N \sim 10^{500}$. We show that it is possible for the fractal prior distribution we find to behave as an effectively flat distribution in a wide class of landscapes, depending on the regime of parameter space. Whether or not this possibility is realized depends on presently unknown details of the landscape.Comment: 13 page

Measures for a Transdimensional Multiverse

The multiverse/landscape paradigm that has emerged from eternal inflation and string theory, describes a large-scale multiverse populated by "pocket universes" which come in a huge variety of different types, including different dimensionalities. In order to make predictions in the multiverse, we need a probability measure. In $(3+1)d$ landscapes, the scale factor cutoff measure has been previously shown to have a number of attractive properties. Here we consider possible generalizations of this measure to a transdimensional multiverse. We find that a straightforward extension of scale factor cutoff to the transdimensional case gives a measure that strongly disfavors large amounts of slow-roll inflation and predicts low values for the density parameter $\Omega$, in conflict with observations. A suitable generalization, which retains all the good properties of the original measure, is the "volume factor" cutoff, which regularizes the infinite spacetime volume using cutoff surfaces of constant volume expansion factor.Comment: 30 pages, 1 figure Minor revisions, reference adde

Probabilities in the inflationary multiverse

Inflationary cosmology leads to the picture of a "multiverse," involving an infinite number of (spatially infinite) post-inflationary thermalized regions, called pocket universes. In the context of theories with many vacua, such as the landscape of string theory, the effective constants of Nature are randomized by quantum processes during inflation. We discuss an analytic estimate for the volume distribution of the constants within each pocket universe. This is based on the conjecture that the field distribution is approximately ergodic in the diffusion regime, when the dynamics of the fields is dominated by quantum fluctuations (rather than by the classical drift). We then propose a method for determining the relative abundances of different types of pocket universes. Both ingredients are combined into an expression for the distribution of the constants in pocket universes of all types.Comment: 18 pages, RevTeX 4, 2 figures. Discussion of the full probability in Sec.VI is sharpened; the conclusions are strengthened. Note added explaining the relation to recent work by Easther, Lim and Martin. Some references adde

Dynamical compactification from de Sitter space

We show that D-dimensional de Sitter space is unstable to the nucleation of non-singular geometries containing spacetime regions with different numbers of macroscopic dimensions, leading to a dynamical mechanism of compactification. These and other solutions to Einstein gravity with flux and a cosmological constant are constructed by performing a dimensional reduction under the assumption of q-dimensional spherical symmetry in the full D-dimensional geometry. In addition to the familiar black holes, black branes, and compactification solutions we identify a number of new geometries, some of which are completely non-singular. The dynamical compactification mechanism populates lower-dimensional vacua very differently from false vacuum eternal inflation, which occurs entirely within the context of four-dimensions. We outline the phenomenology of the nucleation rates, finding that the dimensionality of the vacuum plays a key role and that among vacua of the same dimensionality, the rate is highest for smaller values of the cosmological constant. We consider the cosmological constant problem and propose a novel model of slow-roll inflation that is triggered by the compactification process.Comment: Revtex. 41 pages with 24 embedded figures. Minor corrections and added reference

Exploring a string-like landscape

We explore inflationary trajectories within randomly-generated two-dimensional potentials, considered as a toy model of the string landscape. Both the background and perturbation equations are solved numerically, the latter using the two-field formalism of Peterson and Tegmark which fully incorporates the effect of isocurvature perturbations. Sufficient inflation is a rare event, occurring for only roughly one in $10^5$ potentials. For models generating sufficient inflation, we find that the majority of runs satisfy current constraints from WMAP. The scalar spectral index is less than 1 in all runs. The tensor-to-scalar ratio is below the current limit, while typically large enough to be detected by next-generation CMB experiments and perhaps also by Planck. In many cases the inflationary consistency equation is broken by the effect of isocurvature modes.Comment: 24 pages with 8 figures incorporated, matches version accepted by JCA

An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning

An anthropic principle has made it possible to answer the difficult question of why the observable value of cosmological constant ($\Lambda\sim 10^{-47}$ GeV${}^4$) is so disconcertingly tiny compared to predicted value of vacuum energy density $\rho_{SUSY}\sim 10^{12}$ GeV${}^4$. Unfortunately, there is a darker side to this argument, as it consequently leads to another absurd prediction: that the probability to observe the value $\Lambda=0$ for randomly selected observer exactly equals to 1. We'll call this controversy an infrared divergence problem. It is shown that the IRD prediction can be avoided with the help of a Linde-Vanchurin {\em singular runaway measure} coupled with the calculation of relative Bayesian probabilities by the means of the {\em doomsday argument}. Moreover, it is shown that while the IRD problem occurs for the {\em prediction stage} of value of $\Lambda$, it disappears at the {\em explanatory stage} when $\Lambda$ has already been measured by the observer.Comment: 9 pages, RevTe

Anthropic prediction for a large multi-jump landscape

The assumption of a flat prior distribution plays a critical role in the anthropic prediction of the cosmological constant. In a previous paper we analytically calculated the distribution for the cosmological constant, including the prior and anthropic selection effects, in a large toy ``single-jump'' landscape model. We showed that it is possible for the fractal prior distribution we found to behave as an effectively flat distribution in a wide class of landscapes, but only if the single jump size is large enough. We extend this work here by investigating a large ($N \sim 10^{500}$) toy ``multi-jump'' landscape model. The jump sizes range over three orders of magnitude and an overall free parameter $c$ determines the absolute size of the jumps. We will show that for ``large'' $c$ the distribution of probabilities of vacua in the anthropic range is effectively flat, and thus the successful anthropic prediction is validated. However, we argue that for small $c$, the distribution may not be smooth.Comment: 33 pages, 7 figures Minor revisions made and references added. arXiv admin note: substantial text overlap with arXiv:0705.256

A Stringy Mechanism for A Small Cosmological Constant

Based on the probability distributions of products of random variables, we propose a simple stringy mechanism that prefers the meta-stable vacua with a small cosmological constant. We state some relevant properties of the probability distributions of functions of random variables. We then illustrate the mechanism within the flux compactification models in Type IIB string theory. As a result of the stringy dynamics, we argue that the generic probability distribution for the meta-stable vacua typically peaks with a divergent behavior at the zero value of the cosmological constant. However, its suppression in the single modulus model studied here is modest.Comment: 36 pages, 8 figure

SURVEY OF THE DEPENDENCE ON TEMPERATURE OF THE COERCIVITY OF GARNET-FILMS

The temperature dependence of the domain-wall coercive field of epitaxial magnetic garnets films has been investigated in the entire temperature range of the ferrimagnetic phase, and has been found to be described by a set of parametric exponents. In subsequent temperature regions different slopes were observed, with breaking points whose position was found to be sample dependent. A survey ba.ed on literature Data as well as on a large number of our own samples shows the general existence of this piecewise exponential dependence and the presence of the breaking points. This type of domain-wall coercive field temperature dependence was found in all samples in the large family of the epitaxial garnets (about 30 specimens of more than ten chemical compositionsj and also in another strongly anisotropic material (TbFeCo)