Analytical results for long time behavior in anomalous diffusion

We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor $\lambda$. We obtain as well an exact expression for $\lambda$ for all kinds of diffusion. Moreover, we show that $\lambda$ is a universal parameter determined by the diffusion exponent. The results are then compared with numerical calculations and very good agreement is observed. The method is general and may be applied to many types of stochastic problem

Quantum Properties of a Which-Way Detector

We explore quantum properties of a which-way detector using three versions of an idealized two slit arrangements. Firstly we derive complementarity relations for the detector; secondly we show how the "experiment" may be altered in such a way that using single position measurement on the screen we can obtain quantum erasure. Finally we show how to construct a superposition of "wave" and "particle" components

Collapse of Primordial Clouds

We present here studies of collapse of purely baryonic Population III objects with masses ranging from $10M_\odot$ to $10^6M_\odot$. A spherical Lagrangian hydrodynamic code has been written to study the formation and evolution of the primordial clouds, from the beginning of the recombination era ($z_{rec} \sim 1500$) until the redshift when the collapse occurs. All the relevant processes are included in the calculations, as well as, the expansion of the Universe. As initial condition we take different values for the Hubble constant and for the baryonic density parameter (considering however a purely baryonic Universe), as well as different density perturbation spectra, in order to see their influence on the behavior of the Population III objects evolution. We find, for example, that the first mass that collapses is $8.5\times10^4M_\odot$ for $h=1$, $\Omega=0.1$ and $\delta_i={\delta\rho / \rho}=(M / M_o)^{-1/3}(1+z_{rec})^{-1}$ with the mass scale $M_o=10^{15}M_\odot$. For $M_o=4\times10^{17}M_\odot$ we obtain $4.4\times10^{4}M_\odot$ for the first mass that collapses. The cooling-heating and photon drag processes have a key role in the collapse of the clouds and in their thermal history. Our results show, for example, that when we disregard the Compton cooling-heating, the collapse of the objects with masses $>8.5\times10^4M_\odot$ occurs earlier. On the other hand, disregarding the photon drag process, the collapse occurs at a higher redshift.Comment: 10 pages, MN plain TeX macros v1.6 file, 9 PS figures. Also available at http://www.iagusp.usp.br/~oswaldo (click "OPTIONS" and then "ARTICLES"). MNRAS in pres

Collapse of Primordial Clouds II. The Role of Dark Matter

In this article we extend the study performed in our previous article on the collapse of primordial objects. We here analyze the behavior of the physical parameters for clouds ranging from $10^7M_\odot$ to $10^{15}M_\odot$. We studied the dynamical evolution of these clouds in two ways: purely baryonic clouds and clouds with non-baryonic dark matter included. We start the calculations at the beginning of the recombination era, following the evolution of the structure until the collapse (that we defined as the time when the density contrast of the baryonic matter is greater than $10^4$). We analyze the behavior of the several physical parameters of the clouds (as, e.g., the density contrast and the velocities of the baryonic matter and the dark matter) as a function of time and radial position in the cloud. In this study all physical processes that are relevant to the dynamical evolution of the primordial clouds, as for example photon-drag (due to the cosmic background radiation), hydrogen molecular production, besides the expansion of the Universe, are included in the calculations. In particular we find that the clouds, with dark matter, collapse at higher redshift when we compare the results with the purely baryonic models. As a general result we find that the distribution of the non-baryonic dark matter is more concentrated than the baryonic one. It is important to stress that we do not take into account the putative virialization of the non-baryonic dark matter, we just follow the time and spatial evolution of the cloud solving its hydrodynamical equations. We studied also the role of the cooling-heating processes in the purely baryonic clouds.Comment: 8 pages, MN plain TeX macros v1.6 file, 13 PS figures. Also available at http://www.iagusp.usp.br/~oswaldo (click "OPTIONS" and then "ARTICLES"). MNRAS in pres