We study spin relaxation in n-type bulk GaAs, due to the Dyakonov-Perel mechanism, using ensemble Monte Carlo methods. Our results confirm that spin relaxation time increases with the electronic density in the regime of moderate electronic concentrations and high temperature. We show that the electron-electron scattering in the non-degenerate regime significantly slows down spin relaxation. This result supports predictions by Glazov and Ivchenko. Most importantly, our findings highlight the importance of many-body interactions for spin dynamics: we show that only by properly taking into account electron-electron interactions within the simulations, results for the spin relaxation time-with respect to both electron density and temperature-will reach good quantitative agreement with corresponding experimental data. Our calculations contain no fitting parameters.

We present a novel Bayesian approach to semiotic dynamics, which is a cognitive analogue of the naming game model restricted to two conventions. The one-shot learning that characterizes the agent dynamics in the basic naming game is replaced by a word-learning process, in which agents learn a new word by generalizing from the evidence garnered through pairwise-interactions with other agents. The principle underlying the model is that agents -like humans -can learn from a few positive examples and that such a process is modeled in a Bayesian probabilistic framework. We show that the model presents some analogies but also crucial differences with respect to the dynamics of the basic two-convention naming game model. The model introduced aims at providing a starting point for the construction of a general framework for studying the combined effects of cognitive and social dynamics.

We study the effect of charged impurity screening on spin decoherence in bulk n-type GaAs, and analyse in details the effect of the use of different Born approximations applied to a linearized Thomas-Fermi screening theory. The spin relaxation times are calculated by ensemble Monte Carlo techniques, including electron-electron, electron-impurities, and electron-phonons scattering. We carefully choose a parameter region so that all the physical approximations hold, and, in particular, a Yukawa-type potential can be used to describe the screened Coulomb interaction and the Born series converges. Our results show that including the second order Born approximation yields much shorter spin relaxation times compared to the commonly implemented first Born approximation: spin relaxation times may be reduced by hundreds of picoseconds, with the first Born approximation overestimating results by 30% or more for a large region of parameters. Though our ensemble Monte Carlo simulations include electron-electron and electron-phonon interactions, when considering low to intermediate carrier densities and T > 50 K, but T smaller than the Fermi temperature, our results are in good agreement with Dyakonov-Perel theory when this includes electron-impurity interactions only, which supports this to be the most relevant scattering mechanism for bulk GaAs in this low-intermediate temperature regime.

The present contribution reviews a set of different versions of the basic naming game model, differing in the underlying topology or in the mechanisms regulating the interactions between agents. We include also a Bayesian naming game model recently introduced, which merges the social dynamics of the basic naming game model with the Bayesian learning framework introduced by Tenenbaum and co-workers. The latter model goes beyond the fixed nature of names and concepts of standard semiotic dynamics models and the corresponding one-shot learning process by describing dynamically how agents can generalize a concept from a few examples, according to principles of Bayesian inference.

We study the spin decoherence in n-type bulk GaAs for moderate electronic densities at room temperature using the Ensemble Monte Carlo method. We demonstrate that a technique called "third-body rejection method", devised by Ridley [B. K. Ridley, J. Phys. C: Solid State Phys. 10, 1589, 1977 can be successfully adapted to ensemble Monte Carlo method and used to tackle the problem of the electron-electron contribution to spin decoherence in the parameter region under study, where the electron-electron interaction can be reasonably described by a Yukawa potential. This scattering technique is employed in a doping region where one can expect that multiple collisions may play a role in carrier dynamics. By this technique we are able to calculate spin relaxation times which are in very good agreement with the experimental results found by Oertel et al.[S. Oertel, J. Hübner, M. Oestreich, Appl. Phys. Lett., 93, 13, 2008]. Through this method we show that the electron-electron scattering is overstimated in Born approximation, in agreement with previous results obtained by Kukkonen and Smith [C. A. Kukkonen, H. Smith, Phys. Rev. B, 8, 4601, 1973].