We study the effects of primordial magnetic fields on the inflationary potential in the context of a warm inflation scenario. The model, based on global supersymmetry with a new-inflation-type potential and a coupling between the inflaton and a heavy
intermediate superfield, is already known to preserve the flatness required for slow-roll conditions even after including thermal contributions. Here we show that the magnetic field makes the potential even flatter, retarding the transition and rendering it smoother.
Recently, Harrington et al. (2013) presented an outreach effort to introduce school students to network science and explain why researchers who study networks should be involved in such outreach activities. Based on the modules they designed and thei
r comments on the success and failures of the activity, we have carried out a sequel with students from a high school in Madrid, Spain. We report on how we developed it and the changes we made to the original material.
We present preliminary results on the possible effects that primordial magnetic fields can have for a warm inflation scenario, based on global supersymmetry, with a new-inflation-type potential. This work is motivated by two considerations: first, ma
gnetic fields seem to be present in the universe on all scales, which rises the possibility that they could also permeate the early universe; second, the recent emergence of inflationary models where the inflaton is not assumed to be isolated but instead it is taken as an interacting field, even during the inflationary expansion. The effects of magnetic fields are included resorting to Schwinger proper time method.
In this paper we calculate the non-perturbative Euler-Heisenberg Lagrangian for massless QED in a strong magnetic field $H$, where the breaking of the chiral symmetry is dynamically catalyzed by the external magnetic field via the formation of an ele
ctro-positron condensate. This chiral condensate leads to the generation of dynamical parameters that have to be found as solutions of non-perturbative Schwinger-Dyson equations. Since the electron-positron pairing mechanism leading to the breaking of the chiral symmetry is mainly dominated by the contributions from the infrared region of momenta much smaller than $sqrt{eH}$, the magnetic field introduces a dynamical ultraviolet cutoff in the theory that also enters in the non-perturbative Euler-Heisenberg action. Using this action, we show that the system exhibits a significant paraelectricity in the direction parallel to the magnetic field. The nonperturbative nature of this effect is reflected in the non-analytic dependence of the obtained electric susceptibility on the fine-structure constant. The strong paraelectricity in the field direction is linked to the orientation of the electric dipole moments of the pairs that form the chiral condensate. The large electric susceptibility can be used to detect the realization of the magnetic catalysis of chiral symmetry breaking in physical systems.
During the last few years, much research has been devoted to strategic interactions on complex networks. In this context, the Prisoners Dilemma has become a paradigmatic model, and it has been established that imitative evolutionary dynamics lead to
very different outcomes depending on the details of the network. We here report that when one takes into account the real behavior of people observed in the experiments, both at the mean-field level and on utterly different networks the observed level of cooperation is the same. We thus show that when human subjects interact in an heterogeneous mix including cooperators, defectors and moody conditional cooperators, the structure of the population does not promote or inhibit cooperation with respect to a well mixed population.
We study symmetry restoration at finite temperature in the standard model during the electroweak phase transition in the presence of a weak magnetic field. We compute the finite temperature effective potential up to the contribution of ring diagrams,
using the broken phase degrees of freedom, and keep track of the gauge parameter dependence of the results. We show that under these conditions, the phase transition becomes stronger first order.
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that
describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.
We study the electron propagator in quantum electrodynamics in lower dimensions. In the case of free electrons, it is well known that the propagator in momentum space takes the simple form $S_F(p)=1/(gammacdot p-m)$. In the presence of external elect
romagnetic fields, electron asymptotic states are no longer plane-waves, and hence the propagator in the basis of momentum eigenstates has a more intricate form. Nevertheless, in the basis of the eigenfunctions of the operator $(gammacdot Pi)^2$, where $Pi_mu$ is the canonical momentum operator, it acquires the free form $S_F(p)=1/(gammacdot bar{p}-m)$ where $bar{p}_mu$ depends on the dynamical quantum numbers. We construct the electron propagator in the basis of the $(gammacdot Pi)^2$ eigenfunctions. In the (2+1)-dimensional case, we obtain it in an irreducible representation of the Clifford algebra incorporating to all orders the effects of a magnetic field of arbitrary spatial shape pointing perpendicularly to the plane of motion of the electrons. Such an exercise is of relevance in graphene in the massless limit. The specific examples considered include the uniform magnetic field and the exponentially damped static magnetic field. We further consider the electron propagator for the massive Schwinger model incorporating the effects of a constant electric field to all orders within this framework.
The promotion of cooperation on spatial lattices is an important issue in evolutionary game theory. This effect clearly depends on the update rule: it diminishes with stochastic imitative rules whereas it increases with unconditional imitation. To st
udy the transition between both regimes, we propose a new evolutionary rule, which stochastically combines unconditional imitation with another imitative rule. We find that, surprinsingly, in many social dilemmas this rule yields higher cooperative levels than any of the two original ones. This nontrivial effect occurs because the basic rules induce a separation of timescales in the microscopic processes at cluster interfaces. The result is robust in the space of 2x2 symmetric games, on regular lattices and on scale-free networks.
In the evolutionary Prisoners Dilemma (PD) game, agents play with each other and update their strategies in every generation according to some microscopic dynamical rule. In its spatial version, agents do not play with every other but, instead, inter
act only with their neighbors, thus mimicking the existing of a social or contact network that defines who interacts with whom. In this work, we explore evolutionary, spatial PD systems consisting of two types of agents, each with a certain update (reproduction, learning) rule. We investigate two different scenarios: in the first case, update rules remain fixed for the entire evolution of the system; in the second case, agents update both strategy and update rule in every generation. We show that in a well-mixed population the evolutionary outcome is always full defection. We subsequently focus on two-strategy competition with nearest-neighbor interactions on the contact network and synchronized update of strategies. Our results show that, for an important range of the parameters of the game, the final state of the system is largely different from that arising from the usual setup of a single, fixed dynamical rule. Furthermore, the results are also very different if update rules are fixed or evolve with the strategies. In these respect, we have studied representative update rules, finding that some of them may become extinct while others prevail. We describe the new and rich variety of final outcomes that arise from this co-evolutionary dynamics. We include examples of other neighborhoods and asynchronous updating that confirm the robustness of our conclusions. Our results pave the way to an evolutionary rationale for modelling social interactions through game theory with a preferred set of update rules.
