Time Development of Exponentially Small Non-Adiabatic Transitions

Optimal truncations of asymptotic expansions are known to yield approximations to adiabatic quantum evolutions that are accurate up to exponentially small errors. In this paper, we rigorously determine the leading order non--adiabatic corrections to these approximations for a particular family of two--level analytic Hamiltonian functions. Our results capture the time development of the exponentially small transition that takes place between optimal states by means of a particular switching function. Our results confirm the physics predictions of Sir Michael Berry in the sense that the switching function for this family of Hamiltonians has the form that he argues is universal

When societies crash : a critical analysis of news media's social role in the aftermath of national disasters

Apart from their primary role as news providers in disaster situations, news media can also assume a broader social role. Drawing on a critically informed qualitative content analysis of the Belgian news reporting on a national disaster, the article reveals a twofold articulation of this social role. The first consisted in newspapers highlighting the emotional dimension with potential societal implications of raising compassion and identification. Second, we found a strong articulation of a discourse of (national) unity and community, aimed at restoring the disrupted social order in the disaster’s aftermath. Both aspects were discursively established by a dominant presence of emotional testimonies, strategies of personalization and by the use of inclusive language permeated with references to nation or community. The study highlights the important social role of journalism in disaster situations and events involving human suffering

Exponential Asymptotics in a Singular Limit for nn-Level Scattering Systems

The singular limit \eps\ra 0 of the $S$-matrix associated with the equation i\eps d\psi(t)/dt=H(t)\psi(t) is considered, where the analytic generator H(t)\in M_n(\C) is such that its spectrum is real and non-degenerate for all $t\in\R$. Sufficient conditions allowing to compute asymptotic formulas for the exponentially small off-diagonal elements of the $S$-matrix as \eps\ra 0 are explicited and a wide class of generators for which these conditions are verified is defined. These generators are obtained by means of generators whose spectrum exhibits eigenvalue crossings which are perturbed in such a way that these crossings turn to avoided crossings. The exponentially small asymptotic formulas which are derived are shown to be valid up to exponentially small relative error, by means of a joint application of the complex WKB method together with superasymptotic renormalization. The application of these results to the study of quantum adiabatic transitions in the time dependent Schr\"odinger equation and of the semiclassical scattering properties of the multichannel stationary Schr\"odinger equation closes this paper. The results presented here are a generalization to $n$-level systems, $n\geq 2$, of results previously known for $2$-level systems only.Comment: 35 pages, Late

An Adiabatic Theorem for Singularly Perturbed Hamiltonians

The adiabatic approximation in quantum mechanics is considered in the case where the self-adjoint hamiltonian $H_0(t)$, satisfying the usual spectral gap assumption in this context, is perturbed by a term of the form $\epsilon H_1(t)$. Here $\epsilon \to 0$ is the adiabaticity parameter and $H_1(t)$ is a self-adjoint operator defined on a smaller domain than the domain of $H_0(t)$. Thus the total hamiltonian $H_0(t)+\epsilon H_1(t)$ does not necessarily satisfy the gap assumption, $\forall \epsilon >0$. It is shown that an adiabatic theorem can be proven in this situation under reasonnable hypotheses. The problem considered can also be viewed as the study of a time-dependent system coupled to a time-dependent perturbation, in the limit of large coupling constant.Comment: 17 pages, LaTe

Density of States and Thouless Formula for Random Unitary Band Matrices

We study the density of states measure for some class of random unitary band matrices and prove a Thouless formula relating it to the associated Lyapunov exponent. This class of random matrices appears in the study of the dynamical stability of certain quantum systems and can also be considered as a unitary version of the Anderson model. We further determine the support of the density of states measure and provide a condition ensuring it possesses an analytic density

On the media construction of international disasters

For most people living in western countries, disasters are a priori cases of distant suffering as they mainly affect cultural or ethnic others. News media thus play a pivotal role in giving publicity and meaning to the numerous instances of global suffering as it is essentially through media reports that the (western) world witnesses international disasters. Accordingly, several scholars define a disaster as a media construction; they exist only when recognized and covered by the media. This paper focuses on the conceptualization of a disaster as a media construction by exploring the inherently selective nature of news coverage, the representation of suffering in Flemish news media and the possible societal implications

Research on mediated suffering within social sciences: expert views on identifying a disciplinary home and research agenda

An emerging field of research within social sciences concerns itself with the issue of suffering. Following its growing (mediated) societal prevalence and impact in recent years, suffering has already spurred a rich and diverse body of work. Alongside its emergence within academia, questions arose about its disciplinary home and scope. Drawing on elite interviews with twelve leading scholars, this article positions the on-going research on media and suffering at the heart of social sciences and humanities as well as at the crossroads of different disciplines. This overall open view was reflected in discussions on the current and future scope of the research. Regarding future directions, empirical audience research is high on the academic agenda as are studies that look into the role of new media with regard to suffering. Other widely shared comments referred to a further opening up of the research in terms of methodological and disciplinary approaches