Diffraction catastrophes and semiclassical quantum mechanics for Veselago lensing in graphene

We study the effect of trigonal warping on the focussing of electrons by n-p junctions in graphene. We find that perfect focussing, which was predicted for massless Dirac fermions, is only preserved for one specific sample orientation. In the general case, trigonal warping leads to the formation of cusp caustics, with a different position of the focus for graphene's two valleys. We develop a semiclassical theory to compute these positions and find very good agreement with tight-binding simulations. Considering the transmission as a function of potential strength, we find that trigonal warping splits the single Dirac peak into two distinct peaks, leading to valley polarization. We obtain the transmission curves from tight-binding simulations and find that they are in very good agreement with the results of a billiard model that incorporates trigonal warping. Furthermore, the positions of the transmission maxima and the scaling of the peak width are accurately predicted by our semiclassical theory. Our semiclassical analysis can easily be carried over to other Dirac materials, which generally have different Fermi surface distortions.Comment: 6 pages, 4 figures, plus supplemental material. Important reference added and text update

Economic Growth and Longevity Risk with Adverse Selection

We study a closed economy featuring heterogeneous agents and exhibiting endogenous economic growth due to interfirm external effects. Individual agents differ in terms of their mortality profile. At birth, nature assigns a health status to each agent. Health type is private information and annuity firms can only observe an agent’s age. In the presence of longevity risk, agents want to annuitize their wealth conform the classic result by Yaari (1965). In the first-best case with perfect annuities, the market would feature a separating equilibrium (SE) in which each health type obtains an actuarially fair perfect insurance. In the SE all agents are savers throughout their lives. The informational asymmetry precludes the attainment of the first-best equilibrium, however, as healthy individuals have a strong incentive to misrepresent their type by claiming to be unhealthy. Using the equilibrium concept of Pauly (1974) and Abel (1986), we prove the existence of a second-best pooling equilibrium (PE) in which individuals of all types annuitize at a common pooling rate. As the unhealthy get close to their maximum attainable age, the pooling rate prompts such individuals to become net borrowers. But borrowing would reveal their health status, so the best the unhealthy can do is to impose a borrowing constraint on themselves during their autumn years. Using a plausibly calibrated version of the model we find that the growth- and welfare effects of PE versus SE are rather small, whilst those of PE versus no annuities at all (NAE) are rather large. An imperfect insurance is better than no insurance at all, both at the microeconomic and at the macroeconomic level.annuity markets, adverse selection, endogenous growth, overlapping generations, demography

Stories that move:Fiction, imagination, tourism

The subject of this article is media tourism: the phenomenon of people travelling to places which they associate with novels, films or television series. Existing knowledge about this phenomenon is fragmented and principally based on individual case studies of eye-catching examples. This article aims to go beyond the limited scope of case studies and to explore an underlying, more generic process. It investigates the stories that are remembered by individuals, the associations between these stories and existing places, and decisions about whether or not to undertake travel to these places. Based on a series of in-depth interviews, the article concludes that every human being has a small treasure trove of stories which they love and which are considered part of their identity. The interviews suggest that there is a strong relationship between the recollection of beloved stories and tourist practices – in terms of both destination decision making and tourist experience.</p