Phase Transitions from Saddles of the Potential Energy Landscape

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived. For large systems, the order of the nonanalytic term increases unboundedly, leading to an increasing differentiability of the entropy. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, our results provide an explanation of how, and under which circumstances, saddle points of the potential energy landscape may (or may not) be at the origin of a phase transition in the thermodynamic limit. As an application, the puzzling observations by Risau-Gusman et al. on topological signatures of the spherical model are elucidated.Comment: 5 pages, no figure

Localization Enhanced Mobile Networks

The interest in mobile ad-hoc networks (MANETs) and often more precisely vehicular ad-hoc networks (VANETs) is steadily growing with many new applications, and even anticipated support in the emerging 5G networks. Particularly in outdoor scenarios, there are different mechanisms to make the mobile nodes aware of their geographical location at all times. The location information can be utilized at different layers of the protocol stack to enhance communication services in the network. Specifically, geographical routing can facilitate route management with smaller overhead than the traditional proactive and reactive routing protocols. In order to achieve similar advantages for radio resource management (RRM) and multiple access protocols, the concept of virtual cells is devised to exploit fully distributed knowledge of node locations. The virtual cells define clusters of MANET nodes assuming a predefined set of geographically distributed anchor points. It enables fast response of the network to changes in the nodes spatial configuration. More importantly, the notion of geographical location can be generalized to other shared contexts which can be learned or otherwise acquired by the network nodes. The strategy of enhancing communication services by shared contexts is likely to be one of the key features in the beyond-5G networks

The wage elasticity of recruitment

One of the factors affecting the market power of employers is the extent to which higher wages makes recruitment easier. There is very little research on this. This paper presents a methodology for estimating the wage elasticity of recruitment and applies it to German data. Our estimates of the wage elasticity of recruitment are about 1.4. We also report evidence that high-wage employers are more selective in hiring, in which case the relevant recruitment elasticity should be higher, about 2.2. Together with prior estimates of the quit elasticity these results imply that wages are 72-77% of the marginal product of labour. Further, we find lower elasticities for recruits hired from non-employment as well as for women, non-German nationals, non-prime-age workers, less skilled workers, and workers with less complex jobs

The urban wage premium in imperfect labor markets

Using administrative data for West Germany, this paper investigates whether part of the urban wage premium stems from greater competition in denser labor markets. We show that employers possess less wage-setting power in denser markets. We further document that an important part of the observed urban wage premia can be explained by greater competition in denser labor markets

On the Quantitative Impact of the Schechter-Valle Theorem

We evaluate the Schechter-Valle (Black Box) theorem quantitatively by considering the most general Lorentz invariant Lagrangian consisting of point-like operators for neutrinoless double beta decay. It is well known that the Black Box operators induce Majorana neutrino masses at four-loop level. This warrants the statement that an observation of neutrinoless double beta decay guarantees the Majorana nature of neutrinos. We calculate these radiatively generated masses and find that they are many orders of magnitude smaller than the observed neutrino masses and splittings. Thus, some lepton number violating New Physics (which may at tree-level not be related to neutrino masses) may induce Black Box operators which can explain an observed rate of neutrinoless double beta decay. Although these operators guarantee finite Majorana neutrino masses, the smallness of the Black Box contributions implies that other neutrino mass terms (Dirac or Majorana) must exist. If neutrino masses have a significant Majorana contribution then this will become the dominant part of the Black Box operator. However, neutrinos might also be predominantly Dirac particles, while other lepton number violating New Physics dominates neutrinoless double beta decay. Translating an observed rate of neutrinoless double beta decay into neutrino masses would then be completely misleading. Although the principal statement of the Schechter-Valle theorem remains valid, we conclude that the Black Box diagram itself generates radiatively only mass terms which are many orders of magnitude too small to explain neutrino masses. Therefore, other operators must give the leading contributions to neutrino masses, which could be of Dirac or Majorana nature.Comment: 18 pages, 4 figures; v2: minor corrections, reference added, matches journal version; v3: typo corrected, physics result and conclusions unchange

Hydrogen bond topology and the ice VII/VIII and Ih/XI proton ordering phase transitions

Ice Ih, ordinary ice at atmospheric pressure, is a proton-disordered crystal that when cooled under special conditions is believed to transform to ferroelectric proton-ordered ice XI, but this transformation is still subject to controversy. Ice VII, also proton disordered throughout its region of stability, transforms to proton-ordered ice VIII upon cooling. In contrast to the ice Ih/XI transition, the VII/VIII transition and the crystal structure of ice VIII are well characterized. In order to shed some light on the ice Ih proton ordering transition, we present the results of periodic electronic density functional theory calculations and statistical simulations. We are able to describe the small energy differences among the innumerable H-bond configurations possible in a large simulation cell by using an analytic theory to extrapolate from electronic DFT calculations on small unit cells to cells large enough to approximate the thermodynamic limit. We first validate our methods by comparing our predictions to the well-characterized ice VII/VIII proton ordering transition, finding agreement with respect to both the transition temperature and structure of the low-temperature phase. For ice Ih, our results indicate that a proton-ordered phase is attainable at low temperatures, the structure of which is in agreement with the experimentally proposed ferroelectric Cmc2_1 structure. The predicted transition temperature of 98 K is in qualitative agreement with the observed transition at 72 K on KOH-doped ice samples