A remark on helical waveguides

Motivated by a proposal to create an optical helix-shaped waveguides for cold atoms and molecules, we discuss local perturbations which can create bound states in such a setting. This is known about a local slowdown of the twist; we show that a similar effect can result from a local tube protrusion or a change of the helix radius in correlation with its pitch angle.Comment: LaTeX, 12 page

Behavioural rhythms and parental cooperation in biparentally incubating shorebirds

All organisms exhibit alternating phases of different behaviours. These behavioural rhythms are thought to be under strong selection, influenced by the rhythmicity of the environment. Whereas behavioural rhythms are well studied in isolated individuals under laboratory conditions, in free-living populations, individuals have to temporally synchronize their activities with those of others. The behavioural rhythms that emerge from such social synchronization and the underlying evolutionary and ecological factors that shape them remain poorly understood. Here, we address this issue for biparental care – a complex social behaviour and a particularly sensitive phase of social synchronization – in which pair members potentially compromise their individual rhythms. We use non-model organisms – biparentally-incubating shorebirds – where parents synchronize to achieve continuous coverage of developing eggs, and we use an array of monitoring techniques to record incubation in the wild. We combine a within-species approach (i.e. detailed description of incubation rhythms and field experiments to reveal the drivers of the rhythms using a single species; Chapter 1-3 & 5), with a between-species approach (i.e. comparing incubation rhythms of biparental and uniparental species; Chapter 4), and a phylogenetically informed comparative analyses (i.e. descriptive and hypotheses driven analyses across shorebirds; Chapter 6). Specifically, we tested: (1) how parents share their incubation duties over the day, incubation period and season (Chapter 1), and whether incubation behaviour correlates with off-nest behaviour (Chapter 2); (2) whether incubating parents compensate for the absence of their partner’s care (Chapter 3); (3) whether a complete switch to uniparental incubation is possible (Chapter 4); (4) whether energetic demands of incubation constrain incubation rhythms (Chapter 5 & 6); and finally (5), whether the diversity in incubation rhythms relates to phylogeny, predation risk, energetics and environmental fluctuations (Chapter 6). We first found – in a high Arctic breeding shorebird, the semipalmated sandpiper, Calidris pusilla (Chapter 1) – that overall the daily timing of incubation shifted over the incubation period (i.e. in females from evening–night to night–morning incubation) and over the season. However, the timing varied considerably among pairs: some displayed day-night incubation rhythm, others free-running like incubation rhythm (i.e. pairs shifted the start of incubation bouts between days so that each parent experienced similar conditions across the incubation period). Off-nest behaviour of the semipalmated sandpiper parents varied between sexes, across time and weather conditions, but it did not explain the diverse incubation rhythms (Chapter 2). We later confirmed this lack of evidence for energetic constraint of incubation in a field experiment (Chapter 5) and via comparative analyses (Chapter 6). Off duty parents roamed on average 224 m from their nest, implying that direct communication with the incubating partner is unlikely (Chapter 2). These results suggest that parents communicate only during their brief exchange on the nest. Second, despite this lack of communication between parents, overall, the parents partially compensated for an experimentally-induced temporary absence of their partner’s care (Chapter 3). However, the individual responses span the entire range of what is possible (no, partial and full compensation). Whether some parents may lack the energy for full compensation, or are less responsive to their partner’s absence, is unclear; however, we provide tentative evidence for both. Essentially, since incubating parents do not feed, even the fully compensating parents later left their nest unattended. Nevertheless, where removed parent never returned, nests were incubated uniparentally for median of 4 days (range 0-10 days, N = 7 nests). Third, we found natural cases of such uniparental incubating in 8 out of 15 biparentally incubating shorebird-species (Chapter 4). Such uniparental incubation resembled the incubation of uniparental species. Strikingly, in 5 species we document cases where uniparentally incubating parents brought their clutch to hatching, which in these species reveals a potential for a flexible switch from biparental to uniparental care. Fourth, contrary to prior believe, reducing the energetic demands of incubation by heating or insulating the nest cup had no effect on the length of incubation bouts (Chapter 5). These results convincingly demonstrate that incubation rhythms in semipalmated sandpipers are not primarily driven by the energetic state of the incubating bird. Last, in a large scale comparative study that made use of 729 nests from 91 populations of 32 species we found a remarkable within- and between-species diversity in the socially synchronized incubation rhythms (Chapter 6). The length of incubation bouts was unrelated to variables reflecting energetic demands, but species relying on crypsis had longer incubation bouts than those that are readily visible or actively protect their nest against predators. Rhythms that could be potentially entrained to the 24-h light-dark cycle were less likely at high latitudes and absent in 18 species. Although half of our species are tidal away from their breeding grounds, and some forage in tidal areas also during breeding, in only 5% of nests did pairs display a rhythm that can be entrained by the tide. Hence, unlike the 24-h light-dark cycle, tidal life-history seems to play, at best, a negligible role in determining incubation rhythms. In sum, we reveal unexpected within- and between-species diversity in socially synchronized incubation rhythms of biparental shorebirds (Chapter 1, 3, 4, & 6). Our results demonstrate that under natural conditions social synchronization can generate much more diverse rhythms than previously expected, and that these rhythms often defy the 24-h day, even in day-night environments (Chapter 6). Whereas our descriptive, experimental and comparative evidence consistently rules out risk of starvation as a key factor underlying the diversity and timing of these rhythms (Chapter 2, 5 & 6), we provide novel evidence for the link between the diversity of the rhythms and anti-predation strategy (Chapter 6)

Charge gaps and quasiparticle bands of the ionic Hubbard model

The ionic Hubbard model on a cubic lattice is investigated using analytical approximations and Wilson's renormalization group for the charge excitation spectrum. Near the Mott insulating regime, where the Hubbard repulsion starts to dominate all energies, the formation of correlated bands is described. The corresponding partial spectral weights and local densities of states show characteristic features, which compare well with a hybridized-band picture appropriate for the regime at small $U$, which at half-filling is known as a band insulator. In particular, a narrow charge gap is obtained at half-filling, and the distribution of spectral quasi-particle weight reflects the fundamental hybridization mechanism of the model

Isosbestic points in the spectral function of correlated electrons

We investigate the properties of the spectral function A(omega,U) of correlated electrons within the Hubbard model and dynamical mean-field theory. Curves of A(omega,U) vs. omega for different values of the interaction U are found to intersect near the band-edges of the non-interacting system. For a wide range of U the crossing points are located within a sharply confined region. The precise location of these 'isosbestic points' depends on details of the non-interacting band structure. Isosbestic points of dynamic quantities therefore provide valuable insights into microscopic energy scales of correlated systems.Comment: 16 pages, 5 figure