Casimir-Polder Potential of a Driven Atom

We investigate theoretically the Casimir-Polder potential of an atom which is driven by a laser field close to a surface. This problem is addressed in the framework of macroscopic quantum electrodynamics using the Green's tensor formalism and we distinguish between two different approaches, a perturbative ansatz and a method based on Bloch equations. We apply our results to a concrete example, namely an atom close to a perfectly conducting mirror, and create a scenario where the tunable Casimir-Polder potential becomes similar to the respective potential of an undriven atom due to fluctuating field modes. Whereas the perturbative approach is restricted to large detunings, the ansatz based on Bloch equations is exact and yields an expression for the potential which does not exceed 1/2 of the undriven Casimir-Polder potential.Comment: 13 pages, 8 figure

Diverse forests for climate change: Drought stress tolerance of secondary timber species

Accelerated climate warming in the past decades and a recent increase in the frequency and severity of summer heat-waves in combination with more irregular summer precipitation challenge silvicultural concepts in Europe’s temperate forest region, as some of the main timber species seem to be relatively susceptible to drought and possibly also heat. Notably, Norway spruce (Picea abies (L.) H. Karst.) and European beech (Fagus sylvatica L.) showed drought-related dieback and vitality losses. For that reason, concepts to admix and promote native, putatively drought-tolerant, minor timber species are gaining growing interest in Central Europe. Norway maple (Acer platanoides L.), common hornbeam (Carpinus betulus L.), European ash (Fraxinus excelsior L.), and small-leaved lime (Tilia cordata Mill.) are promising candidates due to their occurrence in the more continental climate of Eastern Europe and scattered knowledge from ecophysiological studies. The present thesis assessed the drought tolerance of the four aforementioned species in comparison to sessile oak (Quercus petraea Matt. Liebl), a well-studied, drought-tolerant, and major timber in Central Europe. A combination of three methodological packages was applied to quantify drought tolerance, namely plant hydraulic traits, fine root inventories and dendroecology. To allow for quantification of the species’ plasticity, the assessment was accomplished in a field study along a precipitation transect from putatively optimal to relatively dry conditions (mean annual precipitation range from ca. 900 to 500 mm) around the Harz mountain range in Central Eastern Germany. Hydraulic efficiency- (xylem conductivity and Huber value) and safety-related traits (xylem embolism resistance, leaf turgor loss point, hydraulic safety margins) were quantified from sun-exposed branches from the uppermost canopy. Although a certain intra-specific trait variability in safety-related traits was observed, the magnitude was small compared to interspecific variability. In contrast, efficiency-related traits showed a high intra-specific trait variability both within populations and within the crowns of single trees. Surprisingly, the observed ITV of all traits was neither driven by climatic or soil water availability, nor by tree height, indicating a complex control of adult trees’ hydraulic traits by the environment. A. platanoides and C. betulus showed very wide safety margins, a highly resistant xylem and higher trait plasticity, whereas T. cordata was vulnerable to embolism and operated with consistently narrow margins. Fine root inventories in the uppermost mineral soil were carried out in spring under ample water supply and after extreme summer drought in 2018, assessing fine root biomass, necromass and morphology. The extent of the root necromass/biomass ratio (N/B) increase and reductions in root tip frequency were used as a measure of the species’ belowground sensitivity to water deficits. Q. petraea showed the smallest fine root density and was the only species not increasing N/B towards drier sites and without losses of root tips after summer drought, indicating the most conservative and resistant fine root system. The other species showed a more susceptible fine root system with distinctly increased N/B towards drier sites, mostly elevated N/B after summer drought (especially on moister sites), and throughout reduced root tip frequencies in response to drought. For the dendroecological assessment, climate-growth relationships, their temporal variation, and the resistance and resilience to climatic droughts was analyzed from increment cores for the past 50 years. While growth responded in all four species positively to summer precipitation and negatively to higher summer temperature and climatic aridity, climate sensitivity of growth decreased in the period of 1967-2016. None of the species showed negative growth trends with recent climate warming and drought sensitivity was not higher at drier sites, indicating a considerable acclimation and adaptation potential. The resistance of radial growth to drought was higher in ring-porous species (F. excelsior, Q. petraea) in comparison to diffuse-porous species (A. platanoides, T. cordata), but resilience was high in all species. The findings of the present work and knowledge from literature were combined to a synoptic evaluation of the species’ abilities to withstand drought and an integration of the drought response strategies into the isohydry-anisohydry syndrome. Q. petraea and F. excelsior are strictly anisohydric and highly drought-tolerant, keeping up high productivity under unfavorable water supply. However, F. excelsior is severely threatened by the fungus Hymenoscyphus fraxineus, causing a pan-European ash dieback and rendering any recommendations for silvicultural planning impossible in the near future. A. platanoides is strictly isohydric with high hydraulic safety, accepting temporary reductions of productivity for the sake of a low drought-related mortality risk. T. cordata did not prove to be highly drought-resistant overall, but pursues a unique semi-isohydric strategy with high stem and leaf water capacitance, buffering well against mediocre droughts. C. betulus showed no drought-resistant fine root system, but fairly drought-resistant hydraulic properties. Early leaf shedding and radial growth stagnation seem to be safety mechanisms of C. betulus in order to provide a certain tenacity in coping with unfavorable conditions. In comparison to F. sylvatica and P. abies, all five species seem to be more drought-resistant, and especially A. platanoides (in addition to Q. petraea) deserves a broader consideration in silvicultural concepts targeted at adapting production forests to climate warming.2021-08-2

Converter control for wind turbines when operating in weak grids containing resonances

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Non-additivity of optical and Casimir-Polder potentials

An atom irradiated by an off-resonant laser field near a surface is expected to experience the sum of two fundamental potentials, the optical potential of the laser field and the Casimir--Polder potential of the surface. Here, we report a new non-additive potential, namely the laser-induced Casimir--Polder potential, which arises from a correlated coupling of the atom with both the laser and the quantum vacuum. We apply this result to an experimentally realizable scenario of an atomic mirror with an evanescent laser beam leaking out of a surface. We show that the non-additive term is significant for realistic experimental parameters, transforming potential barriers into potential wells, which can be used to trap atoms near surfaces.Comment: 5 pages, 3 figure

Integral zeros of a polynomial with linear recurrences as coefficients

Let $K$ be a number field, $S$ a finite set of places of $K$, and $\mathcal{O}_S$ be the ring of $S$-integers. Moreover, let $$G_n^{(0)} Z^d + \cdots + G_n^{(d-1)} Z + G_n^{(d)}$$ be a polynomial in $Z$ having simple linear recurrences of integers evaluated at $n$ as coefficients. Assuming some technical conditions we give a description of the zeros $(n,z) \in \mathbb{N} \times \mathcal{O}_S$ of the above polynomial. We also give a result in the spirit of Hilbert irreducibility for such polynomials.Comment: 13 page