Finite-size effects in the dynamics of few bosons in a ring potential

We study the temporal evolution of a small number $N$ of ultra-cold bosonic atoms confined in a ring potential. Assuming that initially the system is in a solitary-wave solution of the corresponding mean-field problem, we identify significant differences in the time evolution of the density distribution of the atoms when it instead is evaluated with the many-body Schr\"odinger equation. Three characteristic timescales are derived: the first is the period of rotation of the wave around the ring, the second is associated with a "decay" of the density variation, and the third is associated with periodic "collapses" and "revivals" of the density variations, with a factor of $\sqrt N$ separating each of them. The last two timescales tend to infinity in the appropriate limit of large $N$, in agreement with the mean-field approximation. These findings are based on the assumption of the initial state being a mean-field state. We confirm this behavior by comparison to the exact solutions for a few-body system stirred by an external potential. We find that the exact solutions of the driven system exhibit similar dynamical features.Comment: To appear in Journal of Physics

Quaternionic Hyperbolic Function Theory

We are studying hyperbolic function theory in the skew-field of quaternions. This theory is connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric (Formula Presented) in the upper half space (Formula Presented). In the case k = 2, the metric is the hyperbolic metric of the Poincaré upper half-space. Hempfling and Leutwiler started to study this case and noticed that the quaternionic power function xm(m ε Z), is a conjugate gradient of a 2-hyperbolic harmonic function. They researched polynomial solutions. We find fundamental k-hyperbolic harmonic functions depending only on the hyperbolic distance and x3. Using these functions we are able to verify a Cauchy type integral formula. Earlier these results have been verified for quaternionic functions depending only on reduced variables (x0, x1, x2). Our functions are depending on four variables. © Springer Nature Switzerland AG 2019.Peer reviewe

Ecosystem properties and principles of living systems as foundation for sustainable agriculture – Critical reviews of environmental assessment tools, key findings and questions from a course process

With increasing demands on limited resources worldwide, there is a growing interest in sustainable patterns of utilisation and production. Ecological agriculture is a response to these concerns. To assess progress and compliance, standard and comprehensive measures of resource requirements, impacts and agro-ecological health are needed. Assessment tools should also be rapid, standardized, userfriendly, meaningful to public policy and applicable to management. Fully considering these requirements confounds the development of integrated methods. Currently, there are many methodologies for monitoring performance, each with its own foundations, assumptions, goals, and outcomes, dependent upon agency agenda or academic orientation. Clearly, a concept of sustainability must address biophysical, ecological, economic, and sociocultural foundations. Assessment indicators and criteria, however, are generally limited, lacking integration, and at times in conflict with one another. A result is that certification criteria, indicators, and assessment methods are not based on a consistent, underlying conceptual framework and often lack a management focus. Ecosystem properties and principles of living systems, including self-organisation, renewal, embeddedness, emergence and commensurate response provide foundation for sustainability assessments and may be appropriate focal points for critical thinking in an evaluation of current methods and standards. A systems framework may also help facilitate a comprehensive approach and promote a context for meaningful discourse. Without holistic accounts, sustainable progress remains an illdefined concept and an elusive goal. Our intent, in the work with this report, was to use systems ecology as a pedagogic basis for learning and discussion to: - Articulate general and common characteristics of living systems. - Identify principles, properties and patterns inherent in natural ecosystems. - Use these findings as foci in a dialogue about attributes of sustainability to: a. develop a model for communicating scientific rationale. b. critically evaluate environmental assessment tools for application in land-use. c. propose appropriate criteria for a comprehensive assessment and expanded definition of ecological land use

Reading between the lines: attitudinal expressions in text

This is a brief overview of the starting points a project currently proposed and under evaluation by funding agencies. We discuss some of the linguistic methodology we plan to employ to idenitify and analyze attitudinal expressions in text, and touch briefly on how to evaluate our future results

Atom detection and photon production in a scalable, open, optical microcavity

A microfabricated Fabry-Perot optical resonator has been used for atom detection and photon production with less than 1 atom on average in the cavity mode. Our cavity design combines the intrinsic scalability of microfabrication processes with direct coupling of the cavity field to single-mode optical waveguides or fibers. The presence of the atom is seen through changes in both the intensity and the noise characteristics of probe light reflected from the cavity input mirror. An excitation laser passing transversely through the cavity triggers photon emission into the cavity mode and hence into the single-mode fiber. These are first steps towards building an optical microcavity network on an atom chip for applications in quantum information processing.Comment: 4 pages, 4 figures. A typographical error in the published paper has been corrected (equation of the corrected normalized variance, page 3, 2nd paragraph

Vortices in fermion droplets with repulsive dipole-dipole interactions

Vortices are found in a fermion system with repulsive dipole-dipole interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator potential. Such systems have much in common with electrons in quantum dots, where rotation is induced via an external magnetic field. In contrast to the Coulomb interactions between electrons, the (externally tunable) anisotropy of the dipole-dipole interaction breaks the rotational symmetry of the Hamiltonian. This may cause the otherwise rotationally symmetric exact wavefunction to reveal its internal structure more directly.Comment: 5 pages, 5 figure

A theoretical analysis of the chemical bonding and electronic structure of graphene interacting with Group IA and Group VIIA elements

We propose a new class of materials, which can be viewed as graphene derivatives involving Group IA or Group VIIA elements, forming what we refer to as graphXene. We show that in several cases large band gaps can be found to open up, whereas in other cases a semimetallic behavior is found. Formation energies indicate that under ambient conditions, sp$^3$ and mixed sp$^2$/sp$^3$ systems will form. The results presented allow us to propose that by careful tuning of the relative concentration of the adsorbed atoms, it should be possible to tune the band gap of graphXene to take any value between 0 and 6.4 eV.Comment: 5 pages, 4 figures. Transferred to PR

The effect of multiple paternity on genetic diversity during and after colonisation

In metapopulations, genetic variation of local populations is influenced by the genetic content of the founders, and of migrants following establishment. We analyse the effect of multiple paternity on genetic diversity using a model in which the highly promiscuous marine snail Littorina saxatilis expands from a mainland to colonise initially empty islands of an archipelago. Migrant females carry a large number of eggs fertilised by 1 - 10 mates. We quantify the genetic diversity of the population in terms of its heterozygosity: initially during the transient colonisation process, and at long times when the population has reached an equilibrium state with migration. During colonisation, multiple paternity increases the heterozygosity by 10 - 300 % in comparison with the case of single paternity. The equilibrium state, by contrast, is less strongly affected: multiple paternity gives rise to 10 - 50 % higher heterozygosity compared with single paternity. Further we find that far from the mainland, new mutations spreading from the mainland cause bursts of high genetic diversity separated by long periods of low diversity. This effect is boosted by multiple paternity. We conclude that multiple paternity facilitates colonisation and maintenance of small populations, whether or not this is the main cause for the evolution of extreme promiscuity in Littorina saxatilis.Comment: 7 pages, 5 figures, electronic supplementary materia