Equation of motion approach to the Hubbard model in infinite dimensions

We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, $G^{(n)}(\omega),\ n=2,3,\dots\$ . The first $n-1$ equations of motion are exactly fullfilled by $G^{(n)}(\omega)$ and the $n$'th equation of motion is decoupled following a simple set of decoupling rules. $G^{(2)}(\omega)$ corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for $n=2,3,4$.Comment: 10pager, REVTEX, 8-figures not available in postscript, manuscript may be understood without figure

Orbital-selective Mott Transitions in a Doped Two-band Hubbard Model

We extend previous studies on orbital-selective Mott transitions in the paramagnetic state of the half-filled degenerate two-band Hubbard model to the general doped case, using a high-precision quantum Monte Carlo dynamical mean-field theory solver. For sufficiently strong interactions, orbital-selective Mott transitions as a function of total band filling are clearly visible in the band-specific fillings, quasiparticle weights, double occupancies, and spectra. The results are contrasted with those of single-band models for similar correlation strengths.Comment: 12 pages, 12 figure

The composition and origin of Ghana medicine clays

This is the final version of the article. Available from Taylor & Francis via the DOI in this record.The mineral, organic and elemental composition of medicine clays from three shrines in the Tong Hills in northern Ghana (Gbankil, Kusanaab, and Yaane) are assessed to ascertain what additives they might contain and the implications for their recognition, for example in archaeological contexts. These are clays that are widely used for healing purposes being perceived efficacious in curing multiple ailments and which are given a divine provenance, but their collection is ascribed human agency. The Yaane clay is also supplied as part of the process of obtaining the right to operate the shrine elsewhere making it widely dispersed. Organic geochemical analyses revealed a predominance of plant-derived material with a substantial contribution of microbial origin. Based on these (supported by elemental and mineral analyses), no unnatural organic material could be detected, making an exogenous contribution to these clays unlikely. The implications are that these are wholly natural medicinal substances with no anthropogenic input into their preparation, as the traditions suggest. The very similar mineralogy of all the clays, including a non-medicine clay sampled, suggests that, unless the geology radically differed, differentiating between them analytically in an archaeological contexts would be doubtful.The authors are grateful to the Wellcome Trust for funding the research

Ground State Properties of an Asymmetric Hubbard Model for Unbalanced Ultracold Fermionic Quantum Gases

In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive ($U<0$) asymmetric ($t_\uparrow\neq t_\downarrow$) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. Numerical results for unbalanced Fermi-mixtures are presented within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.Comment: 9 pages, 5 figure

Saccadic eye movements estimate prolonged time awake

Prolonged time awake increases the need to sleep. Sleep pressure increases sleepiness, impairs human alertness and performance and increases the probability of human errors and accidents. Human performance and alertness during waking hours are influenced by homeostatic sleep drive and the circadian rhythm. Cognitive functions, especially attentional ones, are vulnerable to circadian rhythm and increasing sleep drive. A reliable, objective and practical metrics for estimating sleepiness could therefore be valuable. Our aim is to study whether saccades measured with electro-oculography (EOG) outside the laboratory could be used to estimate the overall time awake without sleep of a person. The number of executed saccades was measured in 11 participants during an 8-min saccade task. The saccades were recorded outside the laboratory (Naval Academy, Bergen) using EOG every sixth hour until 54 hr of time awake. Measurements were carried out on two occasions separated by 10 weeks. Five participants participated in both measurement weeks. The number of saccades decreased during sustained wakefulness. The data correlated with the three-process model of alertness; performance differed between participants but was stable within individual participants. A mathematically monotonous relation between performance in the saccade task and time awake was seen after removing the circadian rhythm component from measured eye movement data. The results imply that saccades measured with EOG can be used as a time-awake metric outside the laboratory.Peer reviewe

Cluster persistence in one-dimensional diffusion--limited cluster--cluster aggregation

The persistence probability, $P_C(t)$, of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. In the mean-field the problem maps to the survival of three annihilating random walkers with time-dependent noise correlations. For $\gamma \ge 0$ the motion of persistent clusters becomes asymptotically irrelevant and the mean-field theory provides a correct description. For $\gamma < 0$ the spatial fluctuations remain relevant and the persistence probability is overestimated by the random walk theory. The decay of persistence determines the small size tail of the cluster size distribution. For $0 < \gamma < 2$ the distribution is flat and, surprisingly, independent of $\gamma$.Comment: 11 pages, 6 figures, RevTeX4, submitted to Phys. Rev.

Charge-density-wave order parameter of the Falicov-Kimball model in infinite dimensions

In the large-U limit, the Falicov-Kimball model maps onto an effective Ising model, with an order parameter described by a BCS-like mean-field theory in infinite dimensions. In the small-U limit, van Dongen and Vollhardt showed that the order parameter assumes a strange non-BCS-like shape with a sharp reduction near T approx T_c/2. Here we numerically investigate the crossover between these two regimes and qualitatively determine the order parameter for a variety of different values of U. We find the overall behavior of the order parameter as a function of temperature to be quite anomalous.Comment: (5 pages, 3 figures, typeset with ReVTeX4

Molecular oxygen as a signaling component in plant development

While traditionally hypoxia has been studied as a detrimental component of flooding stress, the last decade has flourished with studies reporting the involvement of molecular oxygen availability in plant developmental processes. Moreover, proliferating and undifferentiated cells from different plant tissues were found to reside in endogenously generated hypoxic niches. Thus, stress-associated acute hypoxia may be distinguished from constitutively generated chronic hypoxia. The Cys/Arg branch of the N-degron pathway assumes a central role in integrating oxygen levels resulting in proteolysis of transcriptional regulators that control different aspects of plant growth and development. As a target of this pathway, group VII of the Ethylene Response Factor (ERF-VII) family has emerged as a hub for the integration of oxygen dynamics in root development and during seedling establishment. Additionally, vegetative shoot meristem activity and reproductive transition were recently associated with oxygen availability via two novel substrates of the N-degron pathways: VERNALISATION 2 (VRN2) and LITTLE ZIPPER 2 (ZPR2). Together, these observations support roles for molecular oxygen as a signalling molecule in plant development, as well as in essential metabolic reactions. Here, we review recent findings regarding oxygen-regulated development, and discuss outstanding questions that spring from these discoveries