A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page

Cardiovascular and pharmacological implications of haem-deficient NO-unresponsive soluble guanylate cyclase knock-in mice

Oxidative stress, a central mediator of cardiovascular disease, results in loss of the prosthetic haem group of soluble guanylate cyclase (sGC), preventing its activation by nitric oxide (NO). Here we introduce Apo-sGC mice expressing haem-free sGC. Apo-sGC mice are viable and develop hypertension. The haemodynamic effects of NO are abolished, but those of the sGC activator cinaciguat are enhanced in apo-sGC mice, suggesting that the effects of NO on smooth muscle relaxation, blood pressure regulation and inhibition of platelet aggregation require sGC activation by NO. Tumour necrosis factor (TNF)-induced hypotension and mortality are preserved in apo-sGC mice, indicating that pathways other than sGC signalling mediate the cardiovascular collapse in shock. Apo-sGC mice allow for differentiation between sGC-dependent and -independent NO effects and between haem-dependent and -independent sGC effects. Apo-sGC mice represent a unique experimental platform to study the in vivo consequences of sGC oxidation and the therapeutic potential of sGC activators

Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas

The ability to control and tune interactions in ultracold atomic gases has paved the way towards the realization of new phases of matter. Whereas experiments have so far achieved a high degree of control over short-ranged interactions, the realization of long-range interactions would open up a whole new realm of many-body physics and has become a central focus of research. Rydberg atoms are very well-suited to achieve this goal, as the van der Waals forces between them are many orders of magnitude larger than for ground state atoms. Consequently, the mere laser excitation of ultracold gases can cause strongly correlated many-body states to emerge directly when atoms are transferred to Rydberg states. A key example are quantum crystals, composed of coherent superpositions of different spatially ordered configurations of collective excitations. Here we report on the direct measurement of strong correlations in a laser excited two-dimensional atomic Mott insulator using high-resolution, in-situ Rydberg atom imaging. The observations reveal the emergence of spatially ordered excitation patterns in the high-density components of the prepared many-body state. They have random orientation, but well defined geometry, forming mesoscopic crystals of collective excitations delocalised throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realise exotic phases of matter, thereby laying the basis for quantum simulations of long-range interacting quantum magnets.Comment: 10 pages, 7 figure

Coherent dynamics of Bose-Einstein condensates in high-finesse optical cavities

We study the mutual interaction of a Bose-Einstein condensed gas with a single mode of a high-finesse optical cavity. We show how the cavity transmission reflects condensate properties and calculate the self-consistent intra-cavity light field and condensate evolution. Solving the coupled condensate-cavity equations we find that while falling through the cavity, the condensate is adiabatically transfered into the ground state of the periodic optical potential. This allows time dependent non-destructive measurements on Bose-Einstein condensates with intriguing prospects for subsequent controlled manipulation.Comment: 5 pages, 5 figures; revised version: added reference

A Rydberg Quantum Simulator

Following Feynman and as elaborated on by Lloyd, a universal quantum simulator (QS) is a controlled quantum device which reproduces the dynamics of any other many particle quantum system with short range interactions. This dynamics can refer to both coherent Hamiltonian and dissipative open system evolution. We investigate how laser excited Rydberg atoms in large spacing optical or magnetic lattices can provide an efficient implementation of a universal QS for spin models involving (high order) n-body interactions. This includes the simulation of Hamiltonians of exotic spin models involving n-particle constraints such as the Kitaev toric code, color code, and lattice gauge theories with spin liquid phases. In addition, it provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The key basic building blocks of our architecture are efficient and high-fidelity n-qubit entangling gates via auxiliary Rydberg atoms, including a possible dissipative time step via optical pumping. This allows to mimic the time evolution of the system by a sequence of fast, parallel and high-fidelity n-particle coherent and dissipative Rydberg gates.Comment: 8 pages, 4 figure

Imaging local genetic influences on cortical folding

Recent progress in deciphering mechanisms of human brain cortical folding leave unexplained whether spatially patterned genetic influences contribute to this folding. High-resolution in vivo brain MRI can be used to estimate genetic correlations (covariability due to shared genetic factors) in interregional cortical thickness, and biomechanical studies predict an influence of cortical thickness on folding patterns. However, progress has been hampered because shared genetic influences related to folding patterns likely operate at a scale that is much more local (cm) than that addressed in prior imaging studies. Here, we develop methodological approaches to examine local genetic influences on cortical thickness and apply these methods to two large, independent samples. We find that such influences are markedly heterogeneous in strength, and in some cortical areas are notably stronger in specific orientations relative to gyri or sulci. The overall, phenotypic local correlation has a significant basis in shared genetic factors and is highly symmetric between left and right cortical hemispheres. Furthermore, the degree of local cortical folding relates systematically with the strength of local correlations, which tends to be higher in gyral crests and lower in sulcal fundi. The relationship between folding and local correlations is stronger in primary sensorimotor areas and weaker in association areas such as prefrontal cortex, consistent with reduced genetic constraints on the structural topology of association cortex. Collectively, our results suggest that patterned genetic influences on cortical thickness, measurable at the scale of in vivo MRI, may be a causal factor in the development of cortical folding

Designing spin-1 lattice models using polar molecules

We describe how to design a large class of always on spin-1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a ro-vibrational ground state molecule. Interactions are induced using a microwave field to mix ground states in one hyperfine manifold with the spin entangled dipole-dipole coupled excited states. Using multiple fields anistropic models in one, two, or three dimensions, can be built with tunable spatial range. An illustrative example in one dimension is the generalized Haldane model, which at a specific parameter has a gapped valence bond solid ground state. The interaction strengths are large compared to decoherence rates and should allow for probing the rich phase structure of strongly correlated systems, including dimerized and gapped phases.Comment: 24 pages, 5 figure

Nuclear Inelastic X-Ray Scattering of FeO to 48 GPa

The partial density of vibrational states has been measured for Fe in compressed FeO (w\"ustite) using nuclear resonant inelastic x-ray scattering. Substantial changes have been observed in the overall shape of the density of states close to the magnetic transiton around 20 GPa from the paramagnetic (low pressure) to the antiferromagnetic (high pressure) state. Our data indicate a substantial softening of the aggregate sound velocities far below the transition, starting between 5 and 10 GPa. This is consistent with recent radial x-ray diffraction measurements of the elastic constants in FeO. The results indicate that strong magnetoelastic coupling in FeO is the driving force behind the changes in the phonon spectrum of FeO.Comment: 4 pages, 4 figure

The π\pi, K+K^+, and K0K^0 electromagnetic form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed quark-photon vertex in a self-consistent Poincar\'e-invariant study of the pion and kaon electromagnetic form factors in impulse approximation. We demonstrate explicitly that the current is conserved in this approach and that the obtained results are independent of the momentum partitioning in the Bethe-Salpeter amplitudes. With model gluon parameters previously fixed by the condensate, the pion mass and decay constant, and the kaon mass, the charge radii and spacelike form factors are found to be in good agreement with the experimental data.Comment: 8 pages, 6 figures, Revte