Master equation approach to computing RVB bond amplitudes

We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner dictated by the spin hamiltonian under consideration) toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J1-J2 antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes are radially symmetric and fall off as 1/r^3 in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J2/J1 = 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry.Comment: 8 pages, 7 figure

Modeling of Multicomponent Reactive Systems

In recent engineering applications reaction-diffusion systems obtain more and more importance for the production and design of functional materials. Therefore, in this contribution spinodal decomposition in multicomponent systems subjected to chemical reactions is studied. To this end, the classical Cahn-Hilliard phase field model is extended by additional contributions from chemical reactions. After deriving the reaction-diffusion model in a thermodynamically consistent way, for the first time a numerical simulation of a ternary chemically reactive phase separating system is presented

Direct imaging of long-range ferromagnetic and antiferromagnetic order in a dipolar metamaterial

Magnetic metamaterials such as artificial spin ice offer a route to tailor magnetic properties. Such materials can be fabricated by lithographically defining arrays of nanoscale magnetic islands. The magnetostatic interactions between the elements are influenced by their shape and geometric arrangement and can lead to long-range ordering. We demonstrate how the magnetic order in a two-dimensional periodic array of circular disks is controlled by the lattice symmetry. Antiferromagnetic and ferromagnetic order extending through the entire array is observed for the square and hexagonal lattice, respectively. Furthermore, we show that a minute deviation from perfect circularity of the elements along a preferred direction results in room-temperature blocking and favors collinear spin textures

Tomographic reconstruction of quantum correlations in excited Bose-Einstein condensates

We propose to use quantum tomography to characterize the state of a perturbed Bose-Einstein condensate. We assume knowledge of the number of particles in the zero-wave number mode and of density distributions in space at different times, and we treat the condensate in the Bogoliubov approximation. For states that can be treated with the Gross-Pitaevskii equation, we find that the reconstructed density operator gives excellent predictions of the second moments of the atomic creation- and annihilation operators, including the one-body density matrix. Additional inclusion of the momentum distribution at one point of time enables somewhat reliable predictions to be made for the second moments for mixed states, making it possible to distinguish between coherent and thermal perturbations of the condensate. Finally, we find that with observation of the zero-wave number mode's anomalous second moment the reconstructed density operator gives reliable predictions of the second moments of locally amplitude squeezed states.Comment: 12 pages, 7 figure

Development and characterization of a fluorescent tracer for the free fatty acid receptor 2 (FFA2/GPR43)

The free fatty acid receptor 2 (FFA2/GPR43) is considered a potential target for treatment of metabolic and inflammatory diseases. Here we describe the development of the first fluorescent tracer for FFA2 intended as a tool for assessment of thermodynamic and kinetic binding parameters of unlabeled ligands. Starting with a known azetidine FFA2 antagonist, we used a carboxylic acid moiety known not to be critical for receptor interaction as attachment point for a nitrobenzoxadiazole (NBD) fluorophore. This led to the development of 4 (TUG-1609), a fluorescent tracer for FFA2 with favorable spectroscopic properties and high affinity, as determined by bioluminescence resonance energy transfer (BRET)-based saturation and kinetic binding experiments, as well as a high specific to nonspecific BRET binding signal. A BRET-based competition binding assay with 4 was also established and used to determine binding constants and kinetics of unlabeled ligands

Tomographic reconstruction of quantum states in N spatial dimensions

Most quantum tomographic methods can only be used for one-dimensional problems. We show how to infer the quantum state of a non-relativistic N-dimensional harmonic oscillator system by simple inverse Radon transforms. The procedure is equally applicable to finding the joint quantum state of several distinguishable particles in different harmonic oscillator potentials. A requirement of the procedure is that the angular frequencies of the N harmonic potentials are incommensurable. We discuss what kind of information can be found if the requirement of incommensurability is not fulfilled and also under what conditions the state can be reconstructed from finite time measurements. As a further example of quantum state reconstruction in N dimensions we consider the two related cases of an N-dimensional free particle with periodic boundary conditions and a particle in an N-dimensional box, where we find a similar condition of incommensurability and finite recurrence time for the one-dimensional system.Comment: 8 pages, 1 figur

Non-equivalence of key positively charged residues of the free fatty acid 2 receptor in the recognition and function of agonist versus antagonist ligands

Short chain fatty acids (SCFAs) are produced in the gut by bacterial fermentation of poorly digested carbohydrates. A key mediator of their actions is the G protein-coupled Free Fatty Acid 2 (FFA2) receptor and this has been suggested as a therapeutic target for the treatment of both metabolic and inflammatory diseases. However, a lack of understanding of the molecular determinants dictating how ligands bind to this receptor has hindered development. We have developed a novel radiolabelled FFA2 antagonist in order to probe ligand binding to FFA2 and in combination with mutagenesis and molecular modelling studies define how agonist and antagonist ligands interact with the receptor. Although both agonist and antagonist ligands contain negatively charged carboxylates that interact with two key positively charged arginine residues in transmembrane domains V and VII of FFA2, there are clear differences in how these interactions occur. Specifically, while agonists require interaction with both arginine residues to bind the receptor, antagonists require an interaction with only one of the two. Moreover, different chemical series of antagonist interact preferentially with different arginine residues. A homology model capable of rationalizing these observations was developed and provides a tool that will be invaluable for identifying improved FFA2 agonists and antagonists to further define function and therapeutic opportunities of this receptor