Magnetic phase diagram of a spin-1 condensate in two dimensions with dipole interaction

Several new features arise in the ground-state phase diagram of a spin-1 condensate trapped in an optical trap when the magnetic dipole interaction between the atoms is taken into account along with confinement and spin precession. The boundaries between the regions of ferromagnetic and polar phases move as the dipole strength is varied and the ferromagnetic phases can be modulated. The magnetization of the ferromagnetic phase perpendicular to the field becomes modulated as a helix winding around the magnetic field direction, with a wavelength inversely proportional to the dipole strength. This modulation should be observable for current experimental parameters in $^{87}$Rb. Hence the much-sought supersolid state, with broken continuous translation invariance in one direction and broken global U(1) invariance, occurs generically as a metastable state in this system as a result of dipole interaction. The ferromagnetic state parallel to the applied magnetic field becomes striped in a finite system at strong dipolar coupling.Comment: 11 pages, 7 figures;published versio

Assessing the Performance of the Diffusion Monte Carlo Method as Applied to the Water Monomer, Dimer, and Hexamer

The Diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer, using q-TIP4P/F, one of the most simple, empirical water models with flexible monomers. The bias in the time step ($\Delta\tau$) and population size ($N_w$) is investigated. For the binding energies, the bias in $\Delta\tau$ cancels nearly completely, while a noticeable bias in $N_w$ still remains. However, for the isotope shift, (e.g, in the dimer binding energies between (H$_2$O)$_2$ and (D$_2$O)$_2$) the systematic errors in $N_w$ do cancel. Consequently, very accurate results for the latter (within $\sim 0.01$ kcal/mol) are obtained with relatively moderate numerical effort ($N_w\sim 10^3$). For the water hexamer and its (D$_2$O)$_6$ isotopomer the DMC results as a function of $N_w$ are examined for the cage and prism isomers. For a given isomer, the issue of the walker population leaking out of the corresponding basin of attraction is addressed by using appropriate geometric constraints. The population size bias for the hexamer is more severe, and in order to maintain accuracy similar to that of the dimer, the population size $N_w$ must be increased by about two orders of magnitude. Fortunately, when the energy difference between cage and prism is taken, the biases cancel, thereby reducing the systematic errors to within $\sim 0.01$ kcal/mol when using a population of $N_w=4.8\times 10^5$ walkers. Consequently, a very accurate result for the isotope shift is also obtained. Notably, both the quantum and the isotope effects for the prism-cage energy difference are small.Comment: 11 pages, 5 figures, 36 references. Submitted to the Journal of Physical Chemistr

Decentralized formation control with connectivity maintenance and collision avoidance under limited and intermittent sensing

A decentralized switched controller is developed for dynamic agents to perform global formation configuration convergence while maintaining network connectivity and avoiding collision within agents and between stationary obstacles, using only local feedback under limited and intermittent sensing. Due to the intermittent sensing, constant position feedback may not be available for agents all the time. Intermittent sensing can also lead to a disconnected network or collisions between agents. Using a navigation function framework, a decentralized switched controller is developed to navigate the agents to the desired positions while ensuring network maintenance and collision avoidance.Comment: 8 pages, 2 figures, submitted to ACC 201

Bound states and E_8 symmetry effects in perturbed quantum Ising chains

In a recent experiment on CoNb_2O_6, Coldea et al. [Science 327, 177 (2010)] found for the first time experimental evidence of the exceptional Lie algebra E_8. The emergence of this symmetry was theoretically predicted long ago for the transverse quantum Ising chain in the presence of a weak longitudinal field. We consider an accurate microscopic model of CoNb_2O_6 incorporating additional couplings and calculate numerically the dynamical structure function using a recently developed matrix-product-state method. The excitation spectra show bound states characteristic of the weakly broken E_8 symmetry. We compare the observed bound state signatures in this model to those found in the transverse Ising chain in a longitudinal field and to experimental data.Comment: 4 pages, 3 figure

Omnidirectional Sensory and Motor Volumes in Electric Fish

Active sensing organisms, such as bats, dolphins, and weakly electric fish, generate a 3-D space for active sensation by emitting self-generated energy into the environment. For a weakly electric fish, we demonstrate that the electrosensory space for prey detection has an unusual, omnidirectional shape. We compare this sensory volume with the animal's motor volume—the volume swept out by the body over selected time intervals and over the time it takes to come to a stop from typical hunting velocities. We find that the motor volume has a similar omnidirectional shape, which can be attributed to the fish's backward-swimming capabilities and body dynamics. We assessed the electrosensory space for prey detection by analyzing simulated changes in spiking activity of primary electrosensory afferents during empirically measured and synthetic prey capture trials. The animal's motor volume was reconstructed from video recordings of body motion during prey capture behavior. Our results suggest that in weakly electric fish, there is a close connection between the shape of the sensory and motor volumes. We consider three general spatial relationships between 3-D sensory and motor volumes in active and passive-sensing animals, and we examine hypotheses about these relationships in the context of the volumes we quantify for weakly electric fish. We propose that the ratio of the sensory volume to the motor volume provides insight into behavioral control strategies across all animals