Neel to staggered dimer order transition in a generalized honeycomb lattice Heisenberg model

We study a generalized honeycomb lattice spin-1/2 Heisenberg model with nearest-neighbor antiferromagnetic 2-spin exchange, and competing 4-spin interactions which serve to stabilize a staggered dimer state which breaks lattice rotational symmetry. Using a combination of quantum Monte Carlo numerics, spin wave theory, and bond operator theory, we show that this model undergoes a strong first-order transition between a Neel state and a staggered dimer state upon increasing the strength of the 4-spin interactions. We attribute the strong first order character of this transition to the spinless nature of the core of point-like Z(3) vortices obtained in the staggered dimer state. Unlike in the case of a columnar dimer state, disordering such vortices in the staggered dimer state does not naturally lead to magnetic order, suggesting that, in this model, the dimer and Neel order parameters should be thought of as independent fields as in conventional Landau theory.Comment: 13 pages, 10 fig

Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains

The low-energy properties of a system at a critical point may have additional symmetries not present in the microscopic Hamiltonian. This letter presents the theory of a class of multicritical points that provide an interesting example of this in the phase diagrams of random antiferromagnetic spin chains. One case provides an analytic theory of the quantum critical point in the random spin-3/2 chain, studied in recent work by Refael, Kehrein and Fisher (cond-mat/0111295).Comment: Revtex, 4 pages (2 column format), 2 eps figure

Oscillating mushrooms: adiabatic theory for a non-ergodic system

Can elliptic islands contribute to sustained energy growth as parameters of a Hamiltonian system slowly vary with time? In this paper we show that a mushroom billiard with a periodically oscillating boundary accelerates the particle inside it exponentially fast. We provide an estimate for the rate of acceleration. Our numerical experiments confirms the theory. We suggest that a similar mechanism applies to general systems with mixed phase space.Comment: final revisio

Seismometer Detection of Dust Devil Vortices by Ground Tilt

We report seismic signals on a desert playa caused by convective vortices and dust devils. The long-period (10-100s) signatures, with tilts of ~10$^{-7}$ radians, are correlated with the presence of vortices, detected with nearby sensors as sharp temporary pressure drops (0.2-1 mbar) and solar obscuration by dust. We show that the shape and amplitude of the signals, manifesting primarily as horizontal accelerations, can be modeled approximately with a simple quasi-static point-load model of the negative pressure field associated with the vortices acting on the ground as an elastic half space. We suggest the load imposed by a dust devil of diameter D and core pressure {\Delta}Po is ~({\pi}/2){\Delta}PoD$^2$, or for a typical terrestrial devil of 5 m diameter and 2 mbar, about the weight of a small car. The tilt depends on the inverse square of distance, and on the elastic properties of the ground, and the large signals we observe are in part due to the relatively soft playa sediment and the shallow installation of the instrument. Ground tilt may be a particularly sensitive means of detecting dust devils. The simple point-load model fails for large dust devils at short ranges, but more elaborate models incorporating the work of Sorrells (1971) may explain some of the more complex features in such cases, taking the vortex winds and ground velocity into account. We discuss some implications for the InSight mission to Mars.Comment: Contributed Article for Bulletin of the Seismological Society of America, Accepted 29th August 201

Expected seismicity and the seismic noise environment of Europa

Seismic data will be a vital geophysical constraint on internal structure of Europa if we land instruments on the surface. Quantifying expected seismic activity on Europa both in terms of large, recognizable signals and ambient background noise is important for understanding dynamics of the moon, as well as interpretation of potential future data. Seismic energy sources will likely include cracking in the ice shell and turbulent motion in the oceans. We define a range of models of seismic activity in Europa's ice shell by assuming each model follows a Gutenberg-Richter relationship with varying parameters. A range of cumulative seismic moment release between $10^{16}$ and $10^{18}$ Nm/yr is defined by scaling tidal dissipation energy to tectonic events on the Earth's moon. Random catalogs are generated and used to create synthetic continuous noise records through numerical wave propagation in thermodynamically self-consistent models of the interior structure of Europa. Spectral characteristics of the noise are calculated by determining probabilistic power spectral densities of the synthetic records. While the range of seismicity models predicts noise levels that vary by 80 dB, we show that most noise estimates are below the self-noise floor of high-frequency geophones, but may be recorded by more sensitive instruments. The largest expected signals exceed background noise by $\sim$50 dB. Noise records may allow for constraints on interior structure through autocorrelation. Models of seismic noise generated by pressure variations at the base of the ice shell due to turbulent motions in the subsurface ocean may also generate observable seismic noise.Comment: 24 pages, 11 figures, Added in supplementary information from revision submission, including 3 audio files with sonification of Europa noise records. To view attachments, please download and extract the gzipped tar source file listed under "Other formats

Seismic wave propagation in icy ocean worlds

Seismology was developed on Earth and shaped our model of the Earth's interior over the 20th century. With the exception of the Philae lander, all in situ extraterrestrial seismological effort to date was limited to other terrestrial planets. All have in common a rigid crust above a solid mantle. The coming years may see the installation of seismometers on Europa, Titan and Enceladus, so it is necessary to adapt seismological concepts to the setting of worlds with global oceans covered in ice. Here we use waveform analyses to identify and classify wave types, developing a lexicon for icy ocean world seismology intended to be useful to both seismologists and planetary scientists. We use results from spectral-element simulations of broadband seismic wavefields to adapt seismological concepts to icy ocean worlds. We present a concise naming scheme for seismic waves and an overview of the features of the seismic wavefield on Europa, Titan, Ganymede and Enceladus. In close connection with geophysical interior models, we analyze simulated seismic measurements of Europa and Titan that might be used to constrain geochemical parameters governing the habitability of a sub-ice ocean.Comment: 47 pages, 14 figures, accepted for publication in JGR Planet

Symmetry breaking perturbations and strange attractors

The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the perturbation may cause a substantial change in the asymptotic behavior of the system, e.g. transitions from two sided to one sided strange attractors as the other parameters are varied. Moreover, slight asymmetries may cause substantial asymmetries in the relative size of the basins of attraction of the unforced nearly symmetric attracting regions. These changes seems to be associated with homoclinic bifurcations. Numerical evidence indicates that \textit{strange attractors} appear near curves corresponding to specific secondary homoclinic bifurcations. These curves are found using analytical perturbational tools