Department of Physics Papers

Unraveling the structure of ¹³Be

H Terry Fortune — Thu, 09 May 2013 16:09:09 PDT

Using a simple model for low-lying positive-parity resonances in ¹³Be as ¹⁰Be x (sd)³ and ¹²Be_1p x (sd), I find that the lowest 5/2⁺ state is predominantly (sd)³. I give predictions for several additional states.

Continuum three-body decays of ⁹Be(5/2⁻)

H Terry Fortune et al. — Thu, 09 May 2013 16:09:07 PDT

We describe and discuss various three-body decay mechanisms for ⁹Be(5/2⁻). We find that its decay to n+ ⁸Be(2⁺) is a small fraction of the total decay.

Excited states of ¹⁹Mg

H Terry Fortune et al. — Thu, 09 May 2013 16:09:05 PDT

We have calculated energies of the first two excited states of ¹⁹Mg by using a model that was previously successful for the ground state. Computed excitation energies are 1.12 and 1.54 MeV for (3/2⁻) and (5/2⁻), respectively—somewhat in disagreement with values of 1.38 and 2.14 MeV from a recent experiment.

Mass of ¹⁸Mg(g.s.)

H Terry Fortune et al. — Thu, 09 May 2013 16:09:03 PDT

We use a potential model, together with spectroscopic factors from a combination of weak coupling and a shell-model calculation, to compute the mass of the ground state of ¹⁸Mg, considered as a mirror of ¹⁸C. The result is E_2p=3.87(10)MeV.

0⁺ cross-section ratio in ¹²Be( p,t)¹⁰Be

H Terry Fortune — Thu, 09 May 2013 16:09:00 PDT

Using the well-established wave function of ¹²Be(g.s.), I have estimated the cross-section ratio for the reaction ¹²Be(p,t) populating the ground-state and first excited 0⁺ state of ¹⁰Be. I find that the excited-state to ground-state ratio is small for any reasonable value of configuration mixing in ¹⁰Be.

Retarded Green’s function of a Vainshtein system and Galileon waves

Yi-Zen Chu et al. — Thu, 09 May 2013 16:08:57 PDT

Motivated by the desire to test modified gravity theories exhibiting the Vainshtein mechanism, we solve in various physically relevant limits, the retarded Galileon Green’s function (for the cubic theory) about a background sourced by a massive spherically symmetric static body. The static limit of our result will aid us, in a forthcoming paper, in understanding the impact of Galileon fields on the problem of motion in the solar system. In this paper, we employ this retarded Green’s function to investigate the emission of Galileon radiation generated by the motion of matter lying deep within the Vainshtein radius r_v of the central object: acoustic waves vibrating on its surface, and the motion of compact bodies gravitationally bound to it. If λ is the typical wavelength of the emitted radiation, and r₀ is the typical distance of the source from the central mass, with r₀≪r_v, then, compared to its noninteracting massless scalar counterpart, we find that the Galileon radiation rate is suppressed by the ratio (r_v/λ)^-3/2 at the monopole and dipole orders at high frequencies r_v/λ≫1. However, at high enough multipole order, the radiation rate is enhanced by powers of r_v/r₀. At low frequencies r_v/λ≪1, and when the motion is nonrelativistic, Galileon waves yield a comparable rate for the monopole and dipole terms, and are amplified by powers of the ratio r_v/r₀ for the higher multipoles.

Why Do Axons Differ in Caliber?

Janos A. Perge et al. — Thu, 09 May 2013 16:08:55 PDT

CNS axons differ in diameter (d) by nearly 100-fold (∼0.1–10 μm); therefore, they differ in cross-sectional area (d²) and volume by nearly 10,000-fold. If, as found for optic nerve, mitochondrial volume fraction is constant with axon diameter, energy capacity would rise with axon volume, also as d². We asked, given constraints on space and energy, what functional requirements set an axon's diameter? Surveying 16 fiber groups spanning nearly the full range of diameters in five species (guinea pig, rat, monkey, locust, octopus), we found the following: (1) thin axons are most numerous; (2) mean firing frequencies, estimated for nine of the identified axon classes, are low for thin fibers and high for thick ones, ranging from ∼1 to >100 Hz; (3) a tract's distribution of fiber diameters, whether narrow or broad, and whether symmetric or skewed, reflects heterogeneity of information rates conveyed by its individual fibers; and (4) mitochondrial volume/axon length rises ≥d². To explain the pressure toward thin diameters, we note an established law of diminishing returns: an axon, to double its information rate, must more than double its firing rate. Since diameter is apparently linear with firing rate, doubling information rate would more than quadruple an axon's volume and energy use. Thicker axons may be needed to encode features that cannot be efficiently decoded if their information is spread over several low-rate channels. Thus, information rate may be the main variable that sets axon caliber, with axons constrained to deliver information at the lowest acceptable rate.

Ghost Condensate in N = 1 Supergravity

Michael Koehn et al. — Thu, 09 May 2013 16:08:53 PDT

We present the theory of a supersymmetric ghost condensate coupled to N=1 supergravity. This is accomplished using a general formalism for constructing locally supersymmetric higher-derivative chiral superfield actions. The theory admits a ghost condensate vacuum in de Sitter spacetime. Expanded around this vacuum, the scalar sector of the theory is shown to be ghost-free with no spatial gradient instabilities. By direct calculation, the fermion sector is found to consist of a massless chiral fermion and a massless gravitino. By analyzing the supersymmetry transformations, we find that the chiral fermion transforms inhomogeneously, indicating that the ghost condensate vacuum spontaneously breaks local supersymmetry with this field as the Goldstone fermion. Although potentially able to get a mass through the super-Higgs effect, the vanishing superpotential in the ghost condensate theory renders the gravitino massless. Thus local supersymmetry is broken without the super-Higgs effect taking place. This is in agreement with, and gives an explanation for, the direct calculation.

Nonlocal Lagrangian bias

Ravi K. Sheth et al. — Thu, 09 May 2013 16:08:50 PDT

Halos are biased tracers of the dark matter distribution. It is often assumed that the initial patches from which halos formed are locally biased with respect to the initial fluctuation field, meaning that the halo-patch fluctuation field can be written as a Taylor series in the dark matter density fluctuation field. If quantities other than the local density influence halo formation, then this Lagrangian bias will generically be nonlocal; the Taylor series must be performed with respect to these other variables as well. We illustrate the effect with Monte Carlo simulations of a model in which halo formation depends on the local shear (the quadrupole of perturbation theory) and provide an analytic model that provides a good description of our results. Our model, which extends the excursion set approach to walks in more than one dimension, works both when steps in the walk are uncorrelated, as well as when there are correlations between steps. For walks with correlated steps, our model includes two distinct types of nonlocality: one is due to the fact that the initial density profile around a patch which is destined to form a halo must fall sufficiently steeply around it—this introduces kdependence to even the linear bias factor, but otherwise only affects the monopole of the clustering signal. The other type of nonlocality is due to the surrounding shear field; this affects the quadratic and higher-order bias factors and introduces an angular dependence to the clustering signal. In both cases, our analysis shows that these nonlocal Lagrangian bias terms can be significant, particularly for massive halos; they must be accounted for in, e.g., analyses of higher-order clustering in Lagrangian or Eulerian space. Comparison of our predictions with measurements of the halo bispectrum in simulations is encouraging. Although we illustrate these effects using halos, our analysis and conclusions also apply to the other constituents of the cosmic web—filaments, sheets and voids.

Bubble statistics and coarsening dynamics for quasi-two-dimensional foams with increasing liquid content

A. E. Roth et al. — Thu, 09 May 2013 16:08:48 PDT

We report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. The design of the sample cell permits control of the liquid content, through a constant pressure condition set by the height of the foam above a liquid reservoir. We find that in the scaling regime, all bubble distributions are independent not only of time, but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid; we achieve a factor of 4 reduction from the dry limit. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and decreasing bubble size. We successfully model this behavior by explicitly incorporating the border-blocking effect into the von Neumann argument. Two dimensionless bubble shape parameters naturally arise, one of which is primarily responsible for the violation of von Neumann's law for foams that are not perfectly dry.

Effective-medium theory of a filamentous triangular lattice

Xiaoming Mao et al. — Thu, 09 May 2013 16:08:46 PDT

We present an effective-medium theory that includes bending as well as stretching forces, and we use it to calculate the mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability p. We find a rigidity threshold p_b which has the same value for all positive bending rigidity and a crossover characterizing bending, stretching, and bend-stretch coupled elastic regimes controlled by the central-force rigidity percolation point at p_CF≃2/3 of the lattice when fiber bending rigidity vanishes.

Elasticity of a filamentous kagome lattice

Xiaoming Mao et al. — Thu, 09 May 2013 16:08:43 PDT

The diluted kagome lattice, in which bonds are randomly removed with probability 1−p, consists of straight lines that intersect at points with a maximum coordination number of 4. If lines are treated as semiflexible polymers and crossing points are treated as cross-links, this lattice provides a simple model for two-dimensional filamentous networks. Lattice-based effective-medium theories and numerical simulations for filaments modeled as elastic rods, with stretching modulus μ and bending modulus κ, are used to study the elasticity of this lattice as functions of p and κ. At p=1, elastic response is purely affine, and the macroscopic elastic modulus G is independent of κ. When κ=0, the lattice undergoes a first-order rigidity-percolation transition at p=1. When κ>0, G decreases continuously as p decreases below one, reaching zero at a continuous rigidity-percolation transition at p=p_b≈0.605 that is the same for all nonzero values of κ. The effective-medium theories predict scaling forms for G, which exhibit crossover from bending-dominated response at small κ/μ to stretching-dominated response at large κ/μ near both p=1 and p_b, that match simulations with no adjustable parameters near p=1. The affine response as p→1 is identified with the approach to a state with sample-crossing straight filaments treated as elastic rods.

Geometry dependence of the clogging transition in tilted hoppers

C. C. Thomas et al. — Thu, 09 May 2013 16:08:40 PDT

We report the effects of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size D and with variable angle θ of tilt of the hopper away from horizontal. In general, larger tilt angles make the system more susceptible to clogging. To quantify this effect for a given θ, we measure the distribution of mass discharged between clogging events as a function of aperture size and extrapolate to the critical size at which the average mass diverges. By repeating for different angles, we map out a clogging phase diagram as a function of Dand θ that demarcates the regimes of free flow (large D, small θ) and clogging (small D, large θ). We do this for both circular holes and long rectangular slits. Additionally, we measure four types of grain: smooth spheres (glass beads), compact angular grains (beach sand), disklike grains (lentils), and rodlike grains (rice). For circular apertures, the clogging phase diagram is found to be the same for all grain types. For narrow slit apertures and compact grains, the shape is also the same as for circular holes when expressed in terms of projected area of the aperture against the average flow direction. For lentils and rice discharged from slits, the behavior differs and may be due to alignment between grain and slit axes.

Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Drops of Colloidal Suspensions

Peter J. Yunker et al. — Thu, 09 May 2013 16:08:38 PDT

We study the influence of particle shape on growth processes at the edges of evaporating drops. Aqueous suspensions of colloidal particles evaporate on glass slides, and convective flows during evaporation carry particles from drop center to drop edge, where they accumulate. The resulting particle deposits grow inhomogeneously from the edge in two dimensions, and the deposition front, or growth line, varies spatiotemporally. Measurements of the fluctuations of the deposition front during evaporation enable us to identify distinct growth processes that depend strongly on particle shape. Sphere deposition exhibits a classic Poisson-like growth process; deposition of slightly anisotropic particles, however, belongs to the Kardar-Parisi-Zhang universality class, and deposition of highly anisotropic ellipsoids appears to belong to a third universality class, characterized by Kardar-Parisi-Zhang fluctuations in the presence of quenched disorder.

Surface State Magnetization and Chiral Edge States on Topological Insulators

Fan Zhang et al. — Thu, 09 May 2013 16:08:36 PDT

We study the interaction between a ferromagnetically ordered medium and the surface states of a topological insulator with a general surface termination that were identified recently [F. Zhang et al.Phys. Rev. B 86 081303(R) (2012)]. This interaction is strongly crystal face dependent and can generate chiral states along edges between crystal facets even for a uniform magnetization. While magnetization parallel to quintuple layers shifts the momentum of the Dirac point, perpendicular magnetization lifts the Kramers degeneracy at any Dirac points except on the side face, where the spectrum remains gapless and the Hall conductivity switches sign. Chiral states can be found at any edge that reverses the projection of the surface normal to the stacking direction of quintuple layers. Magnetization also weakly hybridizes noncleavage surfaces.

Prediction of a Linear Spin Bulk Photovoltaic Effect in Antiferromagnets

Steve M. Young et al. — Thu, 09 May 2013 16:08:34 PDT

Here we predict the existence of a linear bulk spin photovoltaic effect, where spin currents are produced in antiferromagnetic materials as a response to linearly polarized light, and we describe the symmetry requirements for such a phenomenon to exist. This effect does not depend on spin-orbit effects or require inversion symmetry breaking, distinguishing it from previously explored methods. We propose that the physical mechanism is the nonlinear optical effect “shift current,” and calculate from first principles the spin photocurrent for hematite and bismuth ferrite. We predict a significant response in these materials, with hematite being especially promising due to its availability, low band gap, lack of charge photocurrents, and negligible spin-orbit effect.

Absence of Luttinger’s Theorem due to Zeros in the Single-Particle Green Function

Kiaran B. Dave et al. — Thu, 09 May 2013 16:08:31 PDT

We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, μ, for a T=0 gapped system is removed by using the unique value μ(T→0), Luttinger’s sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the nonexistence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger’s theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter.

Anisotropic Local Correlations and Dynamics in a Relaxor Ferroelectric

Hiroyuki Takenaka et al. — Thu, 09 May 2013 16:08:30 PDT

Relaxor ferroelectrics have been a focus of intense attention due to their anomalous properties, and understanding the structure and dynamics of relaxors has been one of the long-standing challenges in solid-state physics. We investigate the local structure and dynamics in 75%PbMg_1/3Nb_2/3O₃-25%PbTiO₃ using molecular dynamics simulations and the dynamic pair distribution function technique. We show that relaxor transitions can be described by local order parameters. The relaxor phase is characterized by the presence of highly anisotropic correlations between the local cation displacements that resemble the hydrogen bond network in water. This contradicts the current model of polar nanoregion inside a nonpolar matrix. We therefore suggest a new model of a homogeneous random network of anisotropically coupled dipoles.