Bogoliubov excitation spectrum of an elongated condensate from quasi-one-dimensional to three-dimensional transition

The quasiparticle excitation spectra of a Bose gas trapped in a highly anisotropic trap is studied with respect to varying total number of particles by numerically solving the effective one-dimensional (1D) Gross-Pitaevskii (GP) equation proposed recently by Mateo \textit{et al.}. We obtain the static properties and Bogoliubov spectra of the system in the high energy domain. This method is computationally efficient and highly accurate for a condensate system undergoing a 1D to three-dimensional (3D) cigar-shaped transition, as is shown through a comparison our results with both those calculated by the 3D-GP equation and analytical results obtained in limiting cases. We identify the applicable parameter space for the effective 1D-GP equation and find that this equation fails to describe a system with large number of atoms. We also identify that the description of the transition from 1D Bose-Einstein condensate (BEC) to 3D cigar-shaped BEC using this equation is not smooth, which highlights the fact that for a finite value of $a_\perp/a_s$ the junction between the 1D and 3D crossover is not perfect.Comment: 17 pages, 6 figure

Dynamical Instabilities in a two-component Bose condensate in a 1d optical lattice

In this paper we carry out a stability analysis of the Bloch states of a two-component Bose-Einstein condensate confined to a 1d optical lattice. We consider two concrete systems: a mixture of two hyperfine states of Rubidium-87 and a mixture of Sodium-23 and Rubidium-87. The former is seen to exhibit similar phenomena to a single component condensate while the latter also suffers an instability to phase separation at small Bloch wave vectors. It is shown that sufficiently deep optical lattices can remove this latter instability, potentially allowing imiscible cold atoms species to be held in intimate contact and transported within an experimental system.Comment: 14 Pages, 9 figure

Three-point density correlation functions in the fractional quantum Hall regime

In this paper we consider the three-particle density correlation function for a fractional quantum Hall liquid. The study of this object is motivated by recent experimental studies of fractional quantum Hall systems using inelastic light scattering and phonon absorption techniques. Symmetry properties of the correlation function are noted. An exact sum-rule is derived which this quantity must obey. This sum-rule is used to assess the convolution approximation that has been used to estimate the matrix elements for such experiments. PACS Numbers: 73.40.Hm, 73.20.Mf, 72.10.DiComment: 12 pages + 1 (PS) figur

Simulating quantum transport for a quasi-one-dimensional Bose gas in an optical lattice: the choice of fluctuation modes in the truncated Wigner approximation

We study the effect of quantum fluctuations on the dynamics of a quasi-one-dimensional Bose gas in an optical lattice at zero-temperature using the truncated Wigner approximation with a variety of basis sets for the initial fluctuation modes. The initial spatial distributions of the quantum fluctuations are very different when using a limited number of plane-wave (PW), simple-harmonic-oscillator (SHO) and self-consistently determined Bogoliubov (SCB) modes. The short-time transport properties of the Bose gas, characterized by the phase coherence in the PW basis are distinct from those gained using the SHO and SCB basis. The calculations using the SCB modes predict greater phase decoherence and stronger number fluctuations than the other choices. Furthermore, we observe that the use of PW modes overestimates the extent to which atoms are expelled from the core of the cloud, while the use of the other modes only breaks the cloud structure slightly which is in agreement with the experimental observations [1].Comment: 12 pages, 5 figure

Dynamical excitations in the collision of 2D Bose-Einstein condensates

We carry out simulations of the collision of two components of an adiabatically divided, quasi-2D BEC. We identify under, over and critically damped regimes in the dipole oscillations of the components according to the balance of internal and centre-of-mass (c.m.) energies of the components and investigate the creation of internal excitations. We distinguish the behaviour of this system from previous studies of quasi-1D BEC's. In particular we note that the nature of the internal excitations is only essentially sensitive to an initial phase difference between the components in the overdamped regime.Comment: 17 pages, 9 figure

miR-786 Regulation of a Fatty-Acid Elongase Contributes to Rhythmic Calcium-Wave Initiation in \u3cem\u3eC. elegans\u3c/em\u3e

Background: Rhythmic behaviors are ubiquitous phenomena in animals. In C. elegans, defecation is an ultradian rhythmic behavior: every ∼50 s a calcium wave initiating in the posterior intestinal cells triggers the defecation motor program that comprises three sequential muscle contractions. Oscillatory calcium signaling is central to the periodicity of defecation. The posteriormost intestinal cells function as the pacemaker for this rhythmic behavior, although it is unclear how the supremacy of these cells for calcium-wave initiation is controlled. Results: We describe how the loss of the mir-240/786 microRNA cluster, which results in arrhythmic defecation, causes ectopic intestinal calcium-wave initiation. mir-240/786 expression in the intestine is restricted to the posterior cells that function as the defecation pacemaker. Genetic data indicate that mir-240/786 functions upstream of the inositol 1,4,5-trisphosphate (IP3) receptor. Through rescue analysis, it was determined that miR-786 functions to regulate defecation. Furthermore, we identified elo-2, a fatty-acid elongase with a known role in defecation cycling, as a direct target for miR-786. We propose that the regulation of palmitate levels through repression of elo-2 activity is the likely mechanistic link to defecation. Conclusions: Together, these data indicate that miR-786 confers pacemaker status on posterior intestinal cells for the control of calcium-wave initiation through the regulation of elo-2 and, subsequently, palmitate levels. We propose that a difference in fatty-acid composition in the posterior intestinal cells may alter the activities of membrane proteins, such as IP3-receptor or TRPM channels, that control pacemaker activity in the C. elegans intestine

Surface Instabilities on Liquid Oxygen in an Inhomogeneous Magnetic Field

Liquid oxygen exhibits surface instabilities when subjected to a sufficiently strong magnetic field. A vertically oriented magnetic field gradient both increases the magnetic field value at which the pattern forms and shrinks the length scale of the surface patterning. We show that these effects of the field gradient may be described in terms of an ``effective gravity'', which in our experiments may be varied from 1g to 360g.Comment: 4 pages, 5 embedded figures in eps forma