Observing collapse in two colliding dipolar Bose-Einstein condensates

We study the collision of two Bose-Einstein condensates with pure dipolar interaction. A stationary pure dipolar condensate is known to be stable when the atom number is below a critical value. However, collapse can occur during the collision between two condensates due to local density fluctuations even if the total atom number is only a fraction of the critical value. Using full three-dimensional numerical simulations, we observe the collapse induced by local density fluctuations. For the purpose of future experiments, we present the time dependence of the density distribution, energy per particle and the maximal density of the condensate. We also discuss the collapse time as a function of the relative phase between the two condensates.Comment: 6 pages, 7 figure

Dynamics of a two-species Bose-Einstein condensate in a double well

We study the dynamics of a two-species Bose-Einstein condensate in a double well. Such a system is characterized by the intraspecies and interspecies s-wave scattering as well as the Josephson tunneling between the two wells and the population transfer between the two species. We investigate the dynamics for some interesting regimes and present numerical results to support our conclusions. In the case of vanishing intraspecies scattering lengths and a weak interspecies scattering length, we find collapses and revivals in the population dynamics. A possible experimental implementation of our proposal is briefly discussed.Comment: 7 pages, 5 figure

Unchanged thermopower enhancement at the semiconductor-metal transition in correlated FeSb2−x_{2-x}Tex_x

Substitution of Sb in FeSb$_2$ by less than 0.5% of Te induces a transition from a correlated semiconductor to an unconventional metal with large effective charge carrier mass $m^*$. Spanning the entire range of the semiconductor-metal crossover, we observed an almost constant enhancement of the measured thermopower compared to that estimated by the classical theory of electron diffusion. Using the latter for a quantitative description one has to employ an enhancement factor of 10-30. Our observations point to the importance of electron-electron correlations in the thermal transport of FeSb$_2$, and suggest a route to design thermoelectric materials for cryogenic applications.Comment: 3 pages, 3 figures, accepted for publication in Appl. Phys. Lett. (2011

Detection of a single-charge defect in a metal-oxide-semiconductor structure using vertically coupled Al and Si single-electron transistors

An Al-AlO_x-Al single-electron transistor (SET) acting as the gate of a narrow (~ 100 nm) metal-oxide-semiconductor field-effect transistor (MOSFET) can induce a vertically aligned Si SET at the Si/SiO_2 interface near the MOSFET channel conductance threshold. By using such a vertically coupled Al and Si SET system, we have detected a single-charge defect which is tunnel-coupled to the Si SET. By solving a simple electrostatic model, the fractions of each coupling capacitance associated with the defect are extracted. The results reveal that the defect is not a large puddle or metal island, but its size is rather small, corresponding to a sphere with a radius less than 1 nm. The small size of the defect suggests it is most likely a single-charge trap at the Si/SiO_2 interface. Based on the ratios of the coupling capacitances, the interface trap is estimated to be about 20 nm away from the Si SET.Comment: 5 pages and 5 figure

From random walks to distances on unweighted graphs

Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics has been limited. We introduce and develop a class of techniques for analyzing random walks on graphs using stochastic calculus. Using these techniques we generalize results on the degeneracy of hitting times and analyze a metric based on the Laplace transformed hitting time (LTHT). The metric serves as a natural, provably well-behaved alternative to the expected hitting time. We establish a general correspondence between hitting times of the Brownian motion and analogous hitting times on the graph. We show that the LTHT is consistent with respect to the underlying metric of a geometric graph, preserves clustering tendency, and remains robust against random addition of non-geometric edges. Tests on simulated and real-world data show that the LTHT matches theoretical predictions and outperforms alternatives.Comment: To appear in NIPS 201

Shintani functions, real spherical manifolds, and symmetry breaking operators

For a pair of reductive groups $G \supset G'$, we prove a geometric criterion for the space $Sh(\lambda, \nu)$ of Shintani functions to be finite-dimensional in the Archimedean case. This criterion leads us to a complete classification of the symmetric pairs $(G,G')$ having finite-dimensional Shintani spaces. A geometric criterion for uniform boundedness of $dim Sh(\lambda, \nu)$ is also obtained. Furthermore, we prove that symmetry breaking operators of the restriction of smooth admissible representations yield Shintani functions of moderate growth, of which the dimension is determined for $(G, G') = (O(n+1,1), O(n,1))$.Comment: to appear in Progress in Mathematics, Birkhause

Dipolar effect in coherent spin mixing of two atoms in a single optical lattice site

We show that atomic dipolar effects are detectable in the system that recently demonstrated two-atom coherent spin dynamics within individual lattice sites of a Mott state. Based on a two-state approximation for the two-atom internal states and relying on a variational approach, we have estimated the spin dipolar effect. Despite the absolute weakness of the dipole-dipole interaction, it is shown that it leads to experimentally observable effects in the spin mixing dynamics.Comment: 4 pages, 3 color eps figures, to appear in Phys. Rev. Let

Layered Fabrication of Branched Networks Using Lindenmayer Systems

A current challenge impeding the growth of bone tissue engineering is the lack of functional scaffolds of geometric sizes greater than 10mm due to the inability of cells to survive deep within the scaffold. It is hypothesized that these scaffolds must have an inbuilt nutrient distribution network to sustain the uniform growth of cells. In this paper, we seek to enhance the design and layered fabrication of scaffold internal architecture through the development of Lindenmayer systems, a graphical language based theory to create nutrient delivery networks. The scaffolds are fabricated using the Texas Instruments DLP™ system through UV‐photopolymerization to produce polyethylene glycol hydrogels with internal branch structures. The paper will discuss the Lindenmayer system, process planning algorithms, layered fabrication of samples, challenges and future tasks.Mechanical Engineerin