Existence of Long-Range Order for Trapped Interacting Bosons

We derive an inequality governing ``long range'' order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the specific example of a one-dimensional, harmonically trapped dilute Bose condensate, it is shown that the inequality gives an explicit upper bound for the Thomas-Fermi condensate size which may be tested in current experiments.Comment: 4 pages, 1 figure, RevTex4. Title changed at the request of editors; to appear in Phys. Rev. Letter

Effect of fluctuations on the superfluid-supersolid phase transition on the lattice

We derive a controlled expansion into mean field plus fluctuations for the extended Bose-Hubbard model, involving interactions with many neighbors on an arbitrary periodic lattice, and study the superfluid-supersolid phase transition. Near the critical point, the impact of (thermal and quantum) fluctuations on top of the mean field grows, which entails striking effects, such as negative superfluid densities and thermodynamical instability of the superfluid phase -- earlier as expected from mean-field dynamics. We also predict the existence of long-lived "supercooled" states with anomalously large quantum fluctuations.Comment: 5 pages of RevTex4; as published in Physical Review

Strong interaction of a turbulent spot with a shock-induced separation bubble

Direct numerical simulations have been conducted to study the passage of a turbulent spot through a shock-induced separation bubble. Localized blowing is used to trip the boundary layer well upstream of the shock impingement, leading to mature turbulent spots at impingement, with a length comparable to the length of the separation zone. Interactions are simulated at free stream Mach numbers of two and four, for isothermal (hot) wall boundary conditions. The core of the spot is seen to tunnel through the separation bubble, leading to a transient reattachment of the flow. Recovery times are long due to the influence of the calmed region behind the spot. The propagation speed of the trailing interface of the spot decreases during the interaction and a substantial increase in the lateral spreading of the spot was observed. A conceptual model based on the growth of the lateral shear layer near the wingtips of the spot is used to explain the change in lateral growth rat

On the Limits of Depth Reduction at Depth 3 Over Small Finite Fields

Recently, Gupta et.al. [GKKS2013] proved that over Q any $n^{O(1)}$-variate and $n$-degree polynomial in VP can also be computed by a depth three $\Sigma\Pi\Sigma$ circuit of size $2^{O(\sqrt{n}\log^{3/2}n)}$. Over fixed-size finite fields, Grigoriev and Karpinski proved that any $\Sigma\Pi\Sigma$ circuit that computes $Det_n$ (or $Perm_n$) must be of size $2^{\Omega(n)}$ [GK1998]. In this paper, we prove that over fixed-size finite fields, any $\Sigma\Pi\Sigma$ circuit for computing the iterated matrix multiplication polynomial of $n$ generic matrices of size $n\times n$, must be of size $2^{\Omega(n\log n)}$. The importance of this result is that over fixed-size fields there is no depth reduction technique that can be used to compute all the $n^{O(1)}$-variate and $n$-degree polynomials in VP by depth 3 circuits of size $2^{o(n\log n)}$. The result [GK1998] can only rule out such a possibility for depth 3 circuits of size $2^{o(n)}$. We also give an example of an explicit polynomial ($NW_{n,\epsilon}(X)$) in VNP (not known to be in VP), for which any $\Sigma\Pi\Sigma$ circuit computing it (over fixed-size fields) must be of size $2^{\Omega(n\log n)}$. The polynomial we consider is constructed from the combinatorial design. An interesting feature of this result is that we get the first examples of two polynomials (one in VP and one in VNP) such that they have provably stronger circuit size lower bounds than Permanent in a reasonably strong model of computation. Next, we prove that any depth 4 $\Sigma\Pi^{[O(\sqrt{n})]}\Sigma\Pi^{[\sqrt{n}]}$ circuit computing $NW_{n,\epsilon}(X)$ (over any field) must be of size $2^{\Omega(\sqrt{n}\log n)}$. To the best of our knowledge, the polynomial $NW_{n,\epsilon}(X)$ is the first example of an explicit polynomial in VNP such that it requires $2^{\Omega(\sqrt{n}\log n)}$ size depth four circuits, but no known matching upper bound

Aerosol major ion record at Mount Washington

This study examined the seasonal cycles and regional-scale meteorological controls on the chemical properties of bulk aerosols collected from 1999 to 2004 at Mount Washington, the highest peak in the northeastern United States. The concentrations of NH4+ and SO42− peaked during summer months. The pattern for aerosol NO3− was more complicated with relatively high median concentrations characterizing spring and summer months, but with major elevated events occurring during fall, winter, and spring. The seasonal relationship between NH4+ and SO42− indicated that during warmer months a mixture of (NH4)2SO4 and NH4HSO4 was present, while it was mainly the latter in winter. More acidity and higher concentrations of the major species were generally associated with winds from the southwest and west sectors. The highest (≥95th percentile) concentrations of SO42− and NH4+ were associated with air mass transport from major upwind source regions in the Midwest and along the eastern seaboard. The ionic composition and seasonal cycle observed at Mount Washington were similar to those measured at other northeastern sites, but the range and average concentrations were much lower. These differences were exaggerated during wintertime. Included in this paper are several Eulerian case studies of SO2 conversion to SO42− during transit from Whiteface Mountain, New York, to Mount Washington. The calculations suggest a gas-phase SO2 oxidation rate of ∼1–2% per hour and demonstrate the possibility of using these two sites to investigate the chemical evolution of air masses as they move from Midwestern source regions to northern New England

Status of a DEPFET pixel system for the ILC vertex detector

We have developed a prototype system for the ILC vertex detector based on DEPFET pixels. The system operates a 128x64 matrix (with ~35x25 square micron large pixels) and uses two dedicated microchips, the SWITCHER II chip for matrix steering and the CURO II chip for readout. The system development has been driven by the final ILC requirements which above all demand a detector thinned to 50 micron and a row wise read out with line rates of 20MHz and more. The targeted noise performance for the DEPFET technology is in the range of ENC=100 e-. The functionality of the system has been demonstrated using different radioactive sources in an energy range from 6 to 40keV. In recent test beam experiments using 6GeV electrons, a signal-to-noise ratio of S/N~120 has been achieved with present sensors being 450 micron thick. For improved DEPFET systems using 50 micron thin sensors in future, a signal-to-noise of 40 is expected.Comment: Invited poster at the International Symposium on the Development of Detectors for Particle, AstroParticle and Synchrotron Radiation Experiments, Stanford CA (SNIC06) 6 pages, 12 eps figure

Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions

The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems. We solve the full many-body Schr\"odinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density and interaction strength is assessed. It is found that for contact interactions, the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long-ranged the interactions become. The degree of fragmentation is increasing, keeping the particle number $N$ fixed, when the density is decreasing as expected in one spatial dimension. We demonstrate that this remains, nontrivially, true also for long-range interactions in two spatial dimensions. We, finally, find that within our fully self-consistent approach, the fragmentation degree, to a good approximation, decreases universally as $N^{-1/2}$ when only $N$ is varied.Comment: 8 pages of RevTex4-1, 5 figure

Predicted Colors and Flux Densities of Protostars in the Herschel PACS and SPIRE Filters

Upcoming surveys with the Herschel Space Observatory will yield far-IR photometry of large samples of young stellar objects, which will require careful interpretation. We investigate the color and luminosity diagnostics based on Herschel broad-band filters to identify and discern the properties of low-mass protostars. We compute a grid of 2,016 protostars in various physical congurations, present the expected flux densities and flux density ratios for this grid of protostars, and compare Herschel observations of three protostars to the model results. These provide useful constraints on the range of colors and fluxes of protostar in the Herschel filters. We find that Herschel data alone is likely a useful diagnostic of the envelope properties of young starsComment: Part of HOPS KP papers to the Herschel special A&A issu

Mean-field expansion in Bose-Einstein condensates with finite-range interactions

We present a formal derivation of the mean-field expansion for dilute Bose-Einstein condensates with two-particle interaction potentials which are weak and finite-range, but otherwise arbitrary. The expansion allows for a controlled investigation of the impact of microscopic interaction details (e.g., the scaling behavior) on the mean-field approach and the induced higher-order corrections beyond the s-wave scattering approximation.Comment: 6 pages of RevTex4; extended discussion, added reference