Harmonically Trapped Quantum Gases

We solve the problem of a Bose or Fermi gas in $d$-dimensions trapped by $\delta \leq d$ mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature $T_{c}$ if and only if $d+\delta >2$, and a jump in the specific heat at $T_{c}$ if and only if $d+\delta >4$. Specific heats for both gas types precisely coincide as functions of temperature when $d+\delta =2$. The trapped system behaves like an ideal free quantum gas in $d+\delta$ dimensions. For $\delta =0$ we recover all known thermodynamic properties of ideal quantum gases in $d$ dimensions, while in 3D for $\delta =$ 1, 2 and 3 one simulates behavior reminiscent of quantum {\it wells, wires}and{\it dots}, respectively.Comment: 14 pages including 3 figures and 3 table

Cooper pairs as bosons

Although BCS pairs of fermions are known not to obey Bose-Einstein (BE) commutation relations nor BE statistics, we show how Cooper pairs (CPs), whether the simple original ones or the CPs recently generalized in a many-body Bethe-Salpeter approach, being clearly distinct from BCS pairs at least obey BE statistics. Hence, contrary to widespread popular belief, CPs can undergo BE condensation to account for superconductivity if charged, as well as for neutral-atom fermion superfluidity where CPs, but uncharged, are also expected to form.Comment: 8 pages, 2 figures, full biblio info adde

Real time phase-slopes calculations by correlations using FPGAs

J. Trujillo Sevilla ; M. R. Valido ; L. F. Rodríguez Ramos ; E. Boemo ; F. Rosa ; J. M. Rodríguez Ramos, “Real time phase-slopes calculations by correlations using FPGAs,” Proc. SPIE 7015, Adaptive Optics Systems, 70153B (July 11, 2008), Norbert Hubin; Claire E. Max; Peter L. Wizinowich , 7015 (Issue) 70153B, (2008). Copyright © 2008 SPIE Society of Photo‑Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.ELT laser guide star wavefront sensors are planned to handle an expected amount of data to be overwhelmingly large (1600x1600 pixels at 700 fps). According to the calculations involved, the solutions must consider to run on specialized hardware as Graphical Processing Units (GPUs) or Field Programmable Gate Arrays (FPGAs), among others. In the case of a Shack-Hartmann wavefront sensor is finally selected, the wavefront slopes can be computed using centroid or correlation algorithms. Most of the developments are designed using centroid algorithms, but precision ought to be taken in account too, and then correlation algorithms are really competitive. This paper presents an FPGA-based wavefront slope implementation, capable of handling the sensor output stream in a massively parallel approach, using a correlation algorithm previously tested and compared to the centroid algorithm. Time processing results are shown, and they demonstrate the ability of the FPGA integer arithmetic in the resolution of AO problems. The selected architecture is based in today’s commercially available FPGAs which have a very limited amount of internal memory. This limits the dimensions used in our implementation, but this also means that there is a lot of margin to move real-time algorithms from the conventionalThis work has been partially supported by “Programa Nacional de Diseño y Producción Industrial" (Project DPI 2006- 07906) of the “Ministerio de Educación y Ciencia" of the Spanish Government, and by “European Regional Development Fund" (ERDF)

Flavour constraints on scenarios with two or three heavy squark generations

We re-assess constraints from flavour-changing neutral currents in the kaon system on supersymmetric scenarios with a light gluino, two heavy generations of squarks and a lighter third generation. We compute for the first time limits in scenarios with three heavy squark families, taking into account QCD corrections at the next-to-leading order. We compare our limits with those in the case of two heavy families. We use the mass insertion approximation and consider contributions from gluino exchange to constrain the mixing between the first and second squark generation. While it is not possible to perform a general analysis, we assess the relevance of each kind of flavour- and CP-violating parameters. We also provide ready to use magic numbers for the computation of the Wilson coefficients at 2 GeV for these scenarios.Comment: 23 pages, 14 figures; v3: matches published version (contains improvements in the presentation and clarifications

Bubbling in a co-flow at high Reynolds numbers

The physical mechanisms underlying bubble formation from a needle in a co-flowing liquid environment at high Reynolds numbers are studied in detail with the aid of experiments and boundary-integral numerical simulations. To determine the effect of gas inertia the experiments were carried out with air and helium. The influence of the injection system is elucidated by performing experiments using two different facilities, one where the constancy of the gas flow-rate entering the bubble is ensured, and another one where the gas is injected through a needle directly connected to a pressurized chamber. In the case of constant flow-rate injection conditions, the bubbling frequency has been shown to hardly depend on the gas density, with a bubble size given by db / ro  ? 6U? K * U + k2 /? U- 1? 1/3 for U? 2, where U is the gas-to-liquid ratio of the mean velocities, ro is the radius of the gas injection needle, and k * = 5,84 and k2 = 4,29, whit db / ro3,3U1 / 3 for U1.. Nevertheless, in this case the effect of gas density is relevant to describe the final instants of bubble breakup, which take place at a time scale much smaller than the bubbling time, tb. This effect is evidenced by the liquid jets penetrating the gas bubbles upon their pinch-off. Our measurements indicate that the velocity of the penetrating jets is considerably larger in air bubbles than in helium bubbles due to the distinct gas inertia of both situations. However, in the case of constant pressure supply conditions, the bubble size strongly depends on the density of the gas through the pressure loss along the gas injection needle. Furthermore, under the operating conditions reported here, the equivalent diameters of the bubbles are between 10% and 20% larger than their constant flow-rate counterparts. In addition, the experiments and the numerical results show that, under constant pressure supply, helium bubbles are approximately 10% larger than air bubbles due to the gas density effect on the bubbling process