A Levinson theorem for scattering from a Bose-Einstein condensate

A relation between the number of bound collective excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalises Levinson's theorem. Specific features of the Bogoliubov model such as complex-energy and continuum bound states are discussed and a numerical example is given.Comment: 4 pages, 3 figure

Traveling Dark Solitons in Superfluid Fermi Gases

Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and number of depleted particles completely determines the dynamics of dark solitons on a slowly-varying background density. For the unitary Fermi gas we determine these relations from general scaling arguments and conservation of local particle number. We find solitons to oscillate sinusoidally at the trap frequency reduced by a factor of $1/\sqrt{3}$. Numerical integration of the time-dependent Bogoliubov-de Gennes equation determines spatial profiles and soliton dispersion relations across the BEC-BCS crossover and proves consistent with the scaling relations at unitarity.Comment: Small changes in response to referee's comments; fig 1 revised and refs updated. Cross listed to nucl-th due to interest in the unitary Fermi ga

Effect of high and low glycaemic index recovery diets on intramuscular lipid oxidation during aerobic exercise

Intramyocellular lipid (IMCL) and plasma NEFA are important skeletal muscle fuel sources. By raising blood insulin concentrations, carbohydrate ingestion inhibits lypolysis and reduces circulating NEFA. We hypothesised that differences in the postprandial glycaemic and insulin response to carbohydrates (i.e. glycaemic index; GI) could alter NEFA availability and IMCL use during subsequent exercise. Endurance-trained individuals (n 7) cycled for 90 min at 70 % V?O2peak and then consumed either high GI (HGI) or low GI (LGI) meals over the following 12 h. The following day after an overnight fast, the 90 min cycle was repeated. IMCL content of the vastus lateralis was quantified using magnetic resonance spectroscopy before and after exercise. Blood samples were collected at 15 min intervals throughout exercise and analysed for NEFA, glycerol, glucose, insulin, and lactate. Substrate oxidation was calculated from expired air samples. The 90 min cycle resulted in >2-fold greater reduction in IMCL in the HGI trial (3·5 (sem 1·0) mm/kg wet weight) than the LGI trial (1·6 (sem 0·3) mm/kg wet weight, P < 0·05). During exercise, NEFA availability was reduced in the HGI trial compared to the LGI trial (area under curve 2·36 (sem 0·14) mEq/l per h v. 3·14 (sem 0·28) mEq/l per h, P < 0·05 respectively). No other differences were significant. The findings suggest that HGI carbohydrates reduce NEFA availability during exercise and increase reliance on IMCL as a substrate source during moderate intensity exercise

Geometrical Considerations for the Design of Liquid-phase Biochemical Sensors Using a Cantilever\u27s Fundamental In-plane Mode

The influence of the beam geometry on the quality factor and resonance frequency of resonant silicon cantilever beams vibrating in their fundamental in-plane flexural mode in water has been investigated. Compared to cantilevers vibrating in their first out-of-plane flexural mode, utilizing the in-plane mode results in reduced damping and reduced mass loading by the surrounding fluid. Quality factors as high as 86 have been measured in water for cantilevers with a 20 μm thick silicon layer. Based on the experimental data, design guidelines are established for beam dimensions that ensure maximal Q-factors and minimal mass loading by the surrounding fluid, thus improving the limit-of-detection of mass-sensitive biochemical sensors. Elementary theory is also presented to help explain the observed trends. Additional discussion focuses on the tradeoffs that exist in designing liquid-phase biochemical sensors using in-plane cantilevers

Unconventional Uses of Microcantilevers as Chemical Sensors in Gas and Liquid Media

The use of microcantilevers as (bio)chemical sensors usually involves the application of a chemically sensitive layer. The coated device operates either in a static bending regime or in a dynamic flexural mode. While some of these coated devices may be operated successfully in both the static and the dynamic modes, others may suffer from certain shortcomings depending on the type of coating, the medium of operation and the sensing application. Such shortcomings include lack of selectivity and reversibility of the sensitive coating and a reduced quality factor due to the surrounding medium. In particular, the performance of microcantilevers excited in their standard out-of-plane dynamic mode drastically decreases in viscous liquid media. Moreover, the responses of coated cantilevers operating in the static bending mode are often difficult to interpret. To resolve these performance issues, the following emerging unconventional uses of microcantilevers are reviewed in this paper: (1) dynamic-mode operation without using a sensitive coating, (2) the use of in-plane vibration modes (both flexural and longitudinal) in liquid media, and (3) incorporation of viscoelastic effects in the coatings in the static mode of operation. The advantages and drawbacks of these atypical uses of microcantilevers for chemical sensing in gas and liquid environments are discussed

Soliton Magnetization Dynamics in Spin-Orbit Coupled Bose-Einstein Condensates

Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark soliton excitations that show periodic density dynamics in real space. In addition to the density feature, solitons also carry a localized pseudo-spin magnetization that exhibits a rich and tunable dynamics. Analytic results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.Comment: 3 figures, 5 page

Spontaneous soliton formation and modulational instability in Bose-Einstein condensates

The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Strecker {\it et al.} Nature {\bf 417} 150 (2002)] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton--soliton interactions, produce bursts of hot atoms at different time scales.Comment: 4 pages, 3 figures. Phys. Rev. Lett. in pres

Effect of Hydrodynamic Force on Microcantilever Vibrations: Applications to Liquid-Phase Chemical Sensing

At the microscale, cantilever vibrations depend not only on the microstructure’s properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever’s vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, and improve sensitivity in sensing applications, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include in-plane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. However, such systems require sampling (no in-situ measurements) and a relatively large sample volume (a few milliliters). Moreover, the frequency range is limited to low frequencies (less than 200Hz). To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range