Theory of coherent transport by an ultra-cold atomic Fermi gas through linear arrays of potential wells

Growing interest is being given to transport of ultra-cold atomic gases through optical lattices generated by the interference of laser beams. In this connection we evaluate the phase-coherent transport of a spin-polarized gas of fermionic atoms along linear structures made from potential wells set in four alternative types of sequence. These are periodic chains of either identical wells or pairs of different wells, and chains of pairs of wells arranged in either a Fibonacci quasi-periodic sequence or a random sequence. The transmission coefficient of fermionic matter is evaluated in a T-matrix scattering approach by describing each array through a tight-binding Hamiltonian and by reducing it to an effective dimer by means of a decimation/renormalization method. The results are discussed in comparison with those pertaining to transport by Fermi-surface electrons coupled to an outgoing lead and by an atomic Bose-Einstein condensate. Main attention is given to (i) Bloch oscillations and their mapping into alternating-current flow through a Josephson junction; (ii) interference patterns that arise on period doubling and their analogy with beam splitting in optical interferometry; (iii) localization by quasi-periodic disorder inside a Fibonacci-ordered structure of double wells; and (iv) Anderson localization in a random structure of double wells.Comment: 14 pages, 4 figure

Six methods to determine expiratory time constants in mechanically ventilated patients: a prospective observational physiology study

Abstract Background Expiratory time constant (τ) objectively assesses the speed of exhalation and can guide adjustments of the respiratory rate and the I:E ratio with the goal of achieving complete exhalation. Multiple methods of obtaining τ are available, but they have not been compared. The purpose of this study was to compare six different methods to obtain τ and to test if the exponentially decaying flow corresponds to the measured time constants. Methods In this prospective study, pressure, flow, and volume waveforms of 30 postoperative patients undergoing volume (VCV) and pressure-controlled ventilation (PCV) were obtained using a data acquisition device and analyzed. τ was measured as the first 63% of the exhaled tidal volume (VT) and compared to the calculated τ as the product of expiratory resistance (RE) and respiratory system compliance (CRS), or τ derived from passive flow/volume waveforms using previously published equations as proposed by Aerts, Brunner, Guttmann, and Lourens. We tested if the duration of exponentially decaying flow during exhalation corresponded to the duration of the predicted second and third τ, based on multiples of the first measured τ. Results Mean (95% CI) measured τ was 0.59 (0.57–0.62) s and 0.60 (0.58–0.63) s for PCV and VCV (p = 0.45), respectively. Aerts method showed the shortest values of all methods for both modes: 0.57 (0.54–0.59) s for PCV and 0.58 (0.55–0.61) s for VCV. Calculated (CRS * RE) and Brunner’s τ were identical with mean τ of 0.64 (0.61–0.67) s for PCV and 0.66 (0.63–069) s for VCV. Mean Guttmann’s τ was 0.64 (0.61–0.68) in PCV and 0.65 (0.62–0.69) in VCV. Comparison of each τ method between PCV and VCV was not significant. Predicted time to exhale 95% of the VT (i.e., 3*τ) was 1.77 (1.70–1.84) s for PCV and 1.80 (1.73–1.88) s for VCV, which was significantly longer than measured values: 1.27 (1.22–1.32) for PCV and 1.30 (1.25–1.35) s for VCV (p < 0.0001). The first, the second and the third measured τ were progressively shorter: 0.6, 0.4 and 0.3 s, in both ventilation modes (p < 0.0001). Conclusion All six methods to determine τ show similar values and are feasible in postoperative mechanically ventilated patients in both PCV and VCV modes