A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6

We exhibit an infinite family of {\it triplets} of mutually unbiased bases (MUBs) in dimension 6. These triplets involve the Fourier family of Hadamard matrices, $F(a,b)$. However, in the main result of the paper we also prove that for any values of the parameters $(a,b)$, the standard basis and $F(a,b)$ {\it cannot be extended to a MUB-quartet}. The main novelty lies in the {\it method} of proof which may successfully be applied in the future to prove that the maximal number of MUBs in dimension 6 is three.Comment: 32 pages (with Appendix A and B

Collisions of cold magnesium atoms in a weak laser field

We use quantum scattering methods to calculate the light-induced collisional loss of laser-cooled and trapped magnesium atoms for detunings up to 30 atomic linewidths to the red of the 1S_0-1P_1 cooling transition. Magnesium has no hyperfine structure to complicate the theoretical studies. We evaluate both the radiative and nonradiative mechanisms of trap loss. The radiative escape mechanism via allowed 1Sigma_u excitation is dominant for more than about one atomic linewidth detuning. Molecular vibrational structure due to photoassociative transitions to bound states begins to appear beyond about ten linewidths detuning.Comment: 4 pages with 3 embedded figure

Formation of fundamental structures in Bose-Einstein Condensates

The meanfield interaction in a Bose condensate provides a nonlinearity which can allow stable structures to exist in the meanfield wavefunction. We discuss a number of examples where condensates, modelled by the one dimensional Gross Pitaevskii equation, can produce gray solitons and we consider in detail the case of two identical condensates colliding in a harmonic trap. Solitons are shown to form from dark interference fringes when the soliton structure, constrained in a defined manner, has lower energy than the interference fringe and an analytic expression is given for this condition.Comment: 7 pages, 3 figures, requires ioplppt.st

CSF protein biomarkers predicting longitudinal reduction of CSF β-amyloid42 in cognitively healthy elders.

β-amyloid (Aβ) plaque accumulation is a hallmark of Alzheimer's disease (AD). It is believed to start many years prior to symptoms and is reflected by reduced cerebrospinal fluid (CSF) levels of the peptide Aβ1-42 (Aβ42). Here we tested the hypothesis that baseline levels of CSF proteins involved in microglia activity, synaptic function and Aβ metabolism predict the development of Aβ plaques, assessed by longitudinal CSF Aβ42 decrease in cognitively healthy people. Forty-six healthy people with three to four serial CSF samples were included (mean follow-up 3 years, range 2-4 years). There was an overall reduction in Aβ42 from a mean concentration of 211-195 pg ml(-1) after 4 years. Linear mixed-effects models using longitudinal Aβ42 as the response variable, and baseline proteins as explanatory variables (n=69 proteins potentially relevant for Aβ metabolism, microglia or synaptic/neuronal function), identified 10 proteins with significant effects on longitudinal Aβ42. The most significant proteins were angiotensin-converting enzyme (ACE, P=0.009), Chromogranin A (CgA, P=0.009) and Axl receptor tyrosine kinase (AXL, P=0.009). Receiver-operating characteristic analysis identified 11 proteins with significant effects on longitudinal Aβ42 (largely overlapping with the proteins identified by linear mixed-effects models). Several proteins (including ACE, CgA and AXL) were associated with Aβ42 reduction only in subjects with normal baseline Aβ42, and not in subjects with reduced baseline Aβ42. We conclude that baseline CSF proteins related to Aβ metabolism, microglia activity or synapses predict longitudinal Aβ42 reduction in cognitively healthy elders. The finding that some proteins only predict Aβ42 reduction in subjects with normal baseline Aβ42 suggest that they predict future development of the brain Aβ pathology at the earliest stages of AD, prior to widespread development of Aβ plaques

Control of Raman Lasing in the Nonimpulsive Regime

We explore coherent control of stimulated Raman scattering in the nonimpulsive regime. Optical pulse shaping of the coherent pump field leads to control over the stimulated Raman output. A model of the control mechanism is investigated.Comment: 4 pages, 5 figure