Collective Tunnelling of Strongly Interacting Cold Atoms in a Double-Well Potential

It is known that under resonance conditions, a group of strongly interacting bosonic atoms, trapped in a double-well potential, mimics a single particle, performing Rabi oscillations between the wells. By implication, all atoms need to tunnel at roughly the same time, even though the Bose–Hubbard Hamiltonian accounts only for one-atom-at-a-time transfers. The mechanism of this collective behavior is analyzed, the Rabi frequencies in the process are evaluated, and the limitation of this simple picture is discussed. In particular, it is shown that the small rapid oscillations superimposed on the slow Rabi cycle result from splitting the transferred cluster at the sudden onset of tunnelling, and disappear if tunnelling is turned on gradually.     

Quantum mechanical modeling of Zn-based spinel oxides: Assessing the structural,vibrational, and electronic properties

The structural, electronic, and vibrational properties of two leading representatives of the Zn-based spinel oxides class, normal ZnX₂O₄ (X = Al, Ga, In) and inverse Zn₂MO₄ (M = Si, Ge, Sn) crystals, were investigated. In particular, density functional theory (DFT) was combined with different exchange-correlation functionals: B3LYP, HSE06, PBE0, and PBESol. Our calculations showed good agreement with the available experimental data, showing a mean percentage error close to 3% for structural parameters. For the electronic structure, the obtained HSE06 band-gap values overcome previous theoretical results, exhibiting a mean percentage error smaller than 10.0%. In particular, the vibrational properties identify the significant differences between normal and inverse spinel configurations, offering compelling evidence of a structure-property relationship for the investigated materials. Therefore, the combined results confirm that the range-separated HSE06 hybrid functional performs the best in spinel oxides. Despite some points that cannot be directly compared to experimental results, we expect that future experimental work can confirm our predictions, thus opening a new avenue for understanding the structural, electronic, and vibrational properties in spinel oxides.     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

The Convexity Number of a Graph

 For two vertices u and v of a connected graph G, the set I[u,v] consists of all those vertices lying on a u−v shortest path in G, while for a set S of vertices of G, the set I[S] is the union of all sets I[u,v] for u,v∈S. A set S is convex if I[S]=S. The convexity number con(G) of G is the maximum cardinality of a proper convex set of G. The clique number ω(G) is the maximum cardinality of a clique in G. If G is a connected graph of order n that is not complete, then n≥3 and 2≤ω(G)≤con(G)≤n−1. It is shown that for every triple l,k,n of integers with n≥3 and 2≤l≤k≤n−1, there exists a noncomplete connected graph G of order n with ω(G)=l and con(G)=k. Other results on convex numbers are also presented. Received: August 19, 1998 Final version received: May 17, 2000     

Aggregation of nanosized colloidal silica in the presence of various alkali cations investigated by the electrospray technique

The slow aggregation process of a concentrated silica dispersion (Bindzil 40/220) in the presence of alkali chlorides (LiCl, NaCl, KCl, RbCl, and CsCl) was investigated by means of mobility measurements. At intervals during the aggregation, particles and aggregates were transferred from the liquid phase to the gas phase via electrospray (ES) and subsequently size selected and counted using a scanning mobility particle sizer (SMPS). This method enables the acquisition of particle and aggregate size distributions with a time resolution of minutes. To our knowledge, this is the first time that the method has been applied to study the process of colloidal aggregation. The obtained results indicate that, independent of the type of counterion, a sufficient dilution of the formed gel will cause the particles to redisperse. Hence, the silica particles are, at least initially, reversibly aggregated. The reversibility of the aggregation indicates additional non-DLVO repulsive steric interactions that are likely due to the presence of a gel layer at the surface. The size of the disintegrating aggregates was monitored as a function of the time after dilution. It was found that the most stable aggregates were formed by the ions that adsorb most strongly on the particle surface. This attractive effect was ascribed to an ion-ion correlation interaction.     

Analysis for sulfur as hydrogen sulfide incorporating zirconia pretreatment and preconcentration

The method of analysis for sulfate by reduction of high oxidation state sulfur to hydrogen sulfide, followed by spectrophotometric analysis, has the advantages of allowing small quantities to be measured and some interfering species to be removed. However, it has been found that acid digested samples cannot be analysed by this method due to destruction of the reduction mixture. A column of zirconium(IV) oxide was successfully used to both, remove interfering ions (H(+), Cl(-) and NO(-)(3)) from a sediment digest, as well as perform preconcentration of sulfate. Recoveries from digests of standard sulfur samples were 101 +/- 1%, and from preconcentration solutions 98.8 +/- 1.2%. Comparison of results with independent analyses confirmed that not all sulfur species are detected with the same efficiency by the combined zirconia/reduction-spectrophotometric method.     

Isoelectric focusing nonporous silica reversed-phase high-performance liquid chromatography/electrospray ionization time-of-flight mass spectrometry: a three-dimensional liquid-phase protein separation method as applied to the human erythroleukemia cell-line

A liquid-phase three-dimensional protein separation method has been developed that is used to separate the cytosolic fraction of a HEL cell lysate via isoelectric focusing (IEF), nonporous silica (NPS) reversed-phase high-performance liquid chromatography (RP-HPLC) and electrospray ionization time-of-flight mass spectrometry (ESI-TOFMS), respectively. Several hundred unique protein molecular weights were observed in a pI range from 4.8 to 8.5 and a mass range from 5 to 85 kDa. Proteins were positively identified by analysis of the pI (+/-0.5 pI units), an intact protein molecular weight (+/-150 ppm), and peptide mass mapping results. Using the molecular weight (MW) and peptide mapping results of identified proteins it was possible to characterize their posttranslational (PTMs) and/or sequence modifications. PTMs were detected on both forms of cytosolic actin, heat shock 90 beta, HINT and alpha-enolase. Sequence modifications or conflicts were observed for beta-and gamma-actin, ATP beta-synthase and heat shock 90 beta. IEF-NPS-RP-HPLC/ESI-TOFMS was used to determine experimental pI, MW and relative hydrophobicity values for each protein detected. This data was used to generate a 2-D pI-MS protein map, where proteins are displayed according to their pI and molecular weight. Protein molecular weight peaks are represented as bands in the 2-D pI-MS image where the gray scale of each band is proportional to the intensity of the protein molecular weight peak. In addition, a third hydrophobicity dimension (%B) was added as the % acetonitrile elution to generate a 3-D pI-MS-%B plot where each protein can be tagged according to three parameters.