Phase-Amplitude Relations for a Particle with a Superposition of Two Energy Levels in a Double Potential Well

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use the model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log analytical uncertainty relations are satisfied.     

Formation and dynamics of many-boson fragmented states in one-dimensional attractive ultracold gases

The dynamics of attractive ultracold bosonic clouds in one dimension is studied by solving the many-particle time-dependent Schr?dinger equation. The initially coherent wave packet can dynamically dissociate into two parts when its energy exceeds a threshold value. Noticeably, the time-dependent Gross-Pitaevskii theory does not show up the splitting. We call the split object fragmenton. It possesses remarkable properties; in particular, it is macroscopically fragmented. A simple static model predicts the existence of fragmented states responsible for the formation and dynamics of fragmentons.     

Minimization of the pulse's timing jitter in a dispersion-compensated WDM system

We address the problem of the collision-induced crosstalk between pulses in a dispersion-compensated WDM system composed of a periodic array of cells that include two or three fiber segments. Both the cross- and self-phase-modulation nonlinearities are taken into account. A semi-analytical approximation and direct simulations are used to calculate the frequency shift (FS) of colliding pulses, and to search for conditions which provide for minima of the FS and the temporal shift (TS), including the most promising possibility of minimizing both shifts simultaneously. Semi-analytical results, obtained by means of the perturbation theory, are in qualitative agreement with the numerical findings, especially in regimes near the optimum. In searching for the FS and TS minima, we investigate the effect of changing the initial width and chirp of the pulse, position of the amplifier within the dispersion–compensation period, group-velocity difference between the channels, allocation of the group-velocity-dispersion (GVD) inside the cell, and the average GVD. We conclude that a more sophisticated dispersion–compensation map, with three different local values of GVD, may be significantly more efficient than the one based on two different segments. A global FS minimum, with respect to the variation of all the parameters, is found.     

Determination of trace impurities in high-purity reagents by mercury thin-film anodic-stripping voltammetry

Summary The use of an amalgamated silver-wire electrode, providing a relatively large rate of film area to volume of mercury, seems to present several advantages over the use of the hanging mercury drop electrode (HMDE) for the determination of trace impurities by anodic-stripping voltammetry (ASV). Peak resolution and sensitivity have both been improved by use of the mercury thin-film electrode (MTFE). Preparation, conservation and treatment of the electrode are simple, requiring brief etching of a silver wire with dilute nitric acid, followed by rinsing, drying and direct amalgamation with mercury. The MTFE is stored in mercury, the excess of which is wiped off before use; it is cleaned by anodic-stripping electrolysis at positive potentials. Under these conditions, ASV produces reproducible peak-heights, with excellent dependence on electrolysis time and concentration of impurities. Samples containing nanogram quantities or less of the impurities of interest, are analysed by a four-step procedure: (1) prolonged pre-electrolysis of the supporting electrolyte,in situ in the voltammetric cell, on an auxiliary MTFE; (2) ASV of the supporting electrolyte on a cleaned MTFE; (3) ASV after the dissolution of the sample; (4) ASV after the addition of standards. The method is suitable for the estimation of traces of Zn(II), Cd(II), Tl(I), Pb(II), Sb(III) and Cu(II) in various high-purity reagents. Most impurities have been adequately determined at the 10^–9–10^–8 M level by the regular procedure, and at the 10^–10–10^–9 M level may be determined if the preconcentration (electrolysis) time and rates of potential sweep are increased. The only disadvantage of the method is that the overvoltage of hydrogen evolution is lower for the MTFE than the HMDE.

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Zusammenfassung Die Verwendung einer amalgamierten Silberdrahtelektrode mit einer im Vergleich zum Quecksilbervolumen großen Oberfläche bietet offenbar verschiedene Vorteile bei der Bestimmung von Spurenbeimengungen durch Anodic-stripping Voltammetry (ASV) gegenüber einem hängenden Quecksilbertropfen (HMDE). Peakauflösung und Empfindlichkeit wurden mit Hilfe der Quecksilberdünnschicht-Elektrode (MTFE) verbessert. Herstellung, Aufbewahrung und Behandlung solcher Elektroden sind einfach; sie erfordern eine kurze Anätzung eines Silberdrahtes mit verd. Salpetersäure, Spülung, Trocknung und Amalgamierung mit Quecksilber. Diese Elektroden werden in Quecksilber aufbewahrt, dessen Überschuß vor der Verwendung weggewischt wird. Sie werden durch Anodic-stripping-Elektrolyse bei positivem Potential gereinigt. Unter diesen Bedingungen gibt ASV reproduzierbare Peakhöhen, die zu der Elektrolysezeit und der Konzentration der Beimengungen in gutem Abhängigkeitsverhältnis stehen. Proben, die Nanogrammengen solcher Beimengungen enthalten, werden nach einem Vierstufenverfahren analysiert: 1. verlängerte Vorelektrolyse des Trägerelektrolyten mittels einer Hilfs-MTFE im Voltammetriegefäß; 2. ASV des Trägerelektrolyten mit einer gereinigten MTFE; 3. ASV nach Auflösung der Probe; 4. ASV nach Zugabe der Standards. Die Methode eignet sich zur Bestimmung von Spuren Zn(II), Cd(II), Tl(I), Pb(II), Sb(III) und Cu(II) in verschiedenen hochreinen Reagenzien. Die meisten dieser Verunreinigungen wurden in der Größenordnung 10^–9 bis 10^–8 M mit Hilfe des regulären Verfahrens bestimmt. In der Größenordnung 10^–10 bis 10^–9 M können sie bei Verlängerung der Anreicherungszeit (elektrolytisch) und Erhöhung des Potentialbereichs bestimmt werden. Der einzige Nachteil des Verfahrens ist, daß die Überspannung zur Wasserstoffentwicklung geringer ist als mit dem hängenden Quecksilbertropfen.

     

Pathway from condensation via fragmentation to fermionization of cold bosonic systems

For small scattering lengths, cold bosonic atoms form a condensate the density profile of which is smooth. With increasing scattering length, the density gradually acquires more and more oscillations. Finally, the number of oscillations equals the number of bosons and the system becomes fermionized. On this pathway from condensation to fermionization intriguing phenomena occur, depending on the shape of the trap. These include macroscopic fragmentation and coexistence of condensed and fermionized parts that are separated in space.     

Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices

Quantum phases and phase transitions of weakly to strongly interacting bosonic atoms in deep to shallow optical lattices are described by a single multiorbital mean-field approach in real space. For weakly interacting bosons in one dimension, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with many-body treatments of the Bose-Hubbard model. For strongly interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in each site undergo a Tonks-Girardeau-like transition and localize, and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.     

Extending the current collector into the nanoporous matrix of dye sensitized electrodes

A new type of high surface area TiO(2) electrode for DSSCs is proposed. The new electrode consists of a transparent conductive nanoporous matrix that is coated with a thin layer of TiO(2). This design ensures a distance of several nanometers between the TiO(2)-electrolyte interface and the current collector throughout the nanoporous electrode, in contrast to several micrometers associated with the standard electrode. In addition the new electrode contains inherent screening capability due to the high doping level of the conducting core matrix. Theoretically, this electrode should overcome the collection and image field problems associated with solid-state DSSCs. Using a flat analogue of the new electrode we show that unless the TiO(2) coating is thicker than 6 nm, the electrode performance is very low due to fast recombination. Two mechanisms for the thickness effect on the recombination rate, that are proposed, provide new insight to the DSSC operation.     

Role of excited states in the splitting of a trapped interacting Bose-Einstein condensate by a time-dependent barrier

An essentially exact approach to compute the wave function in the time-dependent many-boson Schr?dinger equation is derived and employed to study accurately the process of splitting a trapped condensate. As the trap transforms from a single to double well the ground state changes from a coherent to a fragmented state. We follow the role played by many-body excited states during the splitting process. Among others, a "counterintuitive" regime is found in which the evolution of the condensate when the splitting is sufficiently slow is not to the fragmented ground state, but to a low-lying excited state which is a coherent state. Experimental implications are discussed.     

Interferences in the density of two Bose-Einstein condensates consisting of identical or different atoms

The density of two initially independent condensates which are allowed to expand and overlap can show interferences as a function of time due to interparticle interaction. Two situations are separately discussed and compared: (1) all atoms are identical and (2) each condensate consists of a different kind of atoms. Illustrative examples are presented.     

Catalytic Microcapsules Assembled from Enzyme–Nanoparticle Conjugates at Oil–Water Interfaces

Involuntary association : Anionic β‐galactosidase enzymes associate with positively charged Au nanoparticles to produce reduced‐charge conjugates, which assemble at oil–water interfaces to result in stable microcapsules (see picture). The microcapsules were formed quickly and showed high enzymatic activity, which makes them promising materials for biotechnology applications.