On the Position Distribution of the Ideal Bose Gas

It is shown that the position distribution of the ideal BOSE gas is an infinitely divisible point process on R^d. Clustering representations of this distribution are considered.     

Advanced Bifunctional Oxygen Reduction and Evolution Electrocatalyst Derived from Surface-Mounted Metal–Organic Frameworks

Metal–organic frameworks (MOFs) and their derivatives are considered as promising catalysts for the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), which are important for many energy provision technologies, such as electrolyzers, fuel cells and some types of advanced batteries. In this work, a “strain modulation” approach has been applied through the use of surface-mounted NiFe-MOFs in order to design an advanced bifunctional ORR/OER electrocatalyst. The material exhibits an excellent OER activity in alkaline media, reaching an industrially relevant current density of 200 mA cm⁻² at an overpotential of only ≈210 mV. It demonstrates operational long-term stability even at a high current density of 500 mA cm⁻² and exhibits the so far narrowest “overpotential window” ΔE_ORR-OER of 0.69 V in 0.1 m KOH with a mass loading being two orders of magnitude lower than that of benchmark electrocatalysts.     

Multi-Electron Reactions Enabled by Anion-Based Redox Chemistry for High-Energy Multivalent Rechargeable Batteries

The development of multivalent metal (such as Mg and Ca) based battery systems is hindered by lack of suitable cathode chemistry that shows reversible multi-electron redox reactions. Cationic redox centres in the classical cathodes can only afford stepwise single-electron transfer, which are not ideal for multivalent-ion storage. The charge imbalance during multivalent ion insertion might lead to an additional kinetic barrier for ion mobility. Therefore, multivalent battery cathodes only exhibit slope-like voltage profiles with insertion/extraction redox of less than one electron. Taking VS₄ as a model material, reversible two-electron redox with cationic–anionic contributions is verified in both rechargeable Mg batteries (RMBs) and rechargeable Ca batteries (RCBs). The corresponding cells exhibit high capacities of >300 mAh g⁻¹ at a current density of 100 mA g⁻¹ in both RMBs and RCBs, resulting in a high energy density of >300 Wh kg⁻¹ for RMBs and >500 Wh kg⁻¹ for RCBs. Mechanistic studies reveal a unique redox activity mainly at anionic sulfides moieties and fast Mg²⁺ ion diffusion kinetics enabled by the soft structure and flexible electron configuration of VS₄.     

Binders for exterior coatings exhibiting low soiling tendency

Elastomeric coatings protect building facades and flat roofs from moisture and weather exposure. As a drawback, these coatings are prone to dirt-pickup due to the low glass transition temperature of the used polymeric binders. Strategies to overcome this enhanced soiling tendency are discussed, and the results of laboratory and outdoor soiling tests are compared. A novel method for the assessment of wet soiling tendency is presented.     

On some experiences with the thr notation for CdI2 polytypes

The advantages of the thr notation are discussed using 12 recently reported polytypes as examples. It is shown that the thr notation combines the advantages of the Zhdanov notation with those of the t-o-f notation. An almost trivial conversion of Zhdanov sequences into thr sequences and vice versa is given. The restrictions in the stacking of CdI₂ polytypes and the relations between homometric structures can be described in the most simple way using the thr notation.     

Characterization of states of infinite boson systems

In a previous paper [11] it was shown that to each locally normal state of a boson system one can associate a point process that can be interpreted as the position distribution of the state. In the present paper the so-called conditional reduced density matrix of a normal or locally normal state is introduced. The whole state is determined completely by its position distribution and this function. There are given sufficient conditions on a point processQ and a functionk ensuring the existence of a state such thatQ is its position distribution andk its conditional reduced density matrix. Several examples will show that these conditions represent effective and useful criteria to construct locally normal states of boson systems. Especially, we will sketch an approach to equilibrium states of infinite boson systems. Further, we consider a class of operators on the Fock space representing certain combinations of position measurements and local measurements (observables related to bounded areas). The corresponding expectations can be expressed by the position distribution and the conditional reduced density matrix. This class serves as an important tool for the construction of states of (finite and infinite) boson systems. Especially, operators of second quantization, creation and annihilation operators are of this type. So, independently of the applications in the above context this class of operators may be of some interest.     

Quantum Teleportation and Beam Splitting

Following the previous paper in which quantum teleportation is rigorously discussed with coherent entangled states given by beam splittings, we further discuss two types of models, the perfect teleportation model and non-perfect teleportation model, in a general scheme. Then the difference among several models, i.e., the perfect models and the non-perfect models, is studied. Our teleportation models are constructed by means of coherent states in some Fock space with counting measures, so that our model can be treated in the frame of usual optical communication. Received: 1 February 2001 / Accepted 19 July 2001