Atoms with bosonic "electrons" in strong magnetic fields

We study the ground state properties of an atom with nuclear charge $Z$ and $N$ bosonic ``electrons'' in the presence of a homogeneous magnetic field $B$. We investigate the mean field limit $N\to\infty$ with $N/Z$ fixed, and identify three different asymptotic regions, according to $B\ll Z^2$, $B\sim Z^2$, and $B\gg Z^2$. In Region 1 standard Hartree theory is applicable. Region 3 is described by a one-dimensional functional, which is identical to the so-called Hyper-Strong functional introduced by Lieb, Solovej and Yngvason for atoms with fermionic electrons in the region $B\gg Z^3$; i.e., for very strong magnetic fields the ground state properties of atoms are independent of statistics. For Region 2 we introduce a general {\it magnetic Hartree functional}, which is studied in detail. It is shown that in the special case of an atom it can be restricted to the subspace of zero angular momentum parallel to the magnetic field, which simplifies the theory considerably. The functional reproduces the energy and the one-particle reduced density matrix for the full $N$-particle ground state to leading order in $N$, and it implies the description of the other regions as limiting cases.Comment: LaTeX2e, 37 page

Translation Invariant States on Twisted Algebras on a Lattice

We construct an algebra with twisted commutation relations and equip it with the shift. For appropriate irregularity of the non-local commutation relations we prove that the tracial state is the only translation-invariant state

Semiparametric Multinomial Logit Models for Analysing Consumer Choice Behaviour

The multinomial logit model (MNL) is one of the most frequently used statistical models in marketing applications. It allows to relate an unordered categorical response variable, for example representing the choice of a brand, to a vector of covariates such as the price of the brand or variables characterising the consumer. In its classical form, all covariates enter in strictly parametric, linear form into the utility function of the MNL model. In this paper, we introduce semiparametric extensions, where smooth effects of continuous covariates are modelled by penalised splines. A mixed model representation of these penalised splines is employed to obtain estimates of the corresponding smoothing parameters, leading to a fully automated estimation procedure. To validate semiparametric models against parametric models, we utilise proper scoring rules and compare parametric and semiparametric approaches for a number of brand choice data sets

Atoms in strong magnetic fields: The high field limit at fixed nuclear charge

Let E(B,Z,N) denote the ground state energy of an atom with N electrons and nuclear charge Z in a homogeneous magnetic field B. We study the asymptotics of E(B,Z,N) as $B\to \infty$ with N and Z fixed but arbitrary. It is shown that the leading term has the form $(\ln B)^2 e(Z,N)$, where e(Z,N) is the ground state energy of a system of N {\em bosons} with delta interactions in {\em one} dimension. This extends and refines previously known results for N=1 on the one hand, and $N,Z\to\infty$ with $B/Z^3\to\infty$ on the other hand

The state space for two qutrits has a phase space structure in its core

We investigate the state space of bipartite qutrits. For states which are locally maximally mixed we obtain an analog of the ``magic'' tetrahedron for bipartite qubits--a magic simplex W. This is obtained via the Weyl group which is a kind of ``quantization'' of classical phase space. We analyze how this simplex W is embedded in the whole state space of two qutrits and discuss symmetries and equivalences inside the simplex W. Because we are explicitly able to construct optimal entanglement witnesses we obtain the border between separable and entangled states. With our method we find also the total area of bound entangled states of the parameter subspace under intervestigation. Our considerations can also be applied to higher dimensions.Comment: 3 figure

Conjoint-Analyse und Marktsegmentierung

Die Marktsegmentierung zählt neben der Neuproduktplanung und Preisgestaltung zu den wesentlichen Einsatzgebieten der Conjoint-Analyse. Neben traditionell eingesetzten zweistufigen Vorgehensweisen, bei denen Conjoint-Analyse und Segmentierung in zwei getrennten Schritten erfolgen, stehen heute mit Methoden wie der Clusterwise Regression oder Mixture-Modellen neuere Entwicklungen, die eine simultane Segmentierung und Präferenzschätzung ermöglichen, zur Verfügung. Der Beitrag gibt einen Überblick über die vorliegenden methodischen Ansätze zur Verknüpfung von Conjoint-Analyse und Marktsegmentierung und zeigt die Vorzüge simultaner Conjointsegmentierungsmethoden gegenüber den in der Unternehmenspraxis noch immer weit verbreiteten zweistufigen Verfahren auf. Along with new product/concept identification and pricing, market segmentation ranks among the primary purposes in commercial conjoint applications. Traditionally, this conjoint segmentation has been accomplished by a two-step procedure, (1) either by first segmenting markets and subsequently estimating conjoint models at the segment level or (2) by first conducting conjoint analysis at the individual level and then clustering individual level part-worths. However, in recent years, some powerful techniques for simultaneously performing market segmentation and calibrating segment-level part-worths such as clusterwise regression procedures and mixture models have been proposed. This article provides an overview of existing conjoint segmentation methods and particularly focuses on the newer simultaneous approaches which offer substantial advantages compared to the traditional two-step procedures.Marktsegmentierung; Conjoint-Analyse ; Simultanverfahren;