<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.     

A phenomenological theory of the isotropic to chiral smectic-C phase transition

In this paper we discuss the direct isotropic to chiral smectic-C phase transition on the basis of a phenomenological theory. The model free energy is written in terms of the coupled order parameters including the spontaneous polarization. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a direct isotropic to chiral smectic-C phase transition is possible when compared to other phase transitions. On the basis of this model the isotropic-smectic-C^* transition is always of first order. The theoretical predictions are compared with the available experimental results.-1     

On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

It is shown that the polynomialp(t) = Tr[(A+tB)^m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof.     

Peripatetic Highlights in Bern

This tour of significant scientific sites in Bern uses the local legacy of its most illustrious scientists, Albert Einstein (1879–1955) and Fritz Houtermans (1903–1966), as its guiding thread through the old town and the university district.Ann M.Hentschel is translator of the correspondence volumes of The Collected Papers of Albert Einstein and is currently employed by the Institute for the History and Philosophy of Science at the University of Bern to write the guide for a city tour of Einsteins old haunts in Bern for the coming jubilee of special relativity in 2005. For the historical companion guidebook, see Hentschel and Grasshoff, Albert Einstein (ref. 4) and the website <.     

光纤热极化过程的实时测试研究

通过热极化可以使中心对称的熔石英光纤中产生二阶非线性效应和线性电光效应。为了解各热极化过程参量对热极化产生的线性电光效应的影响,利用全保偏光纤马赫一曾德尔干涉仪构造了一套光纤热极化的实时线性电光效应测试系统,并利用其进行了光纤热极化全过程的监控测试。在线测试了热极化过程的一些参量,例如极化电压、极化时间、以及极化温度等对热极化光纤中产生的线性电光效应的影响。实时测试研究表明,在光纤中施加尽可能高的极化电场将可能在光纤中产生较高的线性电光效应。对侧边抛磨光纤结构的热极化器件,考虑到器件的抗强电场击穿能力,可选用3．o～4．0kV左右的极化直流电压。当施加3．0kV左右的极化电压时,热极化优化时间约为16min,最佳热极化加热温度约为190℃。     

Chiral structure of the Roper resonance using complex-mass scheme

The pole mass and the width of the Roper resonance are calculated as functions of the pion mass in the framework of low-energy effective field theory of the strong interactions. We implement a systematic power-counting procedure by applying the complex-mass scheme.     

Clusters in weighted macroeconomic networks: the EU case. Introducing the overlapping index of GDP/capita fluctuation correlations

GDP/capita correlations are investigated in various time windows (TW), for the time interval 1990–2005. The target group of countries is the set of 25 EU members, 15 till 2004 plus the 10 countries which joined EU later on. The TW-means of the statistical correlation coefficients are taken as the weights (links) of a fully connected network having the countries as nodes. Thereafter we define and introduce the overlapping index of weighted network nodes. A cluster structure of EU countries is derived from the statistically relevant eigenvalues and eigenvectors of the adjacency matrix. This may be considered to yield some information about the structure, stability and evolution of the EU country clusters in a macroeconomic sense.     

Electron capture into few-electron heavy ions: Independent particle model

We apply the density matrix theory to re-investigate the radiative electron capture into heavy ions with one valence electron. Attention has been paid particularly to the magnetic sublevel population of the residual ions, as described in terms of alignment parameters. Simple method, based on an independent particle model, which takes into account the Pauli principle, is proposed for evaluating the alignment of the excited ionic states. By making use of this method, detailed calculations are performed for electron capture into (initially) hydrogen-like and lithium-like europium, gold and uranium ions, and are compared with the results of the multiconfiguration Dirac-Fock approach.As seen from the calculations and from the comparison with available experimental results, the independent particle model provides a good estimate for the alignment parameters of few-electron heavy ions. Therefore, our simple model may help to understand the basic properties of the X-ray emission from heavy, few-electron ions without the need for invoking sophisticated MCDF calculations.     

Quantum Monte Carlo calculation for the neutron-rich Ca isotopes

We computed ground-state energies of calcium isotopes from ⁴²Ca to ⁴⁸Ca by means of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. Calculations were performed by replacing the ⁴⁰Ca core with a mean-field self-consistent potential computed using the Skyrme interaction. The energy of the external neutrons is calculated by projecting the ground state from a wave function built with the single-particle orbitals computed in the self-consistent external potential. The shells considered were the 1F _7/2 and the 1F _5/2 . The Hamiltonian employed is semi-realistic and includes tensor, spin-orbit and three-body forces. While absolute binding energies are too deep if compared with experimental data, the differences between the energies for nearly all isotopes are in very good agreement with the experimental data.