Time reversal and exceptional points

Eigenvectors of decaying quantum systems are studied at exceptional points of the Hamiltonian. Special attention is paid to the properties of the system under time reversal symmetry breaking. At the exceptional point the chiral character of the system -- found for time reversal symmetry -- generically persists. It is, however, no longer circular but rather elliptic.Received: 20 November 2003, Published online: 15 April 2004PACS: 03.65.Vf Phases: geometric; dynamic or topological - 02.30.-f Function theory, analysis - 05.45.Mt Quantum chaos; semiclassical methods     

Theory of time-reversal symmetry breaking in compound-nucleus reactions

The interpretation of experimental tests of time-reversal symmetry in compound-nucleus reactions requires the theoretical calculation of a correlation coefficientR. We evaluateR in the framework of a statistical model, and relate it to the observables.     

Quick assessment methodology for reliability of solder joints in ball grid array (BGA) assembly—Part I: Creep constitutive relation and fatigue model

In this study, a new unified creep constitutive relation and a modified energy-based fatigue model have been established respectively to describe the creep flow and predict the fatigue life of Sn−Pb solders. It is found that the relation successfully elucidates the creep mechanism related to current constitutive relations. The model can be used to describe the temperature and frequency dependent low cycle fatigue behavior of the solder. The relation and the model are further employed in part II to develop the numerical simulation approach for the long-term reliability assessment of the plastic ball grid array (BGA) assembly. The project supported by the National Natural Science Foundation of China (59705008)     

Interfering proton and neutron transfer in the reaction C(N, N)C

Elastic scattering and one-nucleon transfer reactions induced by ¹⁶O have been investigated in the energy region 45–60 MeV on targets of ²⁶Mg, ²⁷Al, ³⁰Si and ⁴⁸Ca. Angular distributions were measured in the angular range 4°–40°. Optical model parameters were derived from the elastic scattering data and the transfer reaction data were analysed using both no-recoil and full-recoil DWBA codes. In the case of proton transfer reactions on ⁴⁸Ca, good agreement was obtained between the data and the DWBA calculations while the data for the lighter targets could not be satisfactorily reproduced. The oscillatory pattern of the angular distributions is discussed in terms of the three-parameter model of Kahana, and it is found that the model qualitatively explains the observed transition from smooth to oscillatory angular distributions.     

Are resonance decay amplitudes Gaussian variables?

Higher moments of Gaussian statistical variables can be expressed in terms of second moments. Such relations can be experimentally tested on resonance decay amplitudes. In the present paper, the error of such a test is derived. The error is due to the finite numberN of resonances analyzed. The statistical accuracy of presently available experiments turns out to be rather limited.     

Condition for a vanishing cross section at Θ-π/2 in Barshay-Temmer-reactions

The symmetry property of the transition matrix for a reaction producing an isobaric multiplet (or identical particles) is derived from the generalized Pauli principle without any specific assumptions concerning the reaction mechanism. In contrast to previous predictions it is shown that for odd partial waves in the exit channel the cross section will generally not vanish at Θ = π/2 if the channel spin projections of the initial and final channels may be different.     

Strength distributions and symmetry breaking in coupled microwave billiards

Flat microwave cavities can be used to experimentally simulate quantum mechanical systems. By coupling two such cavities, we study the equivalent to symmetry breaking in quantum mechanics. As the coupling is tunable, we can measure resonance strength distributions as a function of the symmetry breaking. We analyze the data by employing a qualitative model based on random matrix theory and show that the results derived from the strength distribution are consistent with those previously obtained from spectral statistics.     

Living Ziegler-Natta polymerization by early transition metals: synthesis and evaluation of cationic zirconium alkyl complexes bearing beta-hydrogens as models for propagating centers

The synthesis and characterization of a series of cationic zirconium and hafnium complexes with alkyl substituents bearing beta-hydrogens of general formula {(eta(5)-C5Me5)MR[N(Et)C(Me)N(t-Bu)]}[B(C6F5)4] [M = Zr; R = Et, n-Pr, i-Pr, n-Bu, i-Bu, and 2-ethylbutyl (5a-f) and M = Hf; R = i-Bu and t-Bu (6 and 7, respectively)] is described, including several isotopically labeled derivatives. The ability of these complexes to serve as model complexes for the living Ziegler-Natta polymerization of olefins that can be effected using the initiator 2a (R = Me in 5) has been addressed. The results obtained shed additional light on the steric and electronic factors that can contribute to the living character of a Ziegler-Natta polymerization based on an early transition metal initiator.