On a variational principle for decaying states

A new variational principle is formulated, in order to obtain the Siegerts eigenvalue problem for decaying states.     

Rules for transition rates in nonequilibrium steady states

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behavior and, for steady shear, gives rise to stress-mediated long-range interactions.     

Jordan blocks and exponentially decaying higher-order Gamow states

In the framework of the rigged Hilbert space, unstable quantum systems associated with first-order poles of the analytically continued S-matrix can be described by Gamow vectors which are generalized vectors with exponential decay and a Breit-Wigner energy distribution. This mathematical formalism can be generalized to quasistationary systems associated with higher-order poles of the S-matrix, which leads to a set of Gamow vectors of higher order with a non-exponential time evolution. One can define a state operator from the set of higher-order Gamow vectors which obeys the exponential decay law. We shall discuss to what extent the requirement of an exponential time evolution determines the form of the state operator for a quasistationary microphysical system associated with a higher-order pole of the S-matrix. Dedicated to Professor L. P. Horwitz on the occasion of his 65th birthday, October 14, 1995.     

On the probability of changing the Auger transition rates between the hyperfine states of a mesic atom in matter

Possibilities of using negative muons are discussed: (i) for understanding the behaviour of wave functions of outer electron shells in the vicinity of a nucleus and (ii) for investigation of the exchange effects in solid state physics. It is noticed that the effective life time of μ bound in light atoms (nuclear spin i≠O) depends on the state of the outer electron shell. This fact can be used for measurement ofK-capture rates from different components of hyperfine structure of a mesic atom and for estimation of the weak interaction constant.     

AbsoluteE0 andE2 transition rates and collective states in116Sn

AbsoluteE0 andE2 transition rates in¹¹⁶Sn have been measured using several newly developed techniques. ManyE2 transitions are observed to have a collective character withB(E2) values of up to 60 W.u. The presence of deformed excited states in¹¹⁶Sn is discussed in view of the results obtained.     

Kaonic nuclear systems KN and KNN as decaying states

The formation spectra of model KN and KNN systems formed by (K(-),n) reactions are investigated in order to obtain a theoretical basis for a proper interpretation of experimental data concerning kaonic nuclear quasi-bound states. It has been clarified that the experimentally observable kaonic nuclear state K(-)pp should be regarded as the decaying state introduced by Kapur-Peierls, which is different from the pole state solution of the Faddeev equation.     

On the electronic density of states of the transition metals

XIS measurements of the elements Ir, Pt and Au are reported. High precision and reproducibility is obtained by the application of a “π/2-method” which approximates a Bragg angle of 90° at the dispersing crystal. Theoretical densities of states exist for Pt and Au. The agreement with the measured isochromats is good. A rigid-band model for Ir, Pt, and Au is ruled out by the measurements. Rather they suggest (combined with results of photoemission experiments) a narrowing of thed-bands from Ir through Pt to Au. Moreover, thed-band of Ir lies relative to thesp-band at a lower energy than thed-bands of Pt and Au. A fitting parameter concerning the experimental resolution is explained and considered as a possible indication of localization for XIS.     

On the electronic density of states of the transition metals

A superposition model is suggested to describe the electronic density of states curves of binary alloys with the aid of those of the component metals. It is based on a charge transfer between the different atomic cells. The application of this model to different spectroscopic methods studying the density of states brings up the question of the localizing and averaging properties of the corresponding experiments.     

On the partial-wave analysis of mesonic resonances decaying to multiparticle final states produced by polarized photons

Meson spectroscopy is going through a revival with the advent of high statistics experiments and new advances in the theoretical predictions. The Constituent Quark Model (CQM) is finally being expanded considering more basic principles of field theory and using discrete calculations of Quantum Chromodynamics (lattice QCD). These new calculations are approaching predictive power for the spectrum of hadronic resonances and decay modes. It will be the task of the new experiments to extract the meson spectrum from the data and compare with those predictions. The goal of this report is to describe one particular technique for extracting resonance information from multiparticle final states. The technique described here, partial wave analysis based on the helicity formalism, has been used at Brookhaven National Laboratory (BNL) using pion beams, and Jefferson Laboratory (JLab) using photon beams. In particular this report broadens this technique to include production experiments using linearly polarized real photons or quasi-real photons. This article is of a didactical nature. We describe the process of analysis, detailing assumptions and formalisms, and is directed towards people interested in starting partial wave analysis.     

类铍离子N3+激发态的能量、振子强度和跃迁几率

利用多组态相互作用方法及Rayleigh-Ritz变分法,计算了类铍N3+ 基态(1s22s21S)和三个激发态(1s22s2p1P0, 1s22s2p3 P0, 1s22p23P)的能量,运用截断变分方法得到能量的改进量,包括了相对论能量和质量极化效应.计算了相关态的振子强度和辐射跃迁率.计算结果与其它理论和实验结果符合得很好.     

Disentanglement,Bell-nonlocality violation and teleportation capacity of the decaying tripartite states

Dynamics of disentanglement as measured by the tripartite negativity and Bell nonlocality as measured by the extent of violation of the multipartite Bell-type inequalities are investigated in this work. It is shown definitively that for the initial three-qubit Greenberger–Horne–Zeilinger (GHZ) or W class state preparation, the Bell nonlocality suffers sudden death under the influence of thermal reservoirs. Moreover, all the Bell-nonlocal states are useful for nonclassical teleportation, while there are entangled states that do not violate any Bell-type inequalities, but still yield nonclassical teleportation fidelity.     

On thed-electron surface density of states of transition metals

Using the moment method and the continued fraction expansion for the one-particle Green's function we have studied thed-electron surface density of states for a transition metal. Besides the reduction of nearest neighbours for a surface atom compared to a bulk atom we have also taken into account the effect that the atomic environment of a surface atom is quite different from that of a bulk atom. This leads to important modifications in the surface density of states which can effect e.g. magnetic surface properties.Work supported in part by the ESIS program (Universities of Liege and Antwerpen)     

On thed-electron surface density of states of transition metals

It is shown that thed-electron surface density of states of a transition metal is strongly influenced not only by “off-diagonal” surface effects (e.g. reduction of nearest neighbors at the surface) but also by “diagonal” surface effects. Latter result from differences in the effective atomic potential for differentd-orbitals. They lead generally to large resonant contributions to the surface density of states. It is demonstrated that the “diagonal” effects must be included in any realistic calculation of the surface density of states.     

Uniqueness of continuum one-dimensional Gibbs states for slowly decaying interactions

We consider one-dimensional grand-canonical continuum Gibbs states corresponding to slowly decaying, superstable, many-body interactions. Absence of phase transitions, in the sense of uniqueness of the tempered Gibbs state, is proved for interactions with anNth body hardcore for arbitrarily largeN.     

On the relative stability of states and first-order phase transition in systems far from equilibrium

A method for classifying the states of a macroscopic dissipative system according to their stability with respect to finite-amplitude localized fluctuations and perturbations is presented. Since the method does not rely on a extremum principle it is applicable to open systems far from equilibrium. It appears that in general there exists at most one absolutely stable state (up to symmetry). Simple examples are given for systems without absolutely stable state.     

Anomalously localised states at the Anderson transition

Non-multifractal critical wave functions at the Anderson transition are numerically investigated for the SU(2) model belonging to the two-dimensional symplectic class. These states can be regarded as anomalously localised states (ALS) at criticality. Giving a quantitative definition of ALS, it has been revealed that the probability to find ALS increases with the system size and remains at a finite value even in the thermodynamic limit. The most probable, namely typical, critical states have the multifractal nature, while its probability measure is zero. In order to understand how ALS affect critical properties in infinite systems, we studied the distribution of the correlation dimension D₂ and the nearest-neighbour level spacing distribution P(s) by paying attention to ALS. Results show that the influence of ALS to these distribution functions is limited. This is because the spatial distribution of amplitudes in tail regions of ALS exhibits multifractality as in the case of typical critical wave functions.     

On the quantum mechanical treatment of decaying non-relativistic systems

The usual treatment of decaying non-relativistic particles by means of a non-unitary irreducible representation of the Galilei group is deduced from a suitable formulation of symmetry principles. In such a formulation time translation is distinguished from time evolution; this point is crucial to obtain the irreversible behaviour of unstable particles.