Ergodic states in a non commutative ergodic theory

Using the Godement mean of positive-type functions over a groupG, we study -abelian systems { , } of aC*-algebra and a homomorphic mapping of a groupG into the homomorphism group of . Consideration of the Godement mean off(g)U _g withf a positive-type function overG andU a unitary representation ofG first yields a generalized mean-ergodic theorem. We then define the Godement mean off(g) ( _g (A)) withA and a covariant representation of the system { , } for which theG-invariant Hilbert space vectors are cyclic and study its properties, notably in relation with ergodic and weakly mixing states over . Finally we investigate the discrete spectrum of covariant representations of { , } (i.e. the direct sum of the finite-dimensional subrepresentations of the associated representations ofG).On leave of absence from Istituto di Fisica G. Marconi Piazzale delle Scienze 5 — Roma.     

Eigenchannel calculation for a soluble model

We examine the accuracy of the eigenchannel method for treating nuclear reactions by a comparison with the exact solution of a problem of two coupled channels. No crucial deviations between the exact and the eigenchannel cross sections are observed. We also discuss the questions connected with the non-orthogonality of the sets of radial states used in the eigenchannel treatment, and show how to minimize the resulting errors. Our conclusion is that, in principle, the eigenchannel method is capable of producing the correct shape of nuclear cross sections, without introducing spurious wiggles.     

On the convergence of perturbation series: theS matrix of the non linear sigma model

The factorization of nonperturbative effects in theS matrix of the non linear sigma model is investigated. We prove that, in each order of 1/N, theS matrix amplitudes can be written as a series in power of a dinamically generated mass times a convergent perturbative series.     

Effective Kondo model for a trimer on a metallic surface

I consider a Hubbard-Anderson model which describes localized orbitals in three different atoms hybridized both among themselves and with a continuum of extended states. Using a generalized Schrieffer-Wolf transformation, I derive an effective Kondo model for the interaction between the doublet ground state of the isolated trimer and the extended states. For an isoceles trimer with distances a, l, l between the atoms, the Kondo temperature is very small for la when a is small. The results agree with experiments for a Cr trimer on Au(111).     

Two-particle density matrix calculation for atom by modified perturbation theory

The two-particle density matrix of hydrogen atoms moving in a solid film is calculated. The probability of surviving a bound state between electron and proton in the course of the atomic motion in the film is discussed. The surviving fraction of the initial beam possesses the increased energy of the Coulomb attraction and lowered energy losses. This fraction can be responsible for the observed number of Rydberg states in the exit beam.     

Electron localization for a model of layered metallic structures

Several exact results are presented for a one-dimensional tight-binding model of layered binary metallic structures for the cases of arbitrary, random, incommensurate, and commensurate layer sequences.     

One-centre multipole calculation of second-order perturbation energies for H+ 2

A knowledge of the H(1s) pseudospectrum allows one to calculate the one-centre second-order perturbation energies for the H(1s)-H⁺ interaction. The efficiency of such calculations is tested in detail for induction, exchange-induction, first-order overlap and Murrell-Shaw-Musher-Amos second-order energies for the ground and excited state H₊ ² at different internuclear distances. It is found that a large number of STO functions accounting for at least the first sixteen non-expanded multipoles is needed to obtain three figure accuracy in the short to medium range of internuclear separations. Higher accuracy can be obtained only in terms of a sensibly smaller number of two-centre functions which automatically satisfy the electron-nucleus cusp requirement.     

Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerically in the past. Here, we present an analytical study for the optimal velocity model with a stepwise specification of the optimal velocity function and a simple kind of perturbation. Despite various approximations, the analytical results are shown to reproduce numerical results very well.     

A metallic domain model for CuCl

A simplified model of small metallic regions embedded in an insulator is presented, to explain the anomalous results found in CuCl by Brandt et al. We set up the Dyson equations for the model and outline a self-consistent procedure, which can be used to obtain detailed solutions. Without solving the equations, we find that the anomalous Green's function for the metallic region is a rapidly decaying function of the distance from the metal-insulator boundary. This indicates the existence of surface superconductivity, which could account for almost ideal diamagnetism as well as non zero resistivity.     

A simplified calculation of parity non conserving E1 transitions in the oscillator shell model

Contributions of excitations of the neutron core to the circular polarization of γ emitted in the transition $\text{5}\text{2}{}^{\mathrm{+}}\text{→}\text{7}\text{2}{}^{\mathrm{+}}\text{in}{}^{181}\text{Ta}$ are calculated. We show in a very simple model that these contributions are coherent and multiply by a factor 2 the polarizations calculated previously with proton-neutron parity-violating potentials.     

COIL简化模型计算

采用简化动力学、增益模型,分析了常规虚共焦非稳腔和含屋脊镜折叠非稳腔这两种腔型在COIL中的应用,计算表明,折叠腔在改善COIL近场光强分布均匀性和提高近场输出功率方面明显优于常规腔。     

COIL简化模型计算

 采用简化动力学、增益模型，分析了常规虚共焦非稳腔和含屋脊镜折叠非稳腔这两种腔型在COIL中的应用，计算表明，折叠腔在改善COIL近场光强分布均匀性和提高近场输出功率方面明显优于常规腔。     

Two-site two-electron generalized Hubbard-Holstein model: a perturbation study

The two-site two-electron generalized Hubbard-Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found including up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections to the ground state energy, as well as to the correlation functions, are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon(e-ph) coupling and electron-electron interactions for different values of the adiabaticity parameter. The simultaneous effect of the e-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.     

Dynamical perturbation for classical fluids: A solvable model

We investigate on a one-dimensional model the perturbation to the timedependent correlations in a classical fluid when a small interaction is added to a hard core. Various formulas have already been proposed for this correction. We verify on this model, for which everything can be calculated explicitly, that the expressions proposed by Frisch and Berne yield strongly divergent time integrals for the diffusion coefficient. On the contrary, when all corrections are accounted for, the correction to the velocity time correlation is shown to decay like (Int)/t ₂ at large times, yielding a finite first-order correction to the diffusion coefficient. The extension of this calculation to a gas of hard rods in the case of a perturbation with an infinite range is discussed.     

Diffusion model for annealing algorithm with perturbation quadratic approximation

We have dealt with the simulated annealing algorithm as a suitable method for finding the global minimum of a functionf(x) of one variable. The convergence properties of this algorithm have been investigated via diffusion equation solved at a fixed temperature. The convergence rate is mainly governed by the first subdominant eigenvalue of the generator. We have tried to calculate approximately this eigenvalue for arbitrary minimized functionf(x). These calculations lead us to propose some parameter for controlling the temperature.