Table of contents

The recently proposed Langevin formulation of quantum dynamics yields the propagator at imaginary time as a noise average involving the solutions to a certain Langevin equation with a Gaussian white noise. The main advantage of this approach is to permit a stochastic treatment of quantum systems even when no solutions to the Schrödinger equation are known. We show how the Langevin formulation works in the space of a (nonrelativistic) particle in a uniform magnetic field with arbitary time dependence. We are able to evaluate the quantum-mechanical propagator exactly. As far as we know, this is a new result of considerable interest for atomic and molecular physics.

We study numerically the diffusion random sequential adsorption (DRSA) and random sequential adsorption (RSA) of hard disks on a one-dimensional lattice segment. The saturation coverages of the two processes, although similar, are clearly different within the errors of the simulation. The difference is explained by the nonuniform adsorption of disks within the available gaps when diffusion is permitted. We conclude that a recently proposed class of generalized parking problems cannot rigorously describe the DRSA process.

Based on the symmetry properties of the constrained Hamiltonian system in phase space, we present a counterexample in which there is no linearization of constraint, for a system with a singular higher-order Lagrangian to show that Dirac's conjecture fails.

The Aharonov-Anandan and Barry phases are determined for the cyclic motions of a nonrelativistic charged spinless particle evolving in the superposition of the fields produced by a Penning trap and a rotating magnetic field. A discussion about the selection of the parameter's space and the relationship between the Berry phase and the symmetry of the binding potential is given.

We consider the nonlinear Schrödinger equation of imaginary time with random time-dependent potential. The scaling laws for averaged displacement and the dispersion are determined in this case with the help of computer simulations.

We derive twenty nontrivial terms of the high-temperature series expansion for the linear relaxation time τ of the time-displaced correlation function C(t) = ⟨m(0) m(t)⟩ of the magnetization m(t) in the two-dimensional nearest-neighbour ferromagnetic Ising model on the square lattice. We study the dynamics introduced by Glauber and compute the longest (characteristic) relaxation time of C(t). We analyse the series by using unbiased and biased methods, such as the ratio method, Padé approximants and generalized differential approximants. It is reassuring that all the methods yield compatible results providing the estimate for the dynamical critical exponent: z = 2.183 ± 0.005.

A parton model for the J/ψ production in hadron-nucleus and nucleus-nucleus collisions is presented. It takes account of the finite-energy constraint along with the requirement of unitarity. Two extreme regimes are found for which the J/ψ- production cross-sections have different behaviours according to nuclear mass numbers.

We analyse the current data on τ-lepton decays and show that they are consistent with the standard model.

The multiplicity distribution of secondary charged particles emitted in 350 GeV/c π^--AgBr interactions was observed in different pseudo-rapidity windows (1.0 ⩽ η_c ⩽ 5.0). The data shows good agreement with the negative binomial distribution (NBD) as well as with the generalized multiplicity distribution (GMD). The value of the parameter k' of GMD is found to be insignificant in all the cases. It signifies the fact that the starting of the branching process is dominated by the quarks (q → qg), not by the gluons (g → gg).

The ionization potential of small Hg_n clusters has been calculated. For the first time good agreement with experimental results has been obtained. It is shown that interatomic Coulomb interactions are important. The energy of Hg_n⁺ is calculated using the unrestricted inhomogeneous Hartree-Fock approximation. As a consequence of a change in the charge distribution in Hg_n⁺, we obtain an abrupt change in the slope of the ionization potential at the critical cluster size n_cr ∼ 14. The presented results are expected to be valid for covalent clusters in between ionized van der Waals clusters and metallic clusters.

We demonstrate confinement of ion clouds in a radio-frequency anharmonic electric potential and investigate the stability of this nonlinear parametric oscillator. Measurements of excitation spectra and the spatial distribution of trapped ion clouds are presented. Further applications of r.f. multipole traps to high-resolution spectroscopy are discussed.

In this letter we demonstrate that the measurement of the reflectivity of a hybrid aligned nematic sample vs. the incidence angle give us detailed information on the local orientation of the molecular director, when the condition of total internal reflection is achieved inside the sample. Moreover theoretical fit of the experimental data shows that the method is suitable to obtain the tilt angles on the boundary walls with a sensitivity < 3°.

The problem of the selection of the wave number of convection rolls by a ramp of the overcriticality is analysed in the two-dimensional situation. It is demonstrated that the configuration which minimizes the Lyapunov functional corresponds to the rolls parallel to the slope of the ramp, while the well-known purely one-dimensional configuration gives rise to a maximum of the functional. It is also demonstrated that, irrespective of the orientation of the rolls, the ramp always selects the wave number coinciding with the centre of the Eckhaus band (which is well-known in the one-dimensional case), except for the above-mentioned case when the rolls are parallel to the ramp's slope. Finally, it is shown that, under certain conditions, the one-dimensional configuration and those close to it may become unstable against infinitesimal disturbance with the wave vector perpendicular to the slope.

Intermittency is commonly connected with non-Gaussian fluctuations of the velocity gradients. Here we show that the r-scaling exponents μ(q) of the moments of the locally averaged energy dissipation ("intermittency exponents") are nonzero even for a Gaussian probability distribution of the velocity gradients. This casts–at least for finite Reynolds numbers–additional doubts on the use of Kolmogorov and Obukhov's refined similarity hypothesis which leads to ζ(m) = m/3 - μ(m/3) for the scaling exponents of the velocity structure functions. Instead, we can use the presumed universality (i.e. independence of the Taylor-Reynolds number) of the μ(q) to predict the degree of the non-Gaussian character of the ∂₁u₁ probability distribution. We explicitly evaluate the Re_λ-dependence of its stretching exponent β together with the Re_λ-scaling exponent of the hyperflatnesses F^(q). Both are found to be in agreement with recent experiments.

The Aslamazov-Larkin paraconductivity term is calculated in the case of sufficiently small superconducting coherence length. It is found that the critical exponent of paraconductivity depends on the short-wavelength cut-off of the fluctuation spectrum in the whole Ginzburg-Landau mean-field region. Hence, it is predicted that the Aslamazov-Larkin universal relation between the critical exponent of paraconductivity and the dimensionality of the superconducting state is no longer valid in short-coherence-length superconductors. This prediction is confirmed by paraconductivity measurements on cuprate superconductors.

Nucleation and growth of Ag on Si(001)(2 × 1) has been studied at tempertures of (300 ÷ 550) K, using intrinsic stress measurement together with several structural methods. Microstructure, growth mode and related intrinsic stress are strongly influenced by the Si(001) dopant concentration. On low p-doped Si(001)(2 × 1) film growth proceeds by Volmer-Weber mode resulting in polycrystalline films at (300 ÷ 400) K and high-quality epitaxial Ag(001) films at (450 ÷ 550) K. On highly doped substrates, on the other hand, epitaxial Ag(111) films grow via Stranski-Krastanov mode at 300 K, indicating the crucial effect of surface dopants on the initial stages of Ag nucleation.

The formation enthalpies of ordered compounds and the mixing enthalpies of random alloys were calculated for Ni-Au, Ni-Pt, and Au-Pt using an Ising-like cluster expansion based on the local-density formalism. We show that relativity i) induces long-range order in Ni-Pt due to a reduction in packing strain and enhancement of s-d coupling, but ii) it leads to phase separation in Au-Pt due to suppression of the Au(s,p) → Pt(d) charge transfer.

I predict that the a.c. hopping resistance increases exponentially with ω²√L when the frequency ω is low and the resistor length L is sufficiently large. This is related to the left-right symmetry breaking. The corresponding a.c. rectification also increases exponentially with ω²√L and may change from one macroscopic sample to another.

We report the pressure and temperature dependences of ¹³C nuclear spin-lattice relaxation time T₁ in the normal state of K₃C₆₀. From the 1/T₁T temperature and pressure profiles, a Fermi-liquid theory is used to investigate the variation of the density of states and the amplitude of electron-electron interaction. Finally the results obtained are shown to support a pairing mechanism for superconductivity that would involve high-frequency modes.

The codeposition of O₂ and Cs on different substrates has been studied by means of near-edge X-ray absorption fine-structure (NEXAFS) experiments. A multiple-scattering analysis shows that the material formed has a tetragonal CsO₂ structure with an O-O distance between 1.35 and 1.40 Å. About 19 shells (52 atoms) are necessary to reproduce the oxygen K-edge absorption spectrum of this superoxide, in contrast with recent results by Ruckman et al. (Phys. Rev. Lett., 67 (1991) 2533) which are based on a free-ion calculation.

The free-energy contribution of a polymer interacting with a bounding surface of a general shape is obtained exactly through a multiple-scattering expansion. Two extreme cases of the polymer interacting with a surface are considered, viz. an ideal polymeric chain sterically excluded from the vicinity of the surface and an ideal polymeric chain adsorbed to the surface. In both cases the thermodynamic properties of the system are obtained in the form of a convergent expansion in powers of the local principal radii of curvature of the bounding surface.