The measured line profiles of the Si iv3s ${\mathrm{}}^2$S–3p ${\mathrm{}}^2$P° doublet during 10-T operation on the Alcator-C tokamak show evidence of a contribution due to the Zeeman effect to these profiles. The assumption that these line profiles are single lines broadened only by instrumental effects and thermal broadening yields apparent kinetic temperatures for the two lines which differ by approximately 50%. Neither of the resulting temperatures is reasonable for Si iv under typical Alcator operating conditions and the difference between the temperatures cannot be explained by Doppler effects. Modifying the nonlinear least-squares fitting routine to include the (unresolved) components predicted by the weak-field limit of the Zeeman effect yields kinetic temperatures for these lines which are in agreement and are reasonable for the region of the plasma in which Si iv exists. Finally, a study of the Zeeman effect in O vii shows that contributions from this process are important in determining ion temperatures from line broadening of the O vii 2s ${\mathrm{}\mathrm{}}^3$${\mathrm{S}}_1$–2p ${\mathrm{}}^3$P°${\mathrm{}}_2$ emission line in the vuv spectrum from Alcator-C plasmas.

The modulation of ion acoustic waves due to interaction with a quasistatic plasma slow response in a magnetized plasma is examined. It is found that an instability arises when the modulation is oblique to the direction of wave propagation, but for a restricted range of angles.

An isomorphism is established between the configurational interaction of one discrete level with a continuum, and a relaxation via spontaneous emission of bosons in one-boson approximation. Conditions of one-boson approximation are derived. This approach enables one to overcome limitations of the Markovian or Weisskopf-Wigner approximations. The results qualitatively differ from those obtained in the master-equation approach. In a general case, the probability to remain in an excited state has asymptotically oscillatory behavior, unlike in the Weisskopf-Wigner approximation in which it tends to zero.

The first Born approximation corrected for the boundary conditions is used to compute total cross sections for charge exchange in ${\mathrm{H}}^{+}$-He, ${\mathrm{H}}^{+}$-N, and ${\mathrm{H}}^{+}$-O collisions at intermediate and high energies. An independent-particle method is employed with a one-electron orbital for the target. Two sets of computation are presented in which the initial state of the active electron is described by the Roothaan-Hartree-Fock and hydrogenlike wave functions. These two approaches yield noticeably different results for the cross sections. Excellent agreement with existing experimental data is obtained at energies ranging from 50 keV to 50 MeV by using the Roothaan-Hartree-Fock wave function as a linear combination of normalized Slater-type orbitals.

Submicrometer-size droplets of monomeric liquid crystals dispersed in a solid polymer matrix are studied by deuterium NMR. Phase-separation processes are used to achieve droplets of a size comparable and less than the magnetic coherence length ξ∼0.5 μm, of the NMR magnetic field, 4.7 T. Selectively deuterated (4’-pentoxy- and 4’-methoxy-) 4-cyanobiphenyl compounds (5OCB-$d_2$) and (1OCB-$d_3$) deuterated in the α and methyl positions, respectively, provide for two different NMR measurement time scales to examine effects of the self-diffusion of the molecules confined to droplets. It is found that the line shape of the spectra depends on several factors which include self-diffusion, size, shape of the droplets, and type of anchoring on the droplet walls. Theoretical director configurations calculated for spherical and nonspherical droplets in the presence of an external field were used to simulate NMR spectra in the presence of self-diffusion. Effects due to external fields present during sample preparation are discussed.

The Hopfield model of neural networks is extended to allow for the storage and retrieval of hierarchically correlated patterns. The overlaps between these patterns form an ultrametric tree. Intermediate states, which serve as ancestors for the following levels, are generated at each level of the tree. The states belonging to each level are stored, by a modified learning rule, in a series of identical networks, one for each level. The retrieval of a particular pattern is preceded and assisted by the successive retrieval of its ancestors. The performance of this scheme is studied analytically and numerically.

We present a probabilistic picture for the Einstein relation which holds for arbitrarily connected structures. The diffusivity is related to mean first-passage times, while the conductance is given as a direct-passage probability. The fractal Einstein relation is an immediate consequence of our result. In addition, we derive a star-triangle transformation for Markov chains and calculate the exact values of the fracton (spectral) dimension for treelike structures. We point to the relevance of the probabilistic interpretation for simulation and experiment.

Using the methods of nonequilibrium thermodynamics, we set up the coupled balance equations for mass and energy flow across the interface between dilute and condensed phases. The rate equations for sublimation, evaporation, and condensation are specified for a one-component system and for a metal in contact with its atomic and dimer vapor phase. Imposing Onsager’s reciprocity relations, we can connect Onsager transport coefficients with experimentally accessible quantities such as condensation coefficients and heats of evaporation and sublimation.

Using techniques of the statistical mechanics of random systems, we present the replica-symmetric solution of the graph-bipartitioning problem. We demonstrate that, in the graph-bipartitioning problem with finite connectivity, it is incorrect to replace the constraint ${\mathcal{J}}_{i=1\mathrm{}}^N$$S_i$=0 by a soft version of the constraint, namely, exp[-λ(${\mathcal{J}}_{i=1\mathrm{}}^N$$S_i$${)}^2$] with λ≫1, in the calculation of the partition function. It is explicitly shown that the constraint must be strictly enforced in order to find the correct solution.

Averages of multifractal moments over random structures (e.g., percolation clusters) may be dominated, in some limits, by a rare subset of these structures. This may yield atypical results, contrary to the usual expectations from average quantities. These effects are demonstrated by discussions of the distribution of currents in dilute resistor networks, of the resistance of nonlinear resistor networks, and of self-avoiding walks on percolating clusters.

The atomic-beam laser-rf double-resonance method has been used to measure precisely the dipole and quadrupole hyperfine structure (hfs) of 11 levels of the 5$d^2$6s configuration and four levels of the 5$d^3$ configuration of ${}_{}{}^{139}{}_{}{}^{}$La i. The results, together with earlier results for lower-lying levels, are compared in detail with new multiconfiguration Dirac-Fock (MCDF) ab initio calculations. The agreement is good to fair overall, but is poor in some areas. The comparison yields new insights and suggests areas in which the theoretical approach must be improved. In particular, the theory underestimates the importance of contact hfs in the 5$d^2$6s configuration by 25–40 %. In addition, there is at present no self-consistent way in the MCDF approach to take account of the large core polarization observed in the 5$d^3$ ${\mathrm{}}^4$F term.

We study the fluctuations in a one-dimensional conductor, coupled to a current source. The latter produces shot noise at the boundary of the conductor. The conductor is treated as a classical system of mobile negative charges (with a neutralizing fixed positive background). The current source is represented by considering time-dependent boundary conditions for the system. We also assume the existence of dissipation in the system, and describe the interacting particles by a Langevin equation. The problem is then transformed into an equivalent quantum-mechanical problem (in an imaginary time) of charged interacting bosons and is solved in the limit of small density fluctuations. We show how the fluctuations, induced by the source, decay along the wire. We find that whereas the boundary conditions represent uncorrelated shot noise, the power spectrum of the current fluctuations in the conductor has a 1/f tail at low frequencies.

A model layered feed-forward neural network is studied and solved exactly in the thermodynamic limit. Layer-to-layer recursion relations are found and analyzed as a function of the relevant external parameters. Stochasticity is introduced by a ‘‘temperature’’ variable. A region of good recall is found, separated from a region of no recall by a first-order line terminating at a critical point. The exact time evolution of mixtures of patterns is given as well.

We discuss a new quantum interference effect between the split paths of a coherent particle beam which is in a uniformly rotating frame. The effect is the mechanical counterpart of the Aharonov-Bohm effect usually associated with interference in magnetic fields. We demonstrate that the effect should be observable even in a frame which is rotating no faster than the second hand on a clock.

In this report new trial functions and Green’s functions for Rosenberg’s modified perturbation theory for scattering in a laser field [L. Rosenberg, Phys. Rev. A 34, 4567 (1986)] are proposed.

A coherently driven quantum system suffers a loss of phase coherence through the excitation of unstable levels. This effect is relevant for three-level systems which might serve as very accurate frequency standards. The effect explains why excitation of the doubly driven three-level system is suppressed, a result which has been recently derived in the context of the optical Bloch equations. Dynamical response times of the driven system play an important role in our discussion, and a formalism which highlights these dynamical effects is proposed.

The triple-differential cross section for the single ionization of helium in the coplanar asymmetric geometry has been calculated by using a second Born approximation which employs an improved choice of the target continuum-state wave function. The contribution of still higher-order terms of the scattering amplitude is also considered via the usual Glauber approximation. The results are compared with the recent data of Jung et al. at an incident energy of 600 eV and are found to be in very good agreement with them.

Recent observations of the effects of a strong electric field on the photodetachment of ${\mathrm{H}}^{\mathrm{-}}$ are accounted for by a frame-transformation analysis. The only input parameter is the binding energy of the negative ion. An absolute cross section that includes the effects of the field is derived. The cross section shows modulations above the detachment threshold. Further, there is now a nonvanishing value below the zero-field threshold as a result of field-assisted tunneling of the photoelectron.

In pattern-forming systems the wave-number bands accessible to the system are drastically reduced if the control parameters are varied slowly in space from supercritical to subcritical. Using a recently derived matching condition, these wave-number bands are calculated in a simple model for Taylor vortex flow. They show qualitatively the same behavior as observed in the experiments on this system: (1) starting from a minimal bandwidth, the band grows both for decreasing as well as increasing control parameter ε; and (2) the dependence of the selected wave number on the system length shows a phase shift of half a wavelength during the crossover from small-ε to large-ε behavior. These results are in quantitative agreement with a numerical simulation of the model.

We have shown by consistent application of the Schrödinger and Heisenberg equations that the differential invariance condition imposed by Brown, Lindenberg, and West [Phys. Rev. A 33, 4104 (1986)] on Hamilton’s function, which was obtained by averaging Fröhlich’s Hamiltonian over Davydov soliton states, is not a correct one. The conclusion that Davydov made an erroneous application of Hamilton’s equations is still valid, based on completely different arguments.