We characterize the notion of stochastic resonance for a wide class of bistable systems driven by a periodic modulation. On developing an adiabatic picture of the underlying relaxation mechanism, we show that the intensity of the effect under study is proportional to the escape rate in the absence of perturbation. The adiabatic model of stochastic resonance accounts for the role of finite damping and finite noise correlation time as well. Our predictions compare well with the results of analogue simulation.

A precise digital simulation of a bistable system under the effect of colored noise is carried out. A set of data for the mean first-passage time is obtained. The results are interpreted and compared with presently available theories, which are revisited following a new insight. Discrepancies that have been discussed in the literature are understood within our framework.

The application of periodic-orbit theory to systems which possess a discrete symmetry is considered. A semiclassical expression for the symmetry-projected Green’s function is obtained; it involves a sum over classical periodic orbits on a symmetry-reduced phase space, weighted by characters of the symmetry group. These periodic orbits correspond to trajectories on the full phase space which are not necessarily periodic, but whose end points are related by symmetry. If the symmetry-projected Green’s functions are summed, the contributions of the unperiodic orbits cancel, and one recovers the usual periodic-orbit sum for the full Green’s function. Several examples are considered, including the stadium billiard, a particle in a periodic potential, the Sinai billiard, the quartic oscillator, and the rotational spectrum of ${\mathrm{SF}}_6$. .AE

A Gaussian polymer chain in simple shear flow is studied using Langevin equations. Incorporating hydrodynamic interactions to first order in ε==4-d (d is the spatial dimensionality) with the aid of field-theoretic methods, we solve these nonlinearly coupled kinetic equations for polymer-solvent dynamics and analytically evaluate the second normal stress coefficient ${\Psi }_2$ for small shear rates. It is found that the mean-field (consistent preaveraging) approximation for hydrodynamic interactions (HI) produces an unphysical positive ${\Psi }_2$, while inclusion of fluctuations in HI leads to a negative value for ${\Psi }_2$, in agreement with experimental evidence.

We have studied theoretically the movement of large molecular groups of DNA double helices in solution, which are driven by the electromagnetic field. The longitudinal vibration of nucleotides and the torsional movement of bases are taken into account at the same time. A set of coupled nonlinear partial differential equations has been established, and we have solved these equations by the method of perturbation. The result shows that there exists resonant absorption of microwave energy for both longitudinal and torsional modes. The resonant frequencies for the former and the latter are in the region of gigahertz and subterahertz, respectively. In addition to an nth-harmonic resonance at ${\omega }_n$, our theory also predicts a subharmonic resonance at ${\omega }_n$/2. The strength of the latter is proportional to $l^{\mathrm{-}3}$, where l is the length of DNA. The necessary conditions to observe these resonances are also discussed.

A model is proposed for electrochemical deposition that can describe the flat, dense pattern constituting an assembly of needles with a flat envelope. The model is represented by a pair of diffusion equations that govern mass transport in the electrostatic field. A linear-stability theory is applied to investigate whether or not the interface of the aggregate is stable, following Saffman and Taylor [Proc. R. Soc. London, Ser. A 245, 312 (1958)]. It is found that the disturbances with a wavelength longer than a critical wavelength become stable on the interface of the aggregate. When the destabilizing force of the Saffman-Taylor instability becomes smaller than the stabilizing force of the electrostatic field at the long-wavelength modes, then the flat, dense pattern occurs.

Hyperfine structure of a few excited states of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}_{}^{+}{}_{}{}^{}$ in the 5${\mathit{p}}^5$5d and 5${\mathit{p}}^5$6p configurations has been measured by laser-induced fluorescence with a collinear laser and slow-ion-beam (∼1.5 keV) apparatus. The hyperfine spectrum for the optical transition at 612.86 nm has been recorded for the first time. The full width at half maximum of the laser-induced fluorescence spectra recorded with our apparatus is typically 45–75 MHz. The magnetic dipole (A) and electric quadrupole (B) hyperfine constants have been determined for the two lower levels 5$p^5$5d ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}\mathrm{F}_4^{}{}_{}{}^{}$ and the two upper levels 5${\mathit{p}}^5$6p (3/2[(3/2${]}_{\mathrm{d}}$, 3)/2 [(5/2${]}_3$ at energies 112 803.99, 112 245.44, 129 998.63, and 129 116.56 ${\mathrm{cm}}^{\mathrm{-}1}$, respectively, above the ground state, 5${\mathit{p}}^6$ ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$.

Various correlation energy density functionals have been used to evaluate the electron affinities of the alkaline-earth atoms. A related approach based on polarization potentials was also tested. The results give evidence for the existence of stable negative ions of the atoms Ca, Sr, and Ba. The various density functionals perform relatively well yielding qualitatively correct predictions.

We consider tunneling from a double-well potential to the continuum. Simple expressions are found for the decay rate. For a special configuration of the potential, where the energy levels in two wells are coinciding, the decay time dependence reveals a peculiar quantum-interference behavior. A possibility for observing these effects is discussed.

In this work we analyze the domain of application of the concept of supersymmetry shape invariance in relation to the solubility of quantum Hamiltonians and show that it is strictly the same as the domain of application of the factorization method of Infeld and Hull [Rev. Mod. Phys. 23, 21 (1951)].

Energy shifts of a bound electron in hydrogenlike uranium due to vacuum-polarization corrections of order α(Zα) and α(Zα${)}^3$ are calculated. It is shown that for Rydberg levels the higher-order Wichmann-Kroll correction of order α(Zα${)}^3$ is greater than the order-α(Zα) Uehling contribution.

Energy shifts in muonic atoms caused by vacuum polarization of order α(Zα${)}^n$ with n≥3 are calculated with nuclear size corrections taken into account. The calculations are performed for all muonic levels from the 1$s_{1/2}$ state to the 5$g_{9/2}$ state in various atoms with nuclear charge number Z between 30 and 100.

The recently proposed method by Papp [Phys. Rev. A 36, 3550 (1987); 38, 2158 (1988)] for determining the shift parameter in the shifted 1/N expansion method has been applied in three approximations to calculate the eigenenergies for the static screened Coulomb potential (SSCP) and Lennard-Jones 12-6 potential. The results are compared with those obtained by the method of Imbo et al. [Phys. Rev. D 29, 1669 (1984)] and the exact values. For the SSCP, comparison is also made with the results obtained by two methods proposed by Doren and Herschbach [Phys. Rev. A 34, 2654 (1986); 34, 2665 (1986)].

A general method of solving Schrödinger equations for systems with a slowly (not necessarily extremely slowly) changing Hamiltonian is proposed. Its zeroth-order approximation gives the improved adiabatic theorem by Berry [Proc. R. Soc. London, Ser. A 392, 45 (1984)]. It shows how transitions between different energy levels occur when the Hamiltonian changes less slowly. Selection rules for such transitions are discussed.

A theory is presented for estimating the stopping of bound electrons, whose internal system described in momentum space is considered as a dense interacting electron gas with a Gaussian occupation probability. With the use of an alternative type of random-phase-approximation dielectric function proposed herein, the shellwise stopping powers for protons are calculated in the specific energy range 1–${10}^4$ keV/amu, where the total stopping powers agree with the data.

A simplified classical trajectory Monte Carlo (CTMC) method is proposed for ion-atom collisions. With the introduction of the prescribed classical trajectories for the internuclear motion, the electronic motion in the time-dependent interaction is solved classically. It gives almost identical integrated cross sections with the ‘‘exact’’ CTMC calculations. Differential cross sections are also calculated for p+H→H+p. The results are in excellent agreement with the experiments.

The response of even- and odd-mass isotopes is found to be very different in several schemes for resonance ionization of Mo and Sn, even when the laser linewidth is greater than the span of the hyperfine structure and isotope shifts.

We present a theory for resonant ionization by broad-band laser radiation with emphasis on the role of laser bandwidth. It is shown that under certain conditions, often encountered in experiments of this type, the amount of ionization will depend on an intricate interplay between atomic and radiation parameters. The theory is discussed in the context of an application to Sn, which enables us to provide quantitative comparison with recent experimental data.

The nonlinear propagation of intense electromagnetic radiation in an electron-positron plasma of a pulsar magnetosphere is investigated. Basic equations describing a macroscopic behavior of an ultrarelativistic plasma (T≫${\mathrm{mc}}^2$) in a covariant form are used to treat the problem. Relativistic and time-derivative ponderomotive nonlinearities are considered. Earlier results of envelope solitons in the weak relativistic case are confirmed, while isolated solitons are found to exist in the ultrarelativistic plasma.

An approximate nonlinear-response theory is derived by maximizing the information theoretic entropy in the space of fluctuations J(t) of the degree of freedom of interest, subject to constant-energy dissipation in the external field. The resulting formalism expresses all cumulant averages of J(t) in an external field in terms of equilibrium cumulants.