The title process with simultaneous rotational deexcitation of molecules was investigated theoretically by using the semiquantal approximation. The dipole Born and dipole Glauber differential cross sections were employed for the electron-molecule rotational deexcitation process. Numerical applications were made to the following systems: Xe+CO, HCl, HF, and LiF. A comparative study of the two approximations was carried out concerning the dependences of the cross sections on the following various quantities: n (principal quantum number), J (initial rotational quantum number), ΔJ (rotational quantum number change), D (dipole moment), V (relative collision velocity). As the molecular dipole moment becomes larger, there appears a prominent difference in the n dependence of the cross section. The Glauber approximation brings about a decrease in the cross section and yields a sawlike n dependence in contrast to a steplike n dependence in the case of the Born approximation. In the collisions involving lowly excited Rydberg atoms, ionization with simultaneous dipole-forbidden transition of a molecule becomes dominant compared to the ionization with simultaneous dipole-allowed transition. The cross section was found to be inversely proportional to the relative collision velocity; thus the ionization rate becomes independent of temperature. A comparison was also made between the experiment for the ionization rate at 300 K for Xe(27f)+HF and Xe(31f)+HCl.

The absorption spectra of a group of selected molecules containing O—C bonds, carbon monoxide, carbon dioxide, carbonyl sulfide, acetone, ethanol, diethylether, tetrahydrofuran, and dioxane, have been recorded in a transmission mode in the energy region from 500 to 1000 eV. Earlier observation of extended x-ray-absorption fine structure (EXAFS) in some of these molecules is confirmed. A systematic analysis of the EXAFS spectra is performed. The results in both phase and amplitude show disagreement with the single-electron single-scattering theory with plane-wave approximation. The measured phase is systematically lower than the theory of Teo and Lee [J. Am. Chem. Soc. 101, 2815 (1979)] by about 0.7–1.5 rad, which may be significant in determining interatomic distances. The EXAFS amplitude function in the molecules containing oxygen-carbon single bonds also shows an appreciable deviation (decrease) in the first-neighbor backscattering from that predicted by theory and an increase in the second-neighbor backscattering at high-k values.

A simple model of ionization, capable of dealing with arbitrarily strong laser fields, is discussed. A model ‘‘atom,’’ consisting of a rectangular well potential of finite depth is perturbed by a train of δ kicks that are alternating in sign. The results of exact (numerical) calculations are compared with those obtained neglecting continuum-continuum transitions. Both the ionization rate and the photoelectron spectra are discussed. Neglecting continuum-continuum transitions leads to good results for the ionization rate which is well approximated by the low-field perturbative expression up to very strong fields. On the contrary photoelectron spectra are sensitive to a detailed form of continuum-continuum matrix elements (both to their singular and regular parts).

Quantum chaos has been demonstrated in several studies of the interaction between N two-level quantum systems and a single-mode radiation field interacting in a resonant cavity. It has been shown that the mechanism for this chaos is dynamically identical to a periodically perturbed, near-separatrix motion of a pendulum. Identification of this mechanism followed from examination of the rotating-wave approximation and corrections to this approximation. Our earlier study established the nature of the corrections on the basis of numerical simulation experiments and heuristic arguments. In this paper we invoke an averaging procedure which enables us to systematically establish the form of these corrections. We first apply this procedure to the Rabi model in order to illustrate its utility and exhibit its structure, and then we apply it to the more complicated problem of quantum chaos.

This paper presents perturbation calculations using the density matrix to describe the nearly degenerate four-wave-mixing spectral response in resonant systems subject to state-specific reservoir coupling. The calculations provide physical insight into the origin of narrow resonances observed in recent experimental work in atomic sodium and ultranarrow resonances in crystals. The calculations are for systems which are homogeneously broadened as well as systems which are inhomogeneously broadened due to velocity effects or random crystal fields. The calculations show that it is possible to eliminate the effects of either kind of broadening and measure the decay rate of the dipole coherence as well as the decay rates of both states of the transition. Furthermore, the calculations indicate that the method of cross-correlated optical fields which was used to eliminate the effects of laser jitter in longitudinal relaxation rate measurements could be extended to the measurements of slow dephasing rates in crystals.

A perturbation scheme based not on the ideal gas but on a system of purely repulsive cores is applied to a typical fully interacting fermion gas. This is ‘‘neutron matter’’ interacting via (a) the repulsive ‘‘Bethe homework-problem’’ potential, (b) a hard-core–plus–square-well potential, and (c) the Baker-Hind-Kahane modification of the latter, suitable for describing a more accurate two-nucleon potential. Padé extrapolation techniques and generalizations thereof are employed to represent both the density dependence as well as the attractive coupling dependence of the perturbation expansion. Equations of state are constructed and compared with Jastrow–Monte Carlo calculations as well as expectations based on semiempirical mass formulas. Excellent agreement is found with the latter.

The correlation of fluctuations of a fluid in a finite container subject to a constant strain is studied with use of both the fluctuating hydrodynamics formalism and a Boltzmann Monte Carlo particle simulation. Good quantitative agreement is demonstrated.

A density-functional model for fluids, containing a one-point and a two-point coupling function, is studied. The field variables of the model are the local fluid density ρ(r) and a coarse-grained density ${\rho }_0$(r). Using the method developed by Meister and Kroll [Phys. Rev. A 31, 4055 (1985)], the coarse-grained density is eliminated as a free variable, which defines a hypersurface in the function space ρ⊗${\rho }_0$. From the variations of the free-energy functional along this hypersurface, we derive a renormalization equation for the two-point coupling, using the direct correlation function as a normalization condition. We solve this equation numerically for the hard-sphere fluid, but the given algorithm can be applied to any other fluid, of which the direct correlation function is known.

The condition for stationary configurations of point vortices (or screw dislocations, line charges, etc.) having arbitrary strengths embedded in an external flow field is expressed as a differential equation for functions whose zeros are the vortex positions. For vortices of unit strength but mixed sign the stationary states are closely related to both the rational and the N-soliton solutions of the Korteweg–de Vries equation. Examples are given for no external flow, uniform flow, and quadrupole flow.

The hydrodynamic fluctuations of nearly spherical vesicles and microemulsion droplets are considered. The incompressibility of the enclosed fluid and surfactant or lipid layer imposes a constraint of constant droplet volume and area on the fluctuations. These overdamped modes, driven by bending energy and damped by viscosity of the surrounding fluids, change the shape of the surface and may scatter neutrons or light. A dynamical structure factor S(q,t) is computed and a first frequency moment at fixed wave number ${\omega }_{\mathrm{char}(\mathrm{q}}$) obtained. In the limit of a stiff droplet at fixed ‘‘excess area,’’ a new mode is obtained —an overdamped oscillation among ellipsoidal shapes about the minimum-energy (usually prolate) shape. Prospects for observing this fluctuation are discussed.

The spontaneous ferroelectric polarization in the chiral smectic-C phase can be measured by monitoring the dynamic response to a changing electric field. A model for the system is presented and analyzed for the two cases of square-wave and sinusoidal voltage applied to a ‘‘bookshelf geometry’’ sample, where the smectic layers are oriented relative to the glass plates as books are to a shelf. The model gives a good description for the observed polarization reversal current and yields the rotational viscosity and one effective elastic constant in addition to the spontaneous polarization. Relations between these parameters and the width of the observed hysteresis loop are derived as well as relations for the contribution of the ferroelectric polarization to the permittivity. The model is applied in evaluating data from measurements on the substance MBRA-8 [2-hydroxy-4(2-methyl-butyloxy)-benzylidene-4-p-n-octyl-aniline].

A forward Hopf bifurcation is characterized by the continuous development of a periodic oscillatory state from a time-independent state as some control parameter is varied. In Rayleigh-Bénard convection the control parameter is the Rayleigh number and the transition is from a stationary convective roll structure to periodic time-dependent convection. We show analytically that close to the bifurcation point the amplitudes of the temporal modes of the oscillatory state scale as (R-$R_0$${)}^{n/2\mathrm{}}$, where n is the mode number. Complex-amplitude equations are also derived which give the transient behavior of these modes. Experimental data on Rayleigh-Bénard convection in a dilute solution of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ agree well with the theory.

A second-order nonlinear differential equation whose general solution can be expressed in terms of elementary functions is studied. Analytical expressions describing both the phase portrait and global bifurcations for all values of the parameters are given. With the advantage of being exactly solvable, this equation models essentially the same physical phenomena as the well-known van der Pol’s equation. In particular, the relaxation limit of the oscillatory regime where systems periodically undergo fast switching between two different kinds of slow motions can be explained on the basis of our model as a consequence of the presence of a saddle-node bifurcation.

The one-dimensional Schrödinger equation can be reformulated in terms of a linear third-order differential eigenvalue equation for ‖Ψ(x)${\Vert }^2$. The bounded physical states are the unique non-negative solutions which are asymptotically zero and have finite moments. Because of this, the eigenvalue-moment methods of Handy and Bessis can be applied to ‖Ψ${\Vert }^2$, thereby yielding rapidly converging lower and upper bounds to the individual discrete-state eigenvalues. Two examples are considered: a one-dimensional nonlinear Schrödinger equation of the form -1/2Ψ‘+${\mathit{x}}^2$(1/2+a〈Ψ‖${\mathit{x}}^2$‖Ψ〉)Ψ=εΨ and the octic potential -1/2Ψ‘+(1/2${\mathit{x}}^2$+λ${\mathit{x}}^8$)Ψ=EΨ.

When the Lagrangian is not quadratic in the velocities, the situation may arise that the expression for the velocities in terms of the momenta is multivalued. As a consequence, the classical motion is unpredictable since at any time one can jump from one branch of the Hamiltonian to another. Yet, the quantum theory turns out to be perfectly smooth, with wave functions which are regular functions of time. We show that the path integral automatically picks up a unique combination of the branch Hamiltonians, which is a natural generalization of the Brouwer degree of the Legendre map.

We study the continuous-time dynamics of a strongly diluted Hopfield model with asymmetric synaptic connections. The model is exactly soluble for static as well as dynamic properties. The time evolution of the autocorrelation, the susceptibility, and the overlap function of two configurations are given in explicit form.

We have measured the distribution of mass $P_s$(r) within a distance r measured from occupied sites in the screened-growth model ($d_f$=1.25, 1.5, and 1.75, where $d_f$ is the fractal dimension), off-lattice diffusion-limited cluster-cluster aggregates ($d_f$=1.43), and off-lattice diffusion-limited aggregation (DLA) clusters. Here $P_s$(r) is the probability that a circle of radius r centered on an occupied site will contain S occupied sites or particles. For the screened-growth and cluster-cluster aggregation models, the distributions $P_s$(r) can be described in terms of the scaling &). The dependence of the moments 〈$S^n$〉/〈S${〉}^n$ on the distance r has also been measured. For the screened-growth and cluster-cluster aggregation models these quantities are essentially independent of r for n≥1. For DLA the simple scaling form for $P_s$(r) does not describe the mass distribution and (1/n)ln(〈$S^n$〉/〈S${〉}^n$), with n=2–10, has a linear dependence on ln(r) with negative slopes which are different for different values of n for small values of r. Since 〈$S^n$〉/〈S${〉}^n$ has a lower bound of 1, this cannot be the true asymptotic behavior for off-lattice DLA. It suggests that DLA has a more complex structure than either the screened-growth model or cluster-cluster aggregation.

A field-theoretic renormalization-group method is used to investigate crossover behavior in nonequilibrium multicritical phenomena of one-component reaction-diffusion systems. A system composed of 2n-1 reactions, lX→l’X (l>l’), lX→l’’X (l’’) (with l=1,2,...,n-1), and nX→n’X (n>n’), is discussed. An expression for crossover exponents is derived and mean-field values of them are obtained as a function of n. For the process of n=3, the crossover exponent is determined to first order in ε=$d_c$-d ($d_c$=3) and logarithmic corrections to scaling at d=$d_c$ are calculated.

A numerical calculation of the entropy of the two-dimensional Ising model is described, for nonzero external field. The calculation makes use of the Monte Carlo method to simulate a kind of microcanonical ensemble.

Experiments with absorbing foils, beam choppers, or an absorbing lattice in one path of a neutron interferometer to expose the difference between stochastic and deterministic absorption in quantum mechanics are reported. The different amplitudes of the interference patterns in stochastic and deterministic absorption when the absorption probability is the same were observed in agreement with prediction. Also the possibility of a gradual transition from deterministic to stochastic absorption was experimentally investigated.