An approximate solution to a scattering problem containing Coulomb and short-range potentials is presented. The method is based on a separable expansion of the short-range part of the interaction in terms of bound-state Coulomb-Sturmian functions. Similarly to the approximation based on the expansion of the scattering wave function on a scattering-state Coulomb-Sturmian basis, the method yields asymptotically correct wave functions. The convergence, however, is much faster in the potential separable-expansion method.

The concept of the self-phase-modulation and related frequency chirp is introduced in the connection of the surface second-harmonic generation, which is induced by a short-duration laser pulse.

Decay widths of metastable hydrogen atoms subjected to the intense field of the currently available ${\mathrm{KrF}}^{\mathrm{*}}$ laser (λ=248 nm) and ${\mathrm{ArF}}^{\mathrm{*}}$ laser (λ=193 nm) are calculated by solving the full (3+1)-dimensional Schrödinger equation in the space-translated frame of reference. The critical intensities, above which the suppression of ionization decay sets in, are found to be ${\mathit{I}}_{\mathit{c}}$≃2.5×${10}^{14}$ and 7×${10}^{14}$ W/${\mathrm{cm}}^2$ for λ=248 and 193 nm, respectively.

We study a two-level quantum system interacting through a coupling strength g with a single-mode radiation field. We show that the rotating-wave-approximation (RWA) Hamiltonian produces quantum-mechanical effects more persistent than those generated by the full Hamiltonian. Within the full Hamiltonian the semiclassical prediction is recovered upon increase of the radiation field intensity, whereas with the RWA Hamiltonian no reconciliation with the predictions of the semiclassical approximation is realized by fields of any intensity, if the interaction strength g is kept unchanged.

The propagation of three-dimensional continuous-wave Gaussian optical beams focused onto an interface between a nonlinear cladding and a linear substrate is studied numerically. Both Kerr-law and saturable self-focusing nonlinearities are considered. The Gaussian input beam profile closely matches the corresponding stationary stripe nonlinear-surface-wave field distribution. Saturable nonlinear media are shown to lead to an increase in the stability of stripe nonlinear surface waves.

The surface tension between coexisting plus and minus ferromagnetic phases of the Widom model [J. Chem. Phys. 84, 6943 (1986)] is computed by performing a seventh-order low-temperature expansion. A functional form for the surface tension is suggested, based on Padé-approximant analysis, for the complete range from T=0 to bulk criticality. The surface tension is computed along the roughening line, which had been recently calculated by a low-temperature expansion [B. Kahng, A. Berera, and K. A. Dawson, Phys. Rev. A 42, 6093 (1990)]. The positivity and well-behaved form of our surface-tension series along this line establishes the validity of the low-temperature approximation in this regime of parameter space. Comparisons of the low-temperature results to mean-field theory are made. A preliminary examination of the critical amplitude is discussed.

The A-${\mathit{B}}_2$ surface-reaction model [R. M. Ziff, E. Gulari, and Y. Barshad, Phys. Rev. Lett. 56, 2553 (1986)] is studied including spontaneous desorption of CO from the catalyst surface. It is found that when the spontaneous desorption probability P is above a critical value ${\mathit{P}}_{\mathit{c}}$>0.039, the system no longer exhibits a first-order kinetic phase transition. The interface between coexisting phases is found to be nonfractal for P below ${\mathit{P}}_{\mathit{c}}$, but it becomes fractal with dimension D=1.46±0.05 when P=${\mathit{P}}_{\mathit{c}}$. The critical behavior of the model is qualitatively described by Dickman’s one-site mean-field approximation.

Molecular-dynamics and Monte Carlo simulations of fluids and of crystals are typically performed using periodic boundary conditions and small numbers of particles, i.e., small compared with Avogadro’s number. For fluids, if the dimensions of the simulated system are large enough compared with the correlation length of the material, the simulation can provide intensive thermodynamic properties that are very close to those for the thermodynamic limit of large system size. For crystals, however, the periodic boundary conditions and the crystal structure impose a constraint that makes it impossible, in practice, for the system to develop an equilibrium concentration of vacancies. The effect of this constraint must be taken into account when inferring thermodynamic properties from the results of computer simulations of crystals. We develop the thermodynamic and statistical thermodynamic theory of a crystal subject to such a constraint. The results include a set of stability conditions that must be satisfied and a criterion for equilibrium. We also describe a method for calculating the equilibrium concentration of vacancies in a crystal from computer simulations.

We present a rigorous approach to the problem of the random clustering of points in one-dimensional Poissonian distributions. Exact expressions for the probability density of clusters are derived, and the statistical properties of the inner configuration of their associated structures are studied in detail. We review previous works in the field, assessing their accuracy in the context of the present approach. Its extension to more general distributions is pointed out, and several of the many practical applications of these works are briefly recalled.

We study the distribution of zeros of the Husimi functions for the spin-boson model, following an approach introduced by Leboeuf and Voros. The interest lies in the model’s double feature of possessing both a classical integrable to chaotic transition and an unbounded four-dimensional phase space. The latter gives rise to several new questions regarding the Husimi zeros which are discussed and partially answered. Some significant results occur in spite of the fact that we treat the case of spin 1/2.

The quasiparticle transfer in a coupled nonlinear dimer-vibration system is analyzed. The quasiparticle is subjected to both an intrasite cubic polarization nonlinearity and an intersite vibration. The system is a realization of a Hamiltonian flow on the foliated phase space represented by the Bloch sphere (density-matrix dynamics of the quasiparticle) and the plane (state of the oscillator). The analysis is performed starting from the uncoupled case for which the Hamiltonian flow on the Bloch sphere is characterized by a homoclinic structure for polarization strength above a critical value dividing the solutions into two different classes of partially trapped and untrapped transfer behavior. Then the modifications for a finite coupling, in particular, how chaos on the Bloch sphere develops, are investigated in detail, applying the Melnikov method and direct numerical integration for increasing coupling strength. The development of chaos on the Bloch sphere implies a transition from partially trapped to untrapped transfer behavior, destroying quasiparticle self-trapping.

We study the dynamic scaling of the growing surface during ballistic deposition of disk-shaped particles with various distribution of the disks’ radii. Our simulations correspond to introducing isotropic random perturbations of widely scattered amplitude. The results for both the Gaussian and for the power-law P(ρ)∼${\mathrm{\rho }}^{\mathrm{-}1\mathrm{-}\mathrm{\mu }}$ (for μ=3) distributions are in good agreement with the previous theoretical and numerical findings obtained for significantly simpler models.

A generalization of the continuum model (Kardar-Parisi-Zhang equation) for growth of self-affine surfaces is considered to take nonlocal effect into account in the simplest way, which leads to unstable growth. A dynamic renormalization-group calculation reveals crossover phenomena with characteristic lengths and times, below both of which the power law remains meaningful. The numerical solutions for (1+1)-dimensional systems show that the morphology of profiles changes to global paraboloid segments joined together by singular cusps after the crossover time.

The Baym-Kadanoff theory of the conserving vertex is discussed within the context of the parquet summation of Feynman diagrams in nonrelativistic many-body theory. Since the parquet language provides a convenient way of characterizing all two-body vertices, the Baym-Kadanoff algorithm for generating a conserving two-body vertex takes a very straightforward form. We present the general theory and then illustrate the results using many of the simple conserving vertices. We then analyze the parquet two-body vertex within the theory, concluding that parquet is not a conserving theory. We show that any conserving theory that generates the direct parquet diagrams must also generate an infinite number of irreducible diagrams and derive integral equations for the minimal set of irreducible diagrams that would be needed in a conserving theory that produced the direct parquet diagrams. We present an algorithm that enables one to determine, for any direct or exchange parquet diagram, the parquet diagram whose contribution to the self-energy, when functionally differentiated, will generate the original parquet diagram. We then show that any set of diagrams for the two-body vertex that includes the bare interaction and satisfies the important properties of being conserving and antisymmetric under exchange of the outgoing particles must necessarily include all diagrams.

This paper is concerned with the dynamical basis of Maxwell’s demon within the framework of classical mechanics. We show that the operation of the demon, whose effect is equivalent to exerting a velocity-dependent force on the gas molecules, can be modeled as a suitable force field without disobeying any laws in classical mechanics. An essential requirement for the models is that the phase-space volume should be noninvariant during time evolution. The necessity of the requirement can be established under general conditions by showing that (1) a mechanical device is able to violate the second law of thermodynamics if and only if it can be used to generate and sustain a robust momentum flow inside an isolated system, and (2) no systems with invariant phase volume are able to support such a flow. The invariance of phase volume appears as an independent factor responsible for the validity of the second law of thermodynamics. When this requirement is removed, explicit mechanical models of Maxwell’s demon can exist.

In this paper we develop a method of finding analytical solutions to the class of nonlinear ordinary differential equations given by f’’+A(f)f’+B(f)f${\mathcal{’}}^2$+C(f)=0. These types of equations appear frequently in mathematical physics and its applications to the kinetics of dissipative critical systems. Except for very special cases, little is known about their analytical solutions. Following a presentation of the method and its results, several particular examples are investigated in some detail.

The motion of a quantum particle in a tight-binding lattice coupled to an Ohmic thermal reservoir is analyzed in the path-integral formalism. We derive exact formal expressions for moments of the probability distribution both for noncorrelated and correlated thermal initial states of the particle-plus-reservoir complex. Based on these expressions we discuss the role of initial conditions on the subsequent motion and calculate the differences in the transient behavior. For a particular value of the damping strength we find the exact solution of the dynamics in analytic form at any time, temperature, and bias for the two kinds of initial states.