A quantum theory of a two-photon laser in a three-level atomic system of the cascade type is presented starting from an original microscopic Hamiltonian. The master equation of the laser operation is derived by using the method of Scully and Lamb [Phys. Rev. A 159, 208 (1967)] for a single-mode laser containing a two-level medium. The photon-number distribution of the laser is studied in detail. The curve of the distribution may have a two-peak structure. One of the peaks located at the origin comes from the single-photon process and reflects the thermal property of the laser, while another comes from the two-photon process and reflects the coherent property of the laser. We cannot find an exact criterion for the threshold of the two-photon laser. The two-photon laser can approximately be considered as a coherent state for certain values of A/C, which can even be much smaller than the threshold for the nonresonant single-mode laser in a two-level system, but it is much larger than the threshold for the resonant one.

A set of coupled non-Markovian equations of motion is derived for the Green’s function of a driven two-level atom. These equations can be expressed in terms of the density-matrix elements only in the Markovian limit, in which case the set reduces to optical Bloch equations. The non-Markovian effect arises from correlations between successive photon emissions, an effect which is neglected in the existing equations of motion. The resulting correction is of the order of ${\gamma }_0$/${\Omega }_0$ in the strong-field region (${\gamma }_0$<${\Omega }_0$) and it vanishes in the weak-field region, where ${\gamma }_0$ is the Einstein A coefficient and ${\Omega }_0$ is the Rabi frequency.

The two-photon emission spectrum of a strongly driven two-level atom is defined and calculated. Such a spectrum reveals details of non-Markovian dynamics which are not observable in the usual experiments. It is shown that a clear separation of Markovian and non-Markovian regimes is possible in the two-photon emission spectrum.

The Gaussian broadening of absorption lines due to the Doppler effect is well known. However, it is shown here for the first time that Doppler splitting occurs for the ordinary-mode electron-cyclotron-resonance absorption in plasmas. Although this absorption is due to the finite size of the electron Larmor orbits it is mainly determined by $T_{?}$ and is only weakly dependent on $T_{\perp }$ via cyclotron-overstability-type terms. This is in contrast to intuitive expectations which would suggest that finite-Larmor-radius effects should depend strongly on $T_{\perp }$.

By rescaling the exact low-density results practical expressions are obtained for the equation of state and the direct correlation function of a fluid of hard D-spheres allowing a unified treatment of both the odd and even space dimensionalities D. The accuracy of these results is tested against those of the current literature and found to be excellent, in particular for hard disks (D=2), whereas the hard-rod results (D=1) are reproduced exactly.

In this paper we present measurements of thermal transport in spherical geometry made with 24 uv (351-nm) beams from the OMEGA laser system of the Laboratory for Laser Energetics of the University of Rochester. The measurements, using time-resolved x-ray spectroscopy on solid glass targets coated with varying thicknesses of plastic, provide absolute measurements of the onset times of the resonance x-ray lines of silicon. From these measurements, the scaling of the instantaneous mass-ablation rate with absorbed intensity is obtained for times before and after the peak of the laser pulse. The observed large burnthrough depths and early onsets of the x-ray lines are explained by carrying out detailed hydrodynamic-code simulations for the range of the estimated laser-intensity distribution on target which is obtained from the superposition of the equivalent target-plane intensity distribution of a single beam. We find that neglecting the effects of laser illumination nonuniformities can lead to erroneous conclusions about the heat transport. We conclude from the analysis that the experimental results can be explained by the presence of significant energy at intensities three times the nominal intensity, contained in hot spots of size less than 20 μm. This is almost twice as much as the maximum intensity obtained from the superposition of the single-beam distribution.

A computer simulation of liquid water using the ab initio Matsuoka-Clementi-Yoshimine-Lie (MCYL) potential has been analyzed in comprehensive detail with use of pertinent auto-correlation and cross-correlation functions of the water molecule’s vibrational, rotational, and translational dynamics. The autocorrelation functions (ACF’s) of dynamical quantities such as atom velocity, center-of-mass velocity, molecular angular momentum, molecular angular velocity, molecular dipole moment, and molecular rotational velocity vectors have been computed with 3400 configurations generated in a simulation with 343 molecules in the laboratory frame and in the frame of the principal molecular moments of inertia. Furthermore, cross-correlation functions (CCF’s) of many different kinds have been computed in both frames in order to study in detail the mutual effects of vibration, rotation, and translation at the single-molecule level. In some respects the inclusion of vibrational effects in the MCYL potential does not significantly change the pattern of dynamical information summarized in these time correlation functions. The rotation-translation CCF’s which were obtained recently by Evans et al. from a rigid empirical model for the intermolecular pair potential energy in liquid water appear once more from the ab initio MCYL potential with the same symmetry and time dependence. This is a strong corroborative evidence for the correctness of the methods used in both cases. However, the inclusion of vibrational effects by Lie and Clementi in their MCYL potential leads in this work to considerable further insight obtained by a detailed study of cross-correlation functions between vibration and rotation and between vibration and center-of-mass translation.

Novel molecular-dynamics calculations have been carried out for a hypervelocity impact of a sphere of 683 atoms (a central atom surrounded by 23 coordination shells) hitting a rectangular plate composed of 8000 atoms (five close-packed planes thick). The ratio of the sphere diameter to the plate thickness was chosen to be approximately 2.4, with the velocity of the sphere chosen such that its kinetic energy was roughly 25 times its binding energy, relative to the bottom of the potential well. Under these conditions, the debris cloud generated by the ball after it penetrates the wall is composed mostly of vaporized material. These microscopic results scale hydrodynamically to macroscopic experiments of a lead sphere hitting a lead plate at $u_p$=6.6 km/s. There are striking similarities between these atomistic calculations and continuum hydrodynamics simulations, as well as notable differences.

Four levels of nonlinear hydrodynamic description are presented for a nondissipative multicondensate solution of superfluids with vorticity. First, the multivelocity superfluid (MVSF) theory is extended to the case of a multivelocity superfluid plasma (MVSP), in which some of the superfluid condensates (protons, say) are charged and coupled electromagnetically to an additional, normal, charged fluid (electrons). The resulting drag-current density is derived due to the electromagnetic coupling of the condensates with the normal fluids. For the case of one charged condensate, the MVSP equations simplify to what we call superfluid Hall magnetohydrodynamics (SHMHD) in the approximation that displacement current and electron inertia are negligible, and local charge neutrality is imposed. The contribution of the charged condensate to the Hall drift force is determined. In turn, neglecting the Hall effect in SHMHD gives the equations of superfluid magnetohydrodynamics (SMHD). Each set of equations (MVSF, MVSP, SHMHD, and SMHD) is shown to be Hamiltonian and to possess a Poisson bracket associated with the dual space of a corresponding semidirect-product Lie algebra with a generalized two-cocycle defined on it. Topological conservation laws (helicities) associated with the kernels of these Lie algebras are also discussed as well as those associated physically with generalized Kelvin theorems for conservation of superfluid circulation around closed loops moving with the normal fluid.

Stark widths of four N ii, fourteen N iii, five N iv, and two N v spectral lines have been measured in a linear-pinch discharge plasma and compared with existing experimental and theoretical results. Electron densities determined with single-wavelength laser interferometry with use of the visible 632.8-nm transition of a He-Ne laser cover the range of (0.40–1.80)×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$. The electron temperature of 50 000 K was determined from the Boltzmann slope of several N iii spectral lines, and from the relative intensity ratios of several N ii to N iii and N iii to N iv spectral lines. Since the majority of investigated N iii spectral lines originate from the 3s-3p and 3p-3d transition arrays, the Stark-width (w) dependence on the upper level ionization potential (I) of corresponding lines belonging to these two transition arrays was discussed and found to be of the form w=${\mathrm{aI}}^{\mathrm{-}b}$, where a and b are constants independent of the ionization potential. Similarly, the overall Stark width trends, using data obtained from the 3s-3p transition of the N ii, N iii, N iv, and N v spectral lines, were determined and discussed including the influence of emitter net charge on the Stark broadening dependence on the upper-level ionization potential. The established overall trend was used to predict the Stark width of uninvestigated spectral lines originating from the given 3s-3p transition with an accuracy better than 30%.

The Soret coefficient (thermal diffusion coefficient) characterizing the coupling between heat and mass transport in more-component systems has been obtained by equilibrium molecular dynamics. Two-component liquid systems of the Lennard-Jones type were considered: three isotopic mixtures and Ar-Kr. Computations 20 times longer than the ones used for a ‘‘usual’’ transport coefficient, as the thermal conductivity, were necessary to obtain this cross coefficient with modest accuracy. The analysis of the Green-Kubo integrand shows that, opposite to the thermal conductivity, the thermal diffusion depends strongly on the terms containing the partial enthalpies of the components. For the isotopic mixtures, it was found that the Soret coefficient grows with the mass ratio in a way consistent with experimental results. For the Ar-Kr system, direct comparisons with nonequilibrium molecular-dynamics data indicated good agreement. As experimental Soret coefficients for Ar-Kr are lacking, we cannot compare our results with data of the real mixture. The order of magnitude found agrees, however, with that experimentally observed for binary liquid mixtures.

Using reflectivity, we observe the effect of steady fluid flow on the growth of gravity-thinned wetting films in a binary-liquid system of nitromethane and carbon disulfide at bulk coexistence. The substrate is a horizontal borosilicate glass surface. The growth process is driven by the substrate-liquid interaction and opposed by a gravity-induced pressure gradient. We find that the steady-state wetting-layer thickness increases with the stirring rate in qualitative agreement with the hydrodynamic theory of Kayser, Moldover, and Schmidt [J. Chem. Soc. Faraday Trans. 2 82, 1701 (1986)] for wetting-layer development. We observe diffusion-limited exponential buildup of the wetting layer toward steady state. The steady-stirring experiments presented here are compared with earlier random stirring results. Finally, we find that at high stirring rate the bulk liquid-liquid interface becomes unstable against the formation of liquid droplets. This instability is responsible for a fast growth mode of the wetting layer.

We have studied the Saffman-Taylor instability in a Hele-Shaw cell containing the nematic liquid crystal 4,4’-n-octylcyanobiphenyl (8CB). Air injected into the center of the cell gives rise to viscous fingering patterns, which show a sequence of dense-branching, dendritic, dense-branching morphologies as a function of temperature. A qualitative explanation of these morphological transitions is given in terms of the flow alignment of the director field and the resulting anisotropic viscosity in the nematic phase of the liquid crystal. The fingering patterns were digitized; analysis of the resulting data shows that while the perimeter of the pattern is fractal, the pattern itself is not. The extent to which the pattern is space filling depends on the morphology and this quantity may serve to indicate the morphological transitions.

The explicit expression in two and three dimensions for the conditional direct correlation function $C_{\mathrm{cond}}$, representing the intrinsic part of the direct correlation function C, is obtained in the capillary-wave model in the limit of unbounded interface fluctuations. $C_{\mathrm{cond}}$ varies in the transverse and the longitudinal directions on intrinsic interface scales, which are expressed only in terms of the bulk correlation length ${\xi }_b$, the surface tension σ, and the temperature T, thus are independent of external conditions stabilizing the interface in space. For d=2, $C_{\mathrm{cond}}$ is strictly short ranged, whereas for d=3, $C_{\mathrm{cond}}$ is long ranged and its Fourier transform in the transverse direction (parallel to the interface) is not analytic at $k_{\perp }$=0 in contrast to the usual assumptions. The relation to the Yvon-Triezenberg-Zwanzig formula is clarified.

We investigate the properties of the solutions of a nonlinear time-delayed differential equation (infinite dimension) as a function of two parameters: the time delay τ and the nonlinearity parameter A. Occurrence of a Hopf bifurcation is a necessary condition for obtaining a period-doubling cascade. It is also a sufficient condition when the parameter τ is fixed and A is varied. However, it is not a sufficient condition when A is fixed and τ is varied. When period doubling occurs, a strange attractor is obtained and the behavior of the largest Lyapunov exponent as a function of τ is different from its behavior as a function of A.

The cascading bifurcation of two-dimensional, steady and periodic, thermal convection states in a rotating box with a uniform temperature distribution on the walls was studied by Magnan and Reiss, SIAM J. Appl. Math. (to be published). We extend that perturbation analysis by considering the effect of a slightly nonuniform temperature distribution on a wall of the box. This imperfection can qualitatively alter the response of the convection system. In particular, our two-parameter study finds that (a) the ‘‘vertical’’ Hopf bifurcation branch of periodic solutions, previously obtained at third order for a uniform temperature distribution, is now ‘‘bent’’ by the imperfection; (b) the number and position of the Hopf bifurcation points on the steady solution branches can vary with the strength of the imperfection and thus the stabilities of these branches can accordingly change; (c) the periodic solution branches, which now bifurcate either to the right or left, terminate in either a Hopf bifurcation point or in an infinite period bifurcation point; and (d) the imperfection can dominate the effects of higher-order terms in the amplitude equations. Furthermore, we establish for a semibounded rotating convection layer that when an imperfection is present the nonlinear interaction of two primary bifurcation steady states can generate stable, periodic solution branches, which has not been shown to occur for ordinary (nonrotating) Rayleigh-Benard convection, or for any other convection system.

We study the ground-state energy of a system of N identical bosons, each having mass m, which interact in one dimension via the pair potential V(x)=γ‖x‖ and obey nonrelativistic quantum mechanics. It is shown that the energy is given by the formula ɛ=C(N)(N-1)(${ħ}^2$/ m${)}^{1/3}$(γN${/2)}^{2/3}$, where 1.01879N≥2. The lower bound is provided by the ‘‘equivalent two-body method’’ whereas the upper bound is derived by the use of collective field theory. The general relation between these complementary theories is investigated.

The statistical mechanics of polymerized surfaces with a finite bending rigidity κ’ is studied via the Monte Carlo method. The model system consists of a hexagon, L atoms across, excised from a triangular lattice embedded in three-dimensional space. Nearest-neighbor atoms interact via an infinite-square-well potential, while the bending energy is proportional to the (negative) scalar product of unit normals to adjacent triangles. Self-avoiding interactions are not included. The largest hexagon considered (L=19) consists of 271 atoms. Unlike linear polymers or liquid membranes, these surfaces undergo a remarkable finite-temperature crumpling transition, with a diverging specific heat. For small κ=κ’/$k_B$T, the surface is crumpled, and the radius of gyration $R_g$ grows as √lnL . For large κ we find that the surface remains flat, i.e., $R_g$∼L. Our results demonstrate the presence of a finite-temperature (second-order) crumpling transition, and provide a lower bound on a related transition in real self-avoiding membranes.

A simple model of aggregation is presented which is built from two distinct monomeric species, A and B, with bonding allowed only between unlike species. This model exhibits novel and unexpected kinetic behavior which depends crucially on whether the mass of the aggregate is odd or even. The kinetics of the even clusters can be accounted for within the framework of the single-species reaction scheme A+A→A, while the odd clusters can be described by the two-species reaction A+B→inert. Consequently, the upper critical dimension, $d_c$, for the kinetics of the even clusters is two, while $d_c$=4 for the odd clusters. Numerical simulations of this A-B model reveal unusual kinetic behavior, including novel dimension dependence below the upper critical dimension, nonuniversality, and a breakdown of scaling for the cluster-mass distribution. The underlying parity dependence of the A-B model leads us to introduce a simpler one-component aggregation model in which the reaction rates depend explicitly on the parity of the reacting clusters. The corresponding rate equations are studied and exact expressions for the exponents describing the decay rate of the aggregates are obtained. It is found that the kinetics of clusters of even and odd mass are, in general, quite different, and that the corresponding exponents are also generally nonuniversal. Furthermore, in two special cases, the complete solution to the rate equations can be obtained, and it is thus demonstrated that a conventional scaling description for the cluster-mass distribution breaks down.

The problem of the activation rate in overdamped (Smoluchowski) bistable oscillators subject to colored noise with correlation time τ is discussed in detail. We show that a nontrivial prescription (the so-called Hänggi’s ansatz) for truncating the τ expansion of the Fokker-Planck equation describing this class of processes can reproduce the results of both analog and digital simulations in the regime of large activation energies. Such a prescription predicts a τ dependence of the Arrhenius factor appearing in the determination of the relevant mean first-passage time but cannot be applied to reproduce the correct τ dependence of the prefactor which may be dominant in the regime of rather small activation energies. An improved expression for the mean first-passage time in a double-well potential coupled to a time-correlated thermal bath is obtained on generalizing Kramer’s theory of the activation rates accordingly. The new determination of the mean first-passage time is meant to bridge previous approximations only valid in the regime of either large or small activation energies.