Density matrices that describe coherent, squeezed, and number eigenstate signals in thermal noise are presented and their properties discussed. The maximum information that these beams can transmit is calculated. A description of realistic instruments within the quantum theory of measurement, with the use of number eigenstates in thermal noise, is also presented.

The standard Glauber coherent states associated with a given boson or oscillator mode have a well-known decomposition in terms of the occupation-number eigenstates. In this paper we study a much more general class of quasicoherent states in which each term of this decomposition acquires its own extra phase factor. These new states are not minimum-uncertainty states, but we show that they may be represented as eigenstates of some new canonical annihilation operator which is obtained from the original one by an appropriate unitary transformation. By choosing particular sets of values for the phases which characterize the quasicoherent states, we show how we are thereby able to study, for example, the effects of (i) optical propagation through a nonlinear medium with an intensity-dependent refractive index, and (ii) phase incoherence caused by the stochasticity typical of an optical source. The quasicoherent states are shown to share many of the same coherence properties as the original Glauber states. Nevertheless, they exhibit a mixture of coherent and incoherent properties. This is particularly illustrated by the important practical example where the phase angles are randomized.

Quantum fluctuations for multiphoton transitions in driven optical systems are treated on the basis of a Fokker-Planck equation for the Wigner function. The equation is considered without adiabatic elimination of the atoms or the field. The linear stability is analyzed and time correlations are derived. A spectrum of transmitted light associated with vacuum Rabi splitting is obtained. The squeezing and antibunching effects in the atomic system and the field are discussed. This theory coincides with the adiabatic elimination theory for the case of both good- and bad-cavity limits.

The transition to temporal and then spatiotemporal chaos in a weakly ionized magnetoplasma system which supports nonlinear flute-type ionization-drift waves was studied. The system is similar to a reaction-diffusion system with additional drift-induced transverse spatial coupling. It follows a complex quasiperiodic route with strong nonlinear mode-mode competition, a narrow frequency-locking interval, and an unstable third independent frequency to temporal chaos. At the onset of the spatial chaos, the discrete spatiotemporal modes decrease down to the noise floor, the temporal correlation reduces more than ten times, and the correlation dimension jumps from less than 8 to greater than 12.

The phase separation of polymer blends with very large molecular weight far from the critical point is discussed, applying the stability problem of a thread. Far from the critical point the interfacial thickness is very narrow. Then different sorts of polymer molecules are not as entangled at the interface as like polymer molecules in the bulk. Thus the effective viscosity at the interfacial region is much smaller than in the bulk. Therefore the interface may easily slide against the shear stress. The instability of a liquid thread with interfacial sliding or interfacial friction is discussed. Then the most unstable mode is extracted to identify the growth rate of interconnected droplets under phase separation. The droplet radius R obeys the well-known growth law: R∝t for small R and large R, whereas it obeys a slower growth law R∝$t^c$ with values of the effective kinetic exponent c=0.7–0.8 in the intermediate droplet size. This is qualitatively in agreement with experimental observations by Hashimoto and co-workers. On the other hand, the wave number $k_m$ for which the thread is most unstable obeys the decay law $k_m$∝$t^{\mathrm{-}3/4}$ for small R, whereas it obeys the decay law $k_m$∝$t^{\mathrm{-}1}$ for large R. This means that there are two length scales showing the invalidity of the dynamical scaling within the framework of the present theory for small R.

A series of dilute tetramethoxysilicon gels was made in order to study the spatial correlations that arise from the presence of solvent. Light-scattering measurements from these gels show a fractal structure on length scales as large as 1 μm. The short-length-scale fractal dimension differs from that observed for the connectivity transition at the gel point, indicating a crossover in universality class. Quasielastic light scattering measurements on the incipient gel demonstrate a critical slowing down in the relaxation of concentration fluctuations, causing frozen inhomogeneities in the final gels. Finally, the growth at early times, where the clusters are smaller than the spatial correlation length of the final gel, is shown to be exponential in time, in accord with models of aggregation. It is concluded that a kinetic model of gelation is needed to describe the short-length-scale structures observed in these gels.

Nonequilibrium molecular dynamics (NEMD) experiments measuring the shearing forces within an atomic fluid undergoing a planar Couette flow [Hoover, Ann. Rev. Phys. Chem. 34, 103 (1983); Evans and Morriss, Comp. Phys. Rep. 1, 299 (1984)] are performed by the subtraction method [Ciccotti et al., J. Stat. Phys. 21, 1 (1979)] at sufficiently low velocity gradient in order to remain within the linear response regime. The resulting stress averaged over many hundreds of NEMD trajectories (segments) and the stress-stress time autocorrelation function evaluated along the available equilibrium trajectory (required for the subtraction method), which are formally related by linear response theory, are shown to yield compatible estimations of the shear viscosity. This confirms the correct limiting behavior of the effective shear viscosity evaluated by similar NEMD experiments at much larger gradients. At the fluid state point far from the melting line that we consider, no size dependence of the viscosity is observed in both types of experiments. A comparison of the efficiency of both methods is not straightforward, as we found that, for a fixed number of time steps, the error estimated on the viscosity is independent of the system size for the Green-Kubo formula but decreases as $N^{\mathrm{-}0.5}$ in the NEMD case.

Nonanalyticities in the generalized dimensions of fractal sets of physical interest are interpreted as phase transitions. We apply the thermodynamical formalism to the fractal set formed by the irrational winding parameter values of critical circle maps and introduce and investigate in detail several distinct fractal measures on this set. The thermodynamic functions associated with different measures are distinct: We discover that, in all cases that we study, they exhibit phase transitions. The numerical estimates of the Hausdorff dimension from various versions of the thermodynamical formalism and a variety of circle maps yield $D_H$=0.8701±0.0003 and are consistent with the conjectured universality of $D_H$.

The generalized-exchange local-spin-density-functional theory (LSD-GX) with self-interaction correction has been used to calculate the ionization potentials for the atoms (atomic number Z from 2 to 38) and the electron affinities for some selected atoms. The effects of the Coulomb correlation correction and relaxation on the ionization potential and electron affinity are discussed using the Stoll, Pavlidou, and Preuss [Theor. Chim. Acta 49, 143 (1978)] correlation-energy expression, and the Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] expression. The theoretical results are compared to experiment. The LSD-GX theory with VWN correlation correction is the best method for calculating ionization potentials and electron affinities for atoms.

The relationship between matrix-element correlations and level-spacing properties is analyzed for typical Hamiltonian systems by introducing both global and local statistical measures. Two-dimensional two-point correlation functions and higher-order traces for Hamiltonian matrices are introduced for abstracting global properties of matrix-element distributions. The global behavior of correlation patterns for Hamiltonian matrices is shown to be markedly different from that for δ-correlated random matrices, which suggests that the Wigner-type spacing characteristic is not a property specific of the standard random matrix but a property of a more general class of nonrandom matrices. A technique of site randomization for matrix elements is introduced for exploring the local property of matrix-element correlations. It is demonstrated that level-spacing distributions for a class of statistically most-realizable matrix element configurations, constructed by a local site randomization from a given Hamiltonian matrix, generally do not coincide with that for a matrix-element configuration of the original Hamiltonian matrix itself.

Exact solutions of the nonlinear Schrödinger equation ${\mathit{i}\mathit{\psi }}_{\mathrm{t}}$+Δψ=${\mathrm{a}}_0$ψ/B +$a_1$ψ‖ψ${\Vert }^2$+$a_2$ψ‖ψ${\Vert }^4$, for which initial conditions can be imposed on a cylinder, are presented. A symmetry group of the equation is used to reduce it to an ordinary differential equation which is then solved with the help of a singularity analysis. Solutions are obtained in terms of elementary functions, Jacobi elliptic functions, and Painlevé transcendents.

We consider steady Brownian motion in the infinite strip with boundaries at x=0,x=L, with the latter absorbing. Our specific interest is to obtain insight into how a prescribed ‘‘far away’’ density at x=0 is mapped onto the absorbing boundary. The diffusion equation description cannot address this problem; instead we utilize an approximate solution of the Fokker-Planck equation. The major result we obtain is qualitative—that there may exist points or regions along the boundary where absorption takes place to a greater (or lesser) extent than might be inferred from the given far away data. A specific example illustrating this point is included.

A theory of the smectic-C–nematic transition in three-dimensional liquid crystals is developed. Within an elastic Hamiltonian constructed from a Lifshitz point model, the corresponding dislocation-loop Hamiltonian is derived. Using a series of transformations and duality arguments, it is found that the elastic model with director fluctuations leads to a continuous transition to an orientationally ordered phase. Some discussions about dislocation-loop systems which are not accompanied by director fluctuations are given.

An exact solution to the nonlinear Bhatnagar-Gross-Krook kinetic equation representing heat transport in one direction is obtained. The velocity distribution function is given explicitly and illustrated for both small and large temperature gradients. The Chapman-Enskog expansion for this function is proved to be divergent but asymptotic. Also, the relationship of this solution to infinite hierarchies of moment equations is discussed. In the following paper this special solution is analyzed in the context of more physical boundary-value problems.

The concept of a Hilbert-class or ‘‘normal’’ solution in kinetic theory refers to one whose space and time dependence is determined entirely through the hydrodynamic variables. Such solutions are expected to apply sufficiently far from the boundaries. We investigate this concept quantitatively for the nonlinear Bhatnagar-Gross-Krook equation to describe a gas between two infinite parallel planes at different uniform temperatures. For sufficiently small average Knudsen numbers, spatial domains are identified for which a normal solution applies. It is shown that these conditions include states far from equilibrium, in the sense that deviations of the normal solution from the first Chapman-Enskog approximation can be large. The special exact solution of the preceding paper is found to be the normal solution in the limit of constant temperature gradient.

Cooling by evaporation from an isolated aggregate can be quite rapid. The possibility of bypassing phase transitions and thus of preparing interesting amorphous materials by this vector must then be considered. Evaporation from binary solutions is identified as an especially attractive mechanism for realizing this prospect.

For the special case in which the irrational winding number is the root of a cubic equation, we present numerical evidence for the validity of some form of residue criterion [Greene, J. Math. Phys. 20, 1182 (1979)]. This is a criterion for the breakup of Kol’mogorov-Arnol’d-Moser tori in two degrees of freedom. The cubic case is essential for future work on four-dimensional maps. While the residues do approach ∞ (respectively, 0) after (respectively, before) the breaking point, it is numerically very difficult to estimate a critical residue value $R_{\mathrm{cr}}$ for this cubic case (0.15≲$R_{\mathrm{cr}\lesssim 0.26}$). We do not find the usual ‘‘scaling’’ (Greene, ibid., and Mackay, Ph.D. thesis, Princeton University, 1982). For one particular cubic irrational, however, we have obtained a different form of scaling: At constant residue (≃0.25) the parameter values $k_n$ do accumulate on a critical value, $k_{\infty }$, for torus breakup like ‖$k_n$-$k_{n\mathrm{-}1}$‖ ∼‖$p_n$/$q_n$-$p_{n\mathrm{-}1}$/$q_{n\mathrm{-}1}$${\Vert }^{\xi }$ as n→∞, with a ‘‘new’’ scaling constant ξ≊0.72, where $p_n$/$q_n$ is the nth rational approximant in the continued-fraction expansion of the cubic irrational. For a quadratic irrational this scaling reduces to the usual power-law scaling ∼${\delta }^{\mathrm{-}n}$.

Continuous-time analog neural networks with symmetric connections will always converge to fixed points when the neurons have infinitely fast response, but can oscillate when a small time delay is present. Sustained oscillation resulting from time delay is relevant to hardware implementations of neural networks where delay due to the finite switching speed of amplifiers can be appreciable compared to the network relaxation time. We analyze the dynamics of continuous-time analog networks with delay, and show that there is a critical delay above which a symmetrically connected network will oscillate. Two different stability analyses are presented for low and high neuron gain. The results are useful as design criteria for building fast but stable electronic networks. We find that for some connection topologies, a delay much smaller than the relaxation time can lead to oscillation, whereas for other topologies, including associative memory networks, even long delays will not produce oscillation. The most oscillation-prone network configuration is the all-inhibitory network; in this configuration, the critical delay for oscillation is smaller than the network relaxation time by a factor of N, the size of the network. Theoretical results are compared with numerical simulations and with experiments performed on a small (eight neurons) electronic network with controllable delay.

By adopting hyperspheroidal coordinates, we obtain the hyper-radial adiabatic potential-energy curves with correct asymptotic energies for the ${\mathrm{HD}}^{+}$ molecular ion. Vibrational-rotational energies are also calculated for the lowest potential-energy curve.

The isotropic-symmetry-breaking bifurcations occurring in a class of liquid-crystal models describing particles with the symmetry of rectangular slabs are studied. The model free-energy functional employed is appropriate to both the mean-field treatment of anisotropic dispersion forces and the Onsager approximation for hard anisometric particles. The symmetry of the bifurcating solutions to the stationary-phase equations is classified in terms of the eigenvalues of the effective pair interaction. Explicit conditions are derived for systems exhibiting crossover behavior between rodlike and platelike ordering. The results are applied to the question of the existence of biaxial phases in systems of uniaxial particles, and to two models for nonaxially symmetric particles: the hard spheroplatelet fluid and the Straley model.