We present the first results of experiments that measure the intensity of light scattered by capillary waves on the surface of free-standing liquid-crystalline thin films. The intensity of the scattered light provides information about the surface tension of the liquid-air interfaces and, more interestingly, about the interactions between the surfaces as a function of the film thickness. Light scattering experiments performed on 4-n-octyl-4’-cyanobiphenyl (8CB) in the nematic phase show the sudden onset of a strong interaction between the interfaces when the film thickness is decreased. The range of this interaction increases with decreasing temperature. The suppression of the out-of-phase capillary waves coincides with the point where the range of surface-induced smectic ordering becomes comparable to the film thickness. We argue that these experiments probe the growth of the interlayer elasticity modulus B. .AE

The recently introduced Gaussian ensemble involves a sample (of size N) thermally connected to a finite heat bath (of size N’) with specific properties. Treating N’ as a parameter, we use a leading-order analysis of the β (inverse temperature) -versus-E (energy of sample) curves to show how static properties of finite samples become ensemble dependent. Inflection points in β(E) at phase transitions, however, appear as nontrivial fixed points with respect to N’ and are defined as the transition temperature of the sample. By developing a fluctuation relation for the heat capacity C we show that, for small N’, states with C<0 are accessible at first-order transitions resulting in van der Waals loops in β(E). Monte Carlo studies of phase transitions in Potts models on two- and three-dimensional lattices confirm the finite-N’ and finite-N effects. We find that the method significantly reduces computer time (sometimes by a factor of 100) compared with canonical-ensemble simulations and is effective in diagnosing the order of phase transition. Specific-heat data at second-order transitions reveal a new phenomenon; the peak in C sharpens as N’ becomes smaller, leading us to speculate on sharp transitions in finite samples.

The dynamics of a one-dimensional harmonic chain in the presence of a strong, incommensurate, sinusoidal potential and a uniform force F is investigated numerically. A threshold force $F_T$ exists above which steady-state motion occurs. Near threshold, the linear and nonlinear responses of the system exhibit nontrivial critical behavior. Critical exponents describing the transition to a moving state are calculated, and scaling relations between them are conjectured.

Combining Kramers’s energy diffusion (at temperature T ) with dissipative quantum tunneling (through a parabolic potential-energy barrier with curvature frequency ${\omega }_b$ and height $U_b$), a model for a localized metastable state (with harmonic frequency ${\omega }_0$) is formulated and solved exactly for its quasiequilibrium distribution ρ(E) and its decay rate Γ. It is shown that ρ remains locally extremely close to (although it essentially differs from) the Boltzmann distribution, unless the Ohmic friction coefficient λ is extremely small (of order Γ). Excluding this latter possibility, the ensuing decay rate is discussed for various temperature and friction regimes. It is shown to comprise several known results as special cases. First, an extended version of Bell’s formula is shown to be valid in the strong-to-moderate friction regime. It involves the recently discovered crossover between thermal hopping and quantum tunneling at temperature $T_0$=ħκ${\omega }_b$/2π$k_B$ (where κ is Kramers’s viscosity correction factor). At high temperatures and very strong damping the result neatly reduces to Kramers’s Smoluchovsky-limit formula. At zero temperature friction strongly suppresses the decay. Second, in the very weak friction regime Γ is shown to reduce to an extended version of Melnikov’s formula. At high temperatures it equals Kramers’s small-viscosity result, whereas at zero temperature and zero damping it attains the expected quantum value, the crossover again being at $T_0$. Third, in the classical limit (ħ→0) an extended version of Büttiker, Harris, and Landauer’s [Phys. Rev. B 28, 1268 (1983)] result is recovered, now valid for any value of the damping. Finally, some remarks are made in relation to recent cryogenic measurements on metastable flux states.

There is a strong feeling among many researchers that certain physical phenomena are fractal in nature. The difficulty, in any given case, is to make precise what one means when one says that something is fractal. An example might help. The Cantor middle third set, discussed in detail here, is a fractal in the sense that its Hausdorff (now often called the fractal) dimension is between zero and 1; it is ln2/ln3, in fact. Now the spectral lines of the hydrogen atom seem to be fractal also, just from a casual observation of the self-similar nature of the various series. They certainly do not have all the properties of the Cantor set and so, we may well ask, in what sense are they fractal? The purpose of this paper is to give one answer to this question.

The storage and retrieval of complex sequences, with bifurcation points, for instance, in fully connected networks of formal neurons, is investigated. We present a model which involves the transmission of informations undergoing various delays from all neurons to one neuron, through synaptic connections, possibly of high order. Assuming parallel dynamics, an exact solution is proposed; it allows one to store without errors a number of elementary transitions which are of the order of the number of synaptic connections related to one neuron. A fast-learning algorithm, requiring a single presentation of the prototype sequences, is derived; it guarantees the exact storage of the transitions. It is shown that local learning procedures with repeated presentations, used for pattern storage, can be generalized to sequence storage.

The sedimentation process is simulated, for the first time, using a discrete model in which gravitation and Brownian motion are considered as competitive processes. This model is capable of producing the whole spectrum of particle-settling behaviors by varying $R_{\mathrm{GB}}$, a relative measure of the gravitation to the Brownian motion. Computer-simulation results are obtained for polydispersed as well as monodispersed systems and for coarse as well as for fine particles.

The general epidemic process, which is a stochastic multiparticle process belonging to the universality class of dynamic percolation, is studied in a semi-infinite geometry. Critical exponents characterizing the fractal properties are calculated to O(ε) (ε=6-d, where d is the spatial dimension) with use of renormalization-group techniques.

The statistical-mechanical theory of inhomogeneous systems is used to derive the grand-potential functional of coexisting isotropic and nematic phases. We employ this result to discuss the isotropic-nematic interface of hard spherocylinders in the square-gradient approximation. Our calculated surface tension is about 40% less than an upper bound derived from a previous, but drastically different, treatment of the interface. The interfacial region is rather narrow and the director of the nematic phase lies parallel to the interface. We compare the formalism to recent experimental studies of the director orientation of nCB’s [4-cyano-4’-(n-alkyl)biphenyl], the phenomenological theory of the interface, and postulate the existence of an interfacial polar order parameter. The theory suggests that polar ordering in the interfacial region can cause the director to assume tilt angles between 0° and 90° even at the square-gradient level.

A generalization of the diffusion-limited-aggregation model is introduced to take into account the effect of the velocity of the moving interface. The growth process is governed by the diffusion field with a convection induced by the growing interface. In the limit of a slow-moving interface, the convection is approximated to be proportional to the local mass flow with changing sign. The convective diffusion field is simulated by the biased-random walker. The development of the distinct morphologies is found with varying strength of the growing interface. The velocity of the moving interface is governed by the dimensionless parameter χ=(${\rho }_g$/${\rho }_a$)ΔC, where ${\rho }_a$ is the density of the aggregate, ${\rho }_g$ the density of the diffusing particles in the diffusion field, and ΔC the concentration difference between the aggregate and the outer boundary. With the increase of χ, the aggregate crosses over to the dense aggregation with the flat interface. The moving interface acts as a stabilizing force on the interface. In the case of a negative χ, the aggregate crosses over to the needle crystal. The growing interface acts as a destabilizing force. The similarities with the pattern formation in the electrochemical deposition and solidification are discussed.

A method introduced by Davydov for modeling energy transport in deformable molecular chains is considered, using for the ansatz function a superposition of tensor products of single-exciton and coherent-phonon states. Treating the time-dependent parameters of the function (exciton and phonon amplitudes) as generalized coordinates, we have shown that the corresponding Euler-Lagrange equations are consistent with the averaged quantum equations, although the ansatz function does not satisfy the Schrödinger equation. For the case of the immobile-exciton limit (in which the quantum-mechanical problem is exactly solvable), it is shown that the ansatz function satisfies the Schrödinger equation, so all predictions based on Davydov’s method are identical to the corresponding exact results (for this particular case).

The soliton states suggested by Davydov as approximate solutions to the Schrödinger equation for one-dimensional systems are examined from the standpoint of the variational principle. We show that the correct equations of motion are, in general, different from those proposed by Davydov. In addition, we comment on the time evolution of these states.

For a quantum system we consider the evolution induced through a Hamiltonian H(R) by an arbitrary closed curve in the space of parameters R. By a proper choice of the basis in the Hilbert space of states, it is shown that one can associate a geometrical phase to each eigenvector of the Hamiltonian. The special cases of adiabatic and cyclic evolution of the state vector are discussed.

A ladder-operator technique for generating isospectral Hamiltonians is presented. The most attractive feature of the scheme is that the results are obtained without any specific realization of the ladder operators. The method is applied to the N-dimensional Coulomb and isotropic oscillator problems. Few new results are presented in addition to those obtained using supersymmetric quantum mechanics.

Both single and double ionization of helium by projectiles of charge q ranging up to 50 are considered at collision velocities corresponding to 1.4 MeV/amu within the independent-electron approximation. A simple calculation using a unitarized semiclassical Coulomb approximation probability is sufficient to provide agreement with the charge dependence of observed total cross sections.

Some lower-lying S-wave resonances in positron-hydrogen scattering associated with the N=3 positronium (Ps) and N=4 hydrogen thresholds are investigated by using the method of complex-coordinate rotation. Using Hylleraas-type wave functions with M=969 terms, several resonances in these energy regions are calculated for the first time. In particular, the lowest resonance associated with the Ps(N=3) threshold is found to lie at E=-0.077 063 Ry, and the lowest resonance associated with the H(N=4) threshold is found to lie at E=-0.067 867 Ry. In addition, we also locate a shape resonance lying just above the Ps(N=3) threshold at E=-0.055 44 Ry.

Elastic scattering of electrons from positronium (Ps) in the ɛ<5.105 eV energy region is considered. The calculations have been done on the basis of the adiabatic method, where this three-body problem reduces to multichannel scattering theory. Our results unambiguously establish the existence of an s-wave resonance at ${\varepsilon }_r$≊0.6 eV.

Dielectronic recombination rate coefficients have been calculated for He-like ions with atomic numbers Z=5, 6, 7, 8, and 9. The calculations include the influence of the Coster-Kronig channels to the excited states of the recombining ion on the rate coefficients. The detailed Auger and radiative rates were calculated using the multiconfiguration Dirac-Fock model in intermediate coupling with configuration interaction. The total dielectronic recombination coefficients for ${\mathrm{B}}^{3+}$, ${\mathrm{N}}^{5+}$, and ${\mathrm{F}}^{7+}$ ions have been found to reduce by 60%, 13%, and 4%, respectively, due to the inclusion of Coster-Kronig channels. For the ${\mathrm{B}}^{3+}$ ion, the dielectronic recombination coefficient from the present work is smaller than the value derived from the Burgess-Merts formula by a factor of 3 at electronic temperature T=100 eV.

We predict a new type of time-resolved cooperative fluorescence (CF) obtainable when a homonuclear alkali-metal diatom dissociating via a ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{\mathrm{*}}{}_{}{}^{}$ state evolves (by nonadiabatic radial coupling) into a superposition of two excited adiabatic states correlated to different doublet levels. CF intensity then combines ‘‘ringing’’ oscillations, caused by time variation of the interference phase between the receding emitting atoms, with quantum beats associated with fine-structure splitting. The calculated CF patterns for ${\mathrm{Li}}_2$ are sensitive to the amplitudes and relative phase of the two superposed adiabatic states.

We show how our previous results [Phys. Rev. A 35, 3291 (1987)] can be used to obtain perturbative and nonperturbative results on the width of the autoionization state coupled to a nearby state via a dc field.