We show that the quantum spectra of simple systems whose classical counterpart is of a mixed nature, i.e., partly regular with widespread chaos, manifest the effects of classical transport through imperfect barriers. The partial barriers are characterized by the flux crossing them. We derive the relationship between this flux and quantum Hamiltonian matrix elements. This in turn predicts new statistical fluctuations properties for the spectrum and partial localization of the wave functions. The example of two coupled quartic oscillators is given in detail.

On the basis of a renormalization group in the space of shapes, conformal mapping techniques, and numerical simulations, it is argued that noise-reduced and regular diffusion-limited aggregates on a lattice are in the same universality class. These models lead to the same asymptotic shape of fractal aggregates. This shape is a fixed point of a functional equation, realized by a conformal transformation.

We show for the first time that the asymmetry comparable to the weak anchorage in anisotropic interfacial interactions between two surface layers of liquid crystals can produce a novel electro-optic effect. The effect depends on the polarity of an external electric field E, but the corresponding phase shift has ${\mathit{E}}^2$ dependence. In a simple geometry with homogeneous boundary conditions, we demonstrate that this polar effect is directly proportional to the difference in the anchoring strengths, and estimate the difference between two aligning polymer layers.

In this Letter we study the behavior, versus temperature, of tracer diffusion in random materials, for example, amorphous solids. By using a combined approach, using the analytical continuous-time random-walk theory and Monte Carlo simulations, we are able to propose a possible explanation for the nearly Arrhenian behavior observed in most amorphous solids by a compensation between site and saddle disorder.

Two-dimensional Fermi-fluid heat-capacity results are presented for the first and second layers of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ adsorbed on graphite. The data exhibit anomalous behavior extending up to 50 mK and a sharp feature which is located at 3.2 mK independent of the areal density.

Assuming an entropic origin for phason elasticity in quasicrystals, we derive predictions for the temperature dependence of grain-boundary structure and free energy, the nature of the elastic instability in these systems, and the behavior of sound damping near the instability. We believe that these will provide decisive tests of the entropic model for quasicrystals.

We report the observation of a spatial quasiperiodicity in high-resolution electron-microscope images of the thermodynamically stable decagonal ${\mathrm{Al}}_{65}$${\mathrm{Cu}}_{15}$${\mathrm{Co}}_{20}$ quasicrystal. Well defined quasiperiods consistent with decagonal symmetry and x-ray-diffraction data have been found. The structure observed is inconsistent with conventional ideal Penrose tiling. There is strong evidence for an entropy stabilization mechanism.

A density-functional study of C, Si, and Ge metallic liquids is reported. Pair potentials are constructed from pseudopotentials which reproduce the Kohn-Sham densities. These lead to structure factors S(k) in good agreement with experiment, and with more elaborate Car-Parrinello calculations. It is predicted that liquid carbon has a single sp band, is highly conducting and strongly compressible, with a broad peak in S(k) located near the ‘‘hump’’ in the S(k) of l-Si.

Ab initio molecular-dynamics simulations were used to predict structures for beryllium clusters of two to twenty atoms. As a function of cluster size (N) the sp hybridization converges quickly to the bulk value by N=6. Clusters with N>7 grow two dimensionally through a mechanism of prism addition and rhombus capping, beginning a growth pattern which quickly leads to an hcp lattice fragment. By N=15 the structure contains an element quantitatively similar to the primitive cell of the bulk. Despite strong directional bonding, the relative stability distribution obeys the predictions of the electronic shell model.

The vibrational properties of ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$As alloys have been studied using large supercells to simulate the disorder and ab initio interatomic force constants. In agreement with recent experimental evidence, our results indicate that well defined GaAs-like and AlAs-like phonon dispersions exist for any concentration. Besides broadening phonon states with definite wave vector, alloying narrows the optic branches and lowers the longitudinal modes more than the transverse ones, thus reducing the LO-TO splitting. The acoustic bands are instead rather insensitive to the composition.

We consider here a 1D tight-binding model with two uncorrelated random site energies ${\mathrm{\epsilon }}_{\mathit{a}}$ and ${\mathrm{\epsilon }}_{\mathit{b}}$ and a constant nearest-neighbor matrix element V. We show that if one (or both) of the site energies is assigned at random to pairs of lattice sites (that is, two sites in succession), an initially localized particle can become delocalized. Its mean-square displacement at long times is shown to grow in time as ${\mathit{t}}^{3/2}$ provided that -2V<${\mathrm{\epsilon }}_{\mathit{a}}$-${\mathrm{\epsilon }}_{\mathit{b}}$<2V. Diffusion occurs if ${\mathrm{\epsilon }}_{\mathit{a}}$-${\mathrm{\epsilon }}_{\mathit{b}}$=±2V and localization otherwise. The dual of the random-dimer model is also shown to exhibit an absence of localization and is shown to be relevant to transmission resonances in Fibonacci lattices.

The shapes of self-avoiding continuum and lattice polygons of N monomers in a plane are studied using Monte Carlo simulations and exact enumeration. To model vesicles, a pressure increment Δp=${\mathit{p}}_{\mathrm{in}}$-${\mathit{p}}_{\mathrm{out}}$, is included. For N≫1 and Δp=0, the usual universal fractal shapes appear; but for Δp≠0, continuously variable fractal shapes are found controlled by the variable x∝Δ${\mathit{pN}}^{2\nu }$ where ν=1/${\mathit{D}}_{\mathit{F}}$=3/4. Thus, the ratio of principal radii of gyration Σ(x)=〈${\mathit{R}}_{\mathit{G},\mathrm{m}\mathrm{i}\mathrm{n}}^2$〉/〈${\mathit{R}}_{\mathit{G},\mathrm{m}\mathrm{a}\mathrm{x}}^2$〉 changes smoothly from Σ(+∞)=1, for circles, through Σ(0)≃0.39, to Σ(-∞)≃0.23, which corresponds to branched polymers.

Energy, number-density, and confinement-time properties of 1-keV/atom ${\mathrm{Al}}_{32}$ and ${\mathrm{Al}}_{63}$ cluster impacts on Al and Au targets have been investigated by molecular-dynamics simulation. Inertial confinement of the incoming clusters leads to number-density increases of ∼2 for very short time periods (<20 fs) in the primary impact zone. Simultaneous and near-simultaneous multiple collisions occasionally increase the potential energy of a particle to more than twice that allowed in isolated two-body collisions. Up to 12% of the kinetic energy of the incoming cluster is transferred to atoms which eject early in the collision cascade.

Measurements of the nonlinear refractive index of several semiconductors using beam-distortion methods and four-wave mixing show a strong systematic dispersion in the bound-electronic nonlinearity (electronic Kerr effect ${\mathit{n}}_2$) near the two-photon-absorption edge. This eventually turns from positive to negative at higher frequencies. We find that by using the two-photon-absorption spectrum as predicted by a two-parabolic-band model, we can predict the observed universal dispersion, scaling, and values of ${\mathit{n}}_2$ that range over 4 orders of magnitude and change sign, using a simple Kramers-Kronig analysis (i.e., relating the real and imaginary parts of the third-order susceptibility). The resulting scaling rule correctly predicts the value of ${\mathit{n}}_2$ for all the 26 different materials we have examined. This includes wide-gap dielectrics which have 3 to 4 orders of magnitude smaller values of ${\mathit{n}}_2$ than semiconductors.

Direct numerical measurement of the power spectrum of the number of particles on the lattice demonstrates in an example of probably broad physical relevance that 1/f behavior can arise due to self-organized criticality. Different versions of the model are studied in order to look for universality.

Using new methods to analyze Monte Carlo data, we have calculated the leading partition-function zero for Su(3) lattice gauge theory on various ${\mathit{L}}_{\mathit{t}}$${\mathit{L}}^3$ lattices. For ${\mathit{L}}_{\mathit{t}}$=4 lattices we find in the range L=4–16 the scaling behavior of a second-order transition with ν=0.468(6). However, for larger lattices (L=14–24), the scaling behavior is consistent with a first-order transition: ν=0.35(2). The first-order nature of the transition is further substantiated by the fact that the finite-size scaling analysis of the specific heat yields a nonvanishing infinite-volume latent heat.

Models of random surfaces defined by means of integrals over quaternion-real self-dual random matrices are solved exactly in a double-scaling limit. Coupled nonlinear ordinary differential equations are obtained for the specific heat, which takes the form r+w’, where r is the specific heat of the corresponding Hermitian-matrix model, and w satisfies a nonlinear differential equation depending on r. It is shown that the k=2 theory, which may describe a new phase of two-dimensional quantum gravity, is unitary. An alternative method of solution, based on a set of symplectically orthogonal polynomials, is indicated.

WE propose that the relative cross sections for the reaction processes ηp,η’p→ηp,η’p,${\mathit{K}}^{+}$Λ and ${\mathrm{\pi }}^{\mathrm{-}}$p→ηn,η’n, induced by pseudoscalar mesons on a proton target, provide a sensitive test for the presence of a strange-antistrange (ss¯) quark component in the nucleon’s wave function.

The onset of chaos is investigated for excited, rapidly rotating nuclei, utilizing a schematic two-body residual interaction added to the cranked Nilsson Hamiltonian. Dynamical effects at various degrees of mixing between regularity and chaos are studied in terms of fragmentation of the collective rotational strength. It is found that the onset of chaos is connected to a saturation of the average standard deviation of the rotational strength function. Still, the rotational-damping width may exhibit motional narrowing in the chaotic regime.

Partial decay schemes in the neutron-rich nuclei ${}_{}{}^{103}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{104}{}_{}{}^{}\mathrm{Zr}$ have been measured for the first time and rotational bands in ${}_{}{}^{100–102}{}_{}{}^{}\mathrm{Zr}$ have been extended to spins of up to 10ħ by observing prompt γ rays from the spontaneous fisson of ${}_{}{}^{248}{}_{}{}^{}\mathrm{Cm}$. These nuclei are among the most deformed known at low spin and excitation energy. The level structures in the odd-A nuclei show that the ${\mathit{h}}_{11/2}$ intruder orbital plays an important role in stabilizing the deformation in this region.