A closed quantum-mechanical system with a large number of degrees of freedom does not necessarily give time averages in agreement with the microcanonical distribution. For systems where the different degrees of freedom are uncoupled, situations are discussed that show a violation of the usual statistical-mechanical rules. By adding a finite but very small perturbation in the form of a random matrix, it is shown that the results of quantum statistical mechanics are recovered. Expectation values in energy eigenstates for this perturbed system are also discussed, and deviations from the microcanonical result are shown to become exponentially small in the number of degrees of freedom.

It is shown that the well-known Onsager paradox of negative temperature of point vortices can be resolved by adopting a proper formula for entropy. We also provide an interpretation of vortex temperature in terms of the geometry of vortex trajectories.

We have extended the simulations on various models of avalanches to three and four dimensions. We have found that multifractal scaling fits to the measured distribution functions are frequently superior to those given by finite-size scaling. Nevertheless, finite-size scaling does work quite well for the small- and intermediate-size events, and seems to fail predominantly for the events of largest size. The critical exponents determined from the finite-size scaling fits are consistent with a renormalization-group calculation in four dimensions, but indicate the possible importance of logarithmic corrections.

We simulate bond-diluted self-avoiding tethered membranes of linear size L=7 to 41. For any p>${\mathit{p}}_{\mathit{c}}$ we find only the flat phase. The three eigenvalues of the inertia tensor (${\lambda }_3$ the largest, ${\lambda }_1$ the smallest eigenvalue) scale with system size according to ${\lambda }_{\mathit{j}}$∼${\mathit{L}}_{\mathit{j}}^{2\nu }$ with ${\nu }_3$(p)=${\nu }_2$(p)=1.0 and ${\nu }_1$(p)≊2/3 for all p>${\mathit{p}}_{\mathit{c}}$. Our data indicate that at the percolation concentration the system is isotropically crumpled with fractal dimension indistinguishable from the Flory prediction. The crossover between the isotropically crumpled and flat fixed point is also studied.

The near-equilibrium nature of dynamic linear response when a system is acted upon by an external force is clarified by using the linearity condition to identify a limited class of near-equilibrium density matrices that characterize the response. The analysis incorporates a distinction between undriven and driven time dependences. Irreversibility is introduced in a traditional way by means of a nonunitary component in the evolution of the undriven dynamics.

It is shown how the known result for the viscosity cross section ${\mathit{Q}}^{\mathrm{}\left(2\right)\mathrm{}}$ can be extended to the unknown general cross sections ${\mathit{Q}}^{\left(\mathit{n}\right)}$ without repeating the complicated asymptotic analysis.

The freezing of a two-dimensional binary hard-disk (BHD) liquid is investigated using an alternative density-functional approach. Our calculation indicates that within disk diameter ratios 0.8<α<1, a BHD liquid freezes into a substitutionally disordered triangular lattice via a weak first-order transition, in contrast to the hexatic phase (for 0.8<α<0.9) predicted from a computer-generated random-packing model. the BHD liquid also does not show the eutectic phase diagram found for binary hard spheres in three dimensions, but only spindle or azeotrope phase diagrams.

We discuss quantum scattering in systems in which a long-living chaotic quasistationary state is excited and show that the existence of this state leads to fluctuations in the cross section, which have a Porter-Thomas distribution.

We analyze the problem of diffusion in a one-dimensional random multiplying medium. We consider the case of a Gaussian δ-correlated field. Exact bounds, valid for any time, are obtained for the averaged concentration. Results of simulations are explained by considering the contribution of random-walk realizations with small spans.

The phase dynamics of Taylor vortex flow close to onset was studied by applying a forced modulation to the upper boundary of a large-aspect-ratio concentric-cylinder system. Our experimental results show that the phase disturbances progress diffusively along the Taylor vortices in the axial direction. Values of the diffusion coefficients obtained experimentally are compared with those found in numerical computations. We also confirm the dependence of the diffusion coefficient on the wave vector of the Taylor vortices predicted by the general theoretical model of Pomeau and Manneville [J. Phys. (Paris) Lett. 40, L609 (1979)].

The general n-point distribution function ${\mathit{H}}_{\mathit{n}}$ characterizes the microstructure of disordered composite and porous media, liquids, and amorphous solids. In this Rapid Communication we obtain an exact analytical representation of ${\mathit{H}}_{\mathit{n}}$ for inhomogeneous ensembles of d-dimensional spheres with a polydispersivity in size. Polydispersivity constitutes a fundamental aspect of the structure of random systems of particles.

Shape deformation of the gas-liquid interface of liquid oxygen condensed in a glass tube in high magnetic fields is investigated by taking photos. It is found that there is a simple relationship between the deformation of the gas-liquid interface and the square of the applied magnetic field in a range of 0–∼2 T, and that the shape of the interface changes tremendously from an ellipsoid into a sharp-pointed form with an increase in the field strength, breaking the linear relation. Regarding these experimental results, we carry out a discussion based on the phenomenological theory of a magnetic fluid.

A general statistical mechanical analysis is presented for networks of graded-response neurons whose dynamics is described by a system of differential RC-charging equations. The analysis requires that the dynamics is governed by a Lyapunov function, a condition that is met for networks whose synaptic matrix is symmetric, and whose neurons have monotonically increasing input-output relations may be arbitrary. In particular, they may vary from neuron to neuron. As examples, we study networks with synaptic couplings as in the Hopfield model: two homogeneous networks consisting of neurons with a sigmoidal or a piecewise linear input-output characteristics. Apart from this, the input-output relation, and a network containing a random mixture of these two neuron types.

The wave function of a particle escaping from a barrier, in general, would have its quasinormal modes, which decay like exp(-γt/2), dominated by anomalous ${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$ terms at asymptotically late times. One implication of the existence of these anomalous terms is that the wave function cannot be expressed as a sum of quasinormal modes. We show that these anomalous terms are related to classical motion linking the initial point (x’,t=0) to the final point (x,t). We then show that when the potential is unbounded from below, such terms do not appear, and more importantly, for such potential, the time development of a wave function initially concentrated in the finite region can be expressed in terms of a summation over quasinormal modes.

The radiation reaction due to magnetic dipole radiation is calculated for a charged-particle system whose magnetic moment changes with time. The explicit expressions for the electric and magnetic fields due to the magnetic dipole radiation reaction are derived, they are found to originate in the fourth-order term in the expansion of the retarded potential, whereas the field due to the electric dipole radiation reaction originates in the second-order term.

A new type of diffraction effect, different from the standard semiclassical ones (rainbow, glory, forward peak, orbiting), takes place near the critical angle for total reflection at a curved interface between two homogeneous media. A theoretical treatment of this new effect is given for Mie scattering, e.g., light scattering by an air bubble in water; it can readily be extended to more general curved interface problems in a variety of different fields (quantum mechanics, acoustics, seismic waves). The relatively slowly varying Mie diffraction pattern associated with near-critical scattering is obscured by rapid fine-structure oscillations due to interference with unrelated ‘‘far-side’’ contributions. These contributions are evaluated and subtracted from the Mie amplitudes to yield the relevant ‘‘near-side’’ effects. A zero-order transitional complex angular momentum (CAM) approximation to the near-side amplitude is developed. The most important contributions arise from partial and total reflection, represented by two new diffraction integrals, designated Fresnel-Fock and Pearcey-Fock, respectively. The total reflection contribution is strongly affected by tunneling, giving rise to a generalized version of the Goos-Hänchen shift. In terms of short-wavelength asymptotic methodology, in a generalized Huygens-Fresnel-type integral representation, the new diffraction features arise from nonanalyticity of the integrand amplitude function within the range of a saddle point. Also discussed are the WKB approximation, a known physical-optics approximation, and a modified version of this approximation: they are compared with the ‘‘exact’’ near-side Mie amplitude obtained by numerical partial-wave summation, at scatterer size parameters (circumference divided by wavelength) ranging from 1000 to 10 000. It is found that the physical-optics approximations lead to large errors in the near-critical region, whereas the zero-order CAM approximation is in good agreement with the exact solution, accounting for the new diffraction effects in near-critical scattering.

Concerns have been raised over the possibility that extremely-low-frequency (ELF) electromagnetic fields are carcinogenic and leukegenic. An examination of the physical interaction of such fields with the body shows that such interactions are too weak to have a significant effect on human biology at the cell level. Because of the high electrical conductivity of tissues, the coupling of external electric fields in air to tissue in the body is such that the effects of the internal fields on cells is smaller than thermal noise. Static magnetic fields smaller than the earth’s field of 50 μT and varying fields weaker than the 4-μT 60-Hz fields that are equivalent in effect to that from walking in the earth’s field, cannot be expected to generate significant biological effects. Moreover, the interactions of such weak fields at the cell level are also small compared to thermal noise. These conclusions would be modified by 60-Hz cell resonances. But such resonances are shown to be incompatible with cell characteristics and the requirement from equipartition that the mean resonance energy must be kT. Hence, any biological effects of weak ELF fields on the cellular level must be found outside of the scope of conventional physics.

The modified self-consistent phonon approximation is generalized to calculate the critical temperature of a DNA double helix with block inserts of different base pair sequences. An iterative method based entirely on the Green’s function is developed to compute efficiently the self-consistent anharmonic force constants and thermal mean-squared vibrational amplitudes in hydrogen bonds. The calculation is carried out for a long guanine-cytosine (G-C) type helix with an insert of d(A${)}_4$-d(T${)}_4$. The melting-associated behavior is predicted to initiate in major groove bonds in the inserted adenine-thymine (A-T) base pairs at 349 K. This temperature is above the mean-field melting temperature of poly(dA)-poly(dT) due to stabilization of the A-T bonds by the G-C helix and below the mean-field melting temperature of poly(dG)-poly(dC), where dA refers to repeating ade- nine bases on one strand and dT the repeating thymine bases on the other strand.

We study the dynamical behavior in the eye lens of a chicken inflicted with a cataract induced by a salt solution. The mean diffusion coefficient D¯ in the cataracted lens estimated in this work is approximately expressed by a power law as a function of the salt concentration of ‖C-${\mathit{C}}^{\mathrm{*}}$‖. Our experimental findings suggest that the salt concentration should be a relevant parameter for describing the dynamical behavior in a cataracted lens. The magnitude of D¯ obtained for the cataracted lens is approximately five times smaller than that for the normal one, which is almost compatible with the earlier work of Tanaka and Benedek [Invest. Ophthalmol. 14, 449 (1975)]. The diffusive decay in the salt-induced cataract, which should be regarded as an osmotic type of cataract, has been discussed in terms of the phase separation associated with the lens opacification following the concept of Tanaka, Ishimoto, and Chylack [Science 197, 1010 (1977)].

The dynamics of a probabilistic neural network is characterized by the distribution ν(x’‖x) of successor states x’ of an arbitrary state x of the network. A prescribed memory or behavior pattern is represented in terms of an ordered sequence of network states ${\mathit{x}}^{\mathrm{}\left(1\right)\mathrm{}}$,${\mathit{x}}^{\mathrm{}\left(2\right)\mathrm{}}$,...,${\mathit{x}}^{\left(\mathit{l}\right)}$. A successful procedure for learning this pattern must modify the neuronal interactions in such a way that the dynamical successor of ${\mathit{x}}^{\left(\mathit{s}\right)}$ is likely to be ${\mathit{x}}^{(\mathit{s}+1)}$, with ${\mathit{x}}^{(\mathit{l}+1)}$=${\mathit{x}}^{\mathrm{}\left(1\right)\mathrm{}}$. The relative entropy G of the probability distribution ${\mathrm{\delta }}_{\mathit{x}}^{(\mathit{s}+1)}$,x’ concentrated at the desired successor state, evaluated with respect to the dynamical distribution ν(x’‖${\mathit{x}}^{\left(\mathit{s}\right)}$), is used to quantify this criterion, by providing a measure of the distance between actual and ideal probability distributions. Minimization of G subject to appropriate resource constraints leads to ‘‘optimal’’ learning rules for pairwise and higher-order neuronal interactions. The degree to which optimality is approached by simple learning rules in current use is considered, and it is found, in particular, that the algorithm adopted in the Hopfield model is more effective in minimizing G than the original Hebb law.