The general relativistic interaction of the electric field with the gravitational field may be observable in a charged-particle interferometer containing a suitable arrangement of fields. Observation of the effect in the earth's field would constitute a new laboratory test of the equivalence principle, involving $e$, $h$, $c$, and $g$. The magnitude of the phase shift induced can be comparable to the Colella-Overhauser-Werner phase shift, for electrons.

If heavy magnetic monopoles exist, then extreme magnetically charged black holes ($P^2=M^2$) with masses as small as 150${\left[\right({10}^{17}\mathrm{G}\mathrm{e}\mathrm{V})/\mathrm{\mu }]}^2$ g will be stable against evaporation over periods of ${10}^{10}$ yr or longer, where $\mu$ is the mass of the lightest monopole. It appears unlikely that such black holes exist in the present universe, but this conclusion depends strongly on the details of the first ${10}^{-24\mathrm{}}$ sec of the universe. Such long-lived small holes will exist in the late universe if there is at least 1 monopole per ${10}^{50}$${\left[\right({10}^{17}\mathrm{G}\mathrm{e}\mathrm{V})/\mathrm{\mu }]}^6$ baryons in the universe.

The equilibrium polymerization of chains and rings can be viewed as a bicritical point in a suitably augmented parameter space. The polymerization of chains in equilibrium with rings is described by the cross-over exponent, $\phi$, for quadratic anisotropy in the $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$ vector model with $n\to 1$. While the total mass fraction of polymerized material is described by the Ising exponent $\alpha$, the mass fraction of chains separately (and therefore also of rings) is described by the exponent ${\alpha }_c=\phi -1+\alpha$.

It is shown numerically that the stability intervals for limit cycles of the circle map form a complete devil's staircase at the onset of chaos. The complementary set to the stability intervals is a Cantor set of fractal dimension $D=0.87\mathrm{}$. This exponent is found to be universal for a large class of functions.

A method is proposed for the approximate numerical solution of operator field equations on a lattice.

Cooperative multiparticle quantum states in an Einstein-Podolsky-Rosen type of experiment are shown to violate a Bell inequality. Thus correlations can occur between wave packets each having $N$ bosons which cannot be explained within local hidden-variable theories. This provides a way to test quantum measurement theory for multiparticle states. In these states, a local, positive probability distribution exists for all $N$. However, the representation of correlations with this probability distribution is different from that in standard (Bell-type) hidden-variable theories.

A new algorithm for the simulation of statistical systems is presented. The procedure produces a random walk through configurations of a constant total energy. It is computationally simple and applicable to systems of both discrete and continuous variables.

A new master equation describing the irreversible process of a quantum mechanical Brownian particle is proposed. The master equation is shown to obey the symmetry of detailed balance leading to a quantum analog of the reciprocity relations, and the fluctuation-dissipation theorem is obtained. The method is applied to the damped harmonic oscillator. The relation to previous approaches is discussed.

A simple model showing a $\frac{1}{f}$ behavior is proposed. It is argued, on the basis of a scaling argument, that is has ${\left(\ln f\right)}^k$ corrections. Numerical simulations confirm this picture.

It is shown that a nonlinear Schrödinger soliton behaves stochastically with random phases in both time and space in the presence of small external oscillating fields and emits small-amplitude plane waves with random phases. Statistical properties of random phases give the energy spectra of the soliton and plane waves.

The feasibility of using Monte Carlo methods in finite fermion systems has been investigated. The basic tool is a (recently suggested) functional integral representation of $Z=\mathrm{tr}\left[\exp \right(-\beta II\left)\right]$ using real coherent states of Slater determinants. Conditions for using the discretized ($N$-point lattice) version as a starting point for Monte Carlo integrations are studied. The limit of large $\beta$ is achieved only with large $\surd N$. For a two-fermion system numerical calculations of the ground-state energy agree farily well with the exact value.

A novel interplay of coherent spatial structure and temporal chaos is reported for the acdriven, damped sine-Gordon system with breather initial conditions and periodic boundary conditions. The competing tendencies of spatial structures to be stable and of single-particle motions to be chaotic can lead to suppression of chaos, spatio-temporal intermillency, and symmetry-breaking tendencies. Dynamic structure factors provide direct evidence for spalial period halving and renormalized-phonon generation in chaotic regimes.

Sensitivity of a nonequilibrium chemical system to small symmetry-breaking influences is analyzed in the context of chiral-symmetry breaking. For a hypothetical model system, with realistic kinetic constants, a reaction energy barrier difference of $\frac{\Delta E}{\mathrm{kt}}={10}^{-17\mathrm{}}-{10}^{-15\mathrm{}}$ is shown to be sufficient to have a strong chiral selectivity. This is in the range of the estimated energy differences between right- and left-handed molecules due to weak neutral currents.

The metric is presented, in terms of six determinants of degree $N$, in a concise closed form, describing $N$ collinear isolated Kerr masses ($N=1, 2, 3, \dots$) balanced by their gravitational spin-spin interaction. Two hitherto unnoticed potentials $L$ and $M$ are introduced to evaluate the metric function $\omega$. The conditions for regularity of the metric on the symmetrical axis are presented.

Recent efforts to estimate the number of modes sufficient for the approximate solutions of Navier-Stokes equations in two dimensions are summarized. Several such estimates have been obtained, and their relations to one another are discussed. The physical significance of the results is noted and used to infer the possible nature of similar estimates in three dimensions.

A new type of bifurcation to chaos is pointed out and discussed. In this bifurcation two unstable fixed points or periodic orbits are created simultaneously with a strange attractor which has a fractal basin boundary. Chaotic transients associated with the coalescence of the unstable-unstable pair are shown to be extraordinarily long-lived.

The $S$-matrix scheme allows a straightforward formalization of the Einstein-Podolsky-Rosen nonseparability either of distant measurements issuing from a common preparation, or of distant preparations converging into a common measurement. This implies Lorentz and $\mathrm{CPT}$ invariance of the causality concept at the elementary level, which is a quantal and relativistic extension of the 1876 Loschmidt reversibility statement.

A nonlinear oscillator externally driven by an impulsive periodic force is investigated. An exact analytical expression is obtained for the stoboscopic or Poincaré map for all values of parameters. The model displays period-doubling sequences and chaotic behavior. The convergence rate of these cascades is in very good agreement with Feingenbaum theory.

Both bound and scattering states of the Pöschl-Teller potential are shown to be connected with unitary representations of certain groups. A family of periodic potentials, and their associated transfer matrices and band structure, can also be obtained from group theory and reduce to the above potential when the real period approaches infinity. These results suggest that the algebraic approach used for treating bound-state problems can be extended to scattering and band-structure problems.

It is shown that the Ashkin-Teller model has self-triality, which is a generalization of Kramers-Wannier self-duality proposed some time ago and illustrated with examples. In the Hamiltonian formalism, it means that the original Hamiltonian may be reexpressed in terms of either of two disorder variables without change of form and that the relation between all three variables is fully symmetric.