We establish the mapping of the master equation for classical motion in random media to a quantum system, describing the motion of a quantum particle in a random potential. Invoking dynamic scaling, the mapping connects the time-dependent mean square displacement of classical motion with the density of states in terms of the classical correlation length. These connections are illustrated for a model with exactly solvable diffusion properties, confirming dynamic scaling. The numerical results for the quantum counterpart reveal energy-dependent localization in terms of the real part of the Lyapunov exponent, which is proportional to the inverse localization length.

An experiment carried out by Kreuzer in 1968 can be interpreted as setting an upper limit on the strength of any intermediate-range coupling to baryon number. The upper limit is one-half the strength obtained by Fischbach et al. in their reanalysis of the Eötvös experiment. The two results are consistent within 2 standard deviations if what Kreuzer calls an "upper bound" is a $1\sigma$ limit.

It is shown that Eötvös-type torsion-balance experiments performed in the vicinity of a large cliff may be used as sensitive tests for the recently postulated existence of a medium-range hypercharge force. The residual nonzero effect found in the original Eötvös results could be mainly due to terrain irregularities and thus be larger than, but still correlated to, the effects expected from the Earth's rotation and the hypercharge hypothesis.

Other experiments testing the suggested new vectorial interaction of subgravitational strength and the possible theoretical interpretations of this interaction are discussed.

A one-dimensional kinetic Ising model, with hierarchical couplings, is solved. We find algebraic relaxation of the magnetization, with a temperature-dependent exponent, and breakdown of dynamic scaling. The nonlinear relaxation time diverges with the system size below a dynamic transition temperature. Possible relevance to dilute Ising systems at percolation is discussed.

We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta. From these, generalized Bethe-Ansatz and functional-integration methods using action-angle variables follow. Results for free energies coincide, and coincide with those that we find by transfer-integral methods. Extension to the quantum case, and quantum Bethe Ansatz, on the lines to be reported elsewhere for the sinh-Gordon equation, is indicated.

We present a solution for the dynamics of an anharmonic oscillator coupled to a zero-temperature heat bath. Comparison of observable properties in a classical and quantum description uses true joint phase-space probability densities. The time evolution of the density in the quantum case is rapidly "reduced" to that given in the classical description. The rate of reduction is proportional to the product of the damping rate and the oscillator's initial energy. Quite rapidly, typical quantum recurrence effects are destroyed and the classical "whorl" structure restored. We point out the close similarity with rapid destruction of quantum coherence through dissipation.

A model of diffusion $\psi (\mathrm{x},t)=\Delta \psi (\mathrm{x},t)+V\left(\mathrm{x}\right)\psi (\mathrm{x},t)$ is studied, where $V\left(\mathrm{x}\right)$ is the Gaussian random potential. It is found that the probability distribution function is concentrated (localized) at some metastable potential attractor, while the localization center hops discontinuously in search of a better metastable attractor. The sample-averaged localization-center displacement is found as ${\chi }_c\sim \frac{t}{2\ln t}$, i.e., it is sub-ballistic.

When a parameter in the Hamiltonian of a one-degree-of-freedom oscillator is slowly varied at rate $\epsilon$, an adiabatic invariant exists which is conserved to all orders in $\epsilon$, except on phase-space orbits which cross a separatrix. In the present work, the change in the adiabatic invariant due to a separatrix crossing is given to order $\epsilon$ for a wide class of Hamiltonian systems. This result is applied to the special case of a charged particle moving under the influence of an electrostatic wave with slowly varying amplitude and frequency.

We sketch the proof of an existence theorem for a time-dependent density-functional theory on the set of $N$-representable densities, extending the constrained-search formulation of Levy into the time-dependent domain, and add a brief comment on practical issues.

We present a new Monte Carlo algorithm for self-avoiding surfaces in a grand canonical ensemble. The topology of the surfaces is kept planar but the boundary is allowed to fluctuate during the simulation. The measured critical exponents $\nu =0.504\mathrm{}\pm 0.016$, $\theta =1.48\mathrm{}\pm 0.17$ indicate that this model belongs to the universality class of branched polymers in three dimensions.

A general relationship is established between wave-packet evolution and quantization in classically integrable systems. Because of wave-packet spreading, one cannot simply take the Fourier transform of the time evolution of a wave packet. Instead, one must propagate the wave packet using the actions as Hamiltonians. The energy eigenvalues which result are the Einstein-Brillouin-Keller values, and new forms for the eigenfunctions appear. These are free of caustic singularities, and represent averages of wave packets over the invariant torus.

A sufficient condition for the quantum entropy, $-\mathrm{Tr}\left(\rho \ln \rho \right)$, to be nondecreasing under a tracepreserving positive linear map is that the "totally random" state, $\rho \propto 1$, be stationary. It is argued that this condition will be satisfied by the quantum system consisting of the region external to one or more black holes. This would explain why a "generalized second law of thermodynamics" appears to hold in the presence of black holes.

Under a certain assumption (which is satisfied whenever there is a dense infinite cluster in the half-space), we prove a differential inequality for the infinite-cluster density, $P_{\infty }\mathrm{}\left(p\right)\mathrm{}$, in Bernoulli percolation. The principal implication of this result is that if $P_{\infty }\mathrm{}\left(p\right)\mathrm{}$ vanishes with critical exponent $\beta$, then $\beta$ obeys the mean-field bound $\beta <~1$. As a corollary, we also derive an inequality relating the backbone density, the truncated susceptibility, and the infinite-cluster density.

Breakdown of time-reversal invariance can be detected in macroscopic samples as a magnetic alignment along an electric field. We show that both fundamental and practical limits to the detection of this effect in paramagnets correspond to measurement of electron electric dipole moments down to $d_e\sim {10}^{-28\mathrm{}}e·\mathrm{cm}$ on 50-g quantities of EuS near its Curie point; this compares to the current limit of $d_e<~{10}^{-24\mathrm{}}e·\mathrm{cm}$. Strategies for still greater sensitivity are outlined.

It is shown that there is a correspondence between the supersymmetric sine-Gordon theory in the vicinity of ${\beta }^2=4\mathrm{}\pi$ and an anisotropic $N=3\mathrm{}$ Ashkin-Teller model. Thus the latter model displays a line of first-order transition which turns into a line of continuous transition with varying critical exponents via a multicritical point of the Kosterlitz-Thouless type.

The location of a Hopf bifurcation in parameter space may be postponed or advanced by multiplicative colored noise depending on the interplay between the time scale of the noise and the rotation period of the phase variable.

A conventional fermion interferometer, in which the fermions enter only one of the two input ports, can achieve a phase sensitivity $\Delta \phi =\frac{1}{\sqrt{n}}$, where $n$ is the total number of fermions which have passed through the interferometer. Here it is shown that by injection of fermions into both input ports the phase sensitivity can approach $\frac{1}{n}$ provided that the fermions in the two input beams are suitably correlated.

A new approach to Preisach's hysteresis model, which emphasizes its phenomenological nature and mathematical generality, is briefly described. Then the theorem which gives the necessary and sufficient conditions for the representation of actual hysteresis nonlinearities by Preisach's model is proven. The significance of this theorem is that it establishes the limits of applicability of this model.

Instabilities in the electrical conductivity of barium sodium niobate crystals are studied with ac and dc fields. Phase portraits, Poincaré sections, and return maps are constructed from measured signals in the quasiperiodic state. We show that the dynamical behavior of the system can be modeled by a 1D circle map. Mode locking is observed in the system prior to the transition to chaos; the mode-locked intervals exhibit a devil's staircase behavior.