A quantum Kolmogorov-Arnol'd-Moser-like theorem is formulated with use of an existence condition of a unique transformation between eigenstates of integrable and nonintegrable Hamiltonians. This condition determines the ability to assign local quantum numbers to eigenstates of nonintegrable Hamiltonians and explains localization phenomena.

A statistical model of interacting linear domain walls (occurring, e.g., in monolayer adsorbates) is solved on the square lattice with use of exact and numerical results of an equivalent eight-vertex model. For attractive walls a commensurate and an incommensurate phase are separated by a first-order line for stiff walls and by a fluid phase for flexible walls. The phase boundaries with the fluid phase are Ising-like. For repulsive stiff walls an intermediate striped phase with a nonuniversal boundary occurs which vanishes for higher flexibilities. Moreover, disorder lines are located.

An exact equivalence is established between the directed-site animals-enumeration (DSAE) problem in $d$ dimensions and a crystal-growth model defined on the same lattice. In special cases, the latter reduces to the calculation of the free energy of a ($d-1\mathrm{}$)-dimensional lattice gas with extended hard cores. The author solves a DSAE problem with $d=3\mathrm{}$ exactly by using its equivalence to the hard-hexagon problem, and shows that the exponent $\theta =\frac{5}{6}$. A new and simpler solution to the DSAE problem on the square and triangular lattices is given.

The familiar minimum-uncertainty wave packets for masses are generalized in analogy with the two-photon coherent states of the radiation field. The free evolution of a subclass of these states, the contractive states, leads to a narrowing of the position uncertainty in contrast with the usual minimum-uncertainty wave packets. As a consequence the standard quantum limit for monitoring the positions of a free mass can be breached. Further implications on quantum nondemolition measurements are discussed.

A new and relatively simple method has been developed to focus and guide electron beams without the use of a magnetic field. The scheme relies on the electrostatic charging of a highly resistive wire in the presence of a beam. The beam is then strongly guided and focused by the oppositely charged wire. In addition, the highly anharmonic nature of the wire potential leads to rapid phase-mix damping of transverse beam displacements and radial pulsations.

The behavior of autocorrelation functions in a $K$ system (the stadium billiard) is studied, and the existence of long-time tails is demonstrated both analytically and numerically. The tails are shown to depend on the presence of arbitrary long segments of regular motion in the time evolution of the stochastic orbits. It is surmised that an analogous mechanism might be responsible for long-time tails in a large class of systems.

A new form of the Navier-Stokes equation resulting from a change of variables is presented. The new form has several advantages: It yields a new asymptotic behavior of the flow for long times and vanishingly small viscosity. In addition an interpretation of the new equation in terms of a simple random walk yields immediately not only the Kolmogorov $\frac{2}{3}$-power law but also an intermittency exponent well within the experimental uncertainty.

A model of classical particles in one space dimension with an elementary length and general finite-range interaction with hard core is considered. It is shown that such a model must have a periodic ground state.

A simple model is discussed for a periodically forced oscillator with a constraint which leads to motions with impacts. For "perfectly plastic" impacts the dynamics is represented by a discontinuous map defined on the circle. The map is shown to undergo perioddoubling bifurcations followed by complex sequences of transitions, due to the discontinuities, in which arbitrarily long superstable periodic motions occur.

By minimization of a Hamiltonian with respect to its interaction parameters, new Hamiltonians are generated. The same minimization procedure is carried out with the free energy of the initial Hamiltonian, and it is proven that in the thermodynamic limit the minimized free energy is the free energy of the minimized Hamiltonian. This method is illustrated with two-dimensional Ising models generalized to include both nearest-neighbor bonds and infinite-range bond-bond interactions. New critical behavior is observed.

In contrast to some earlier studies, good agreement has been found between the asymptotic random-walk exponent for particles restricted to the occupied sites of a simplecubic lattice, and the dynamical scaling prediction of Gefen, Aharony, and Alexander. For the first time, up to ${10}^7$ steps were used in the Monte Carlo study, which moreover employed larger lattices (${180}^3$) than earlier studies.

It is shown that a $d$-dimensional statistical system of a single U(1) variable, $\exp \left(i\varphi \right)$, whose Hamiltonian is invariant under the transformation $\varphi (x_1,\cdots ,x_d)\to \varphi (x_1,\cdots ,x_d)+\Lambda (x_3,\cdots ,x_d)$, with $\Lambda$ an arbitrary function, has no long-range order, so that $〈\exp \left(i\varphi \right)〉=0\mathrm{}$ for all nonzero temperatures. Moreover, the full planar symmetry reflected in the above transformation law is also unbroken for all $T>\mathrm{}0\mathrm{}$. When $d=2\mathrm{}$ the usual Mermin-Wagner result is recovered. Various extensions and physical implications of this theorem are briefly discussed.

The component formulation of the Wess-Zumino superspace action leads, when compared with the general results of Cremmer et al., to a nonminimal version of $N=1\mathrm{}$ supergravity. A new superpotential, $g_2\mathrm{}\left(z\right)\mathrm{}$, has been found that gives a scalar potential $V\left(z\right)\mathrm{}$ that is even in $z$ and which breaks supersymmetry inside the circle of radius $\frac{\sqrt{6}}{\kappa }$ in the complex $〈z〉$ plane.

Total magnetic flux trapped in a tiny toroidal magnet is measured by an electron holography technique to test predicted flux quantization. The experimental results show that the magnetic flux is quantized neither by $\frac{h}{e}$ units nor by $\frac{h}{2e}$ units. This fact provides further evidence for the existence of the Aharonov-Bohm effect.

The chaotic nature of "caviton turbulence" is studied in one-dimensional, many-Fourier-mode numerical simulations of the driven dissipative Zakharov equations. Above the modulational instability threshold the system evolves into a variety of stable patterns of cavitons which become chaotic for stronger driving. The cavitons remain coherent for times long compared to the shortest Lyapunov time.

The current state of theoretical understanding related to the question posed in the title is incomplete. This paper presents results of numerical experiments which are consistent with a positive answer. These results also bear on the problem of characterizing possible routes to chaos in nonlinear dynamical systems.

The Kramers theory for the escape rate of a Brownian particle moving in a potential well is generalized to account for the full viscosity range. An expression for the escape rate, which is valid for all values of the friction and yields the Kramers results in the appropriate limits, is obtained.

The problem of determining the deviation $\delta V\left(\overrightarrow{\mathrm{r}}\right)$ of a local scattering potential $V\left(\overrightarrow{\mathrm{r}}\right)=V_0\left(\overrightarrow{\mathrm{r}}\right)+\delta V\left(\overrightarrow{\mathrm{r}}\right)$ from a known background potential $V_0\left(\overrightarrow{\mathrm{r}}\right)$ by use of scattered-field data is addressed within the distorted-wave Born approximation. A procedure is presented that allows $\delta V\left(\overrightarrow{\mathrm{r}}\right)$ to be approximately reconstructed from the potential's scattering amplitude $f(k\overrightarrow{\mathrm{s}},k{\overrightarrow{\mathrm{s}}}_0)$ assumed specified for fixed $k$ and all incident (${\overrightarrow{\mathrm{s}}}_0$) and observation ($\overrightarrow{\mathrm{s}}$) directions. The reconstruction method is shown to be a generalization of an inversion procedure developed earlier, to which it reduces when $V_0\left(\overrightarrow{\mathrm{r}}\right)\equiv 0$.

A new method based on the $S$-matrix factorization is developed for the thermodynamics of the massive Thirring model. The method can be applied to any charge sector and coupling constant. In the zero-charge sector, the present theory reproduces all the Bethe-Ansatz-theory results in the attractive-coupling regime, and agrees with a perturbation calculation in the repulsive-coupling regime.

Within a real-space renormalization-group framework, the spin-½ Heisenberg ferromagnet in the presence of an Ising-like anisotropy on a self-dual hierarchical lattice is discussed. The results are exact for this lattice but can also be considered as a quite satisfactory approximation for the simple square one. The controversial point on how $T_c$ vanishes in the isotropic Heisenberg limit is analyzed: Quite strong evidence is presented favoring a continuous function of anisotropy. The crossover from the isotropic Heisenberg model to the pure Ising one is exhibited.