We present theoretical arguments (based on infinite dimensional bifurcation theory) and numerical evidence (based on nonperturbative methods) that the boundaries of analyticity of invariant curves can be described as an accumulation of branch points, which are typically of order 2. We show how this fact would explain previous numerical results of several authors and how it suggests more efficient numerical algorithms, which we implement.

We study the domain of coupling constants for which a 3-body or 4-body system is bound while none of its subsystems is bound. Limits on the size of the domain are derived from a variant of the Hall-Post inequalities which relate $N$-body to ($N-1\mathrm{}$) body energies at given coupling. Possible applications to halo nuclei and hypernuclei are briefly outlined.

We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena are RG equations. The renormalized perturbation approach may be simpler to use than other approaches, because it does not require the use of asymptotic matching and yields practically superior approximations.

The interaction of interfacial solitary waves of algebraic type is investigated on the basis of a higher-order Benjamin-Ono equation. By developing a multisoliton perturbation theory, we show analytically that the overtaking collision between two solitary waves exhibits the phase shift but the amplitudes are not altered after interaction. The predication of the phase shift that takes place between algebraic solitary waves is the first example reported in the literature.

The phase diagram of a two-temperature kinetic Ising model which evolves by Kawasaki dynamics is studied using Monte Carlo simulations in dimension $d=2\mathrm{}$ and solving a mean-spherical approximation in general $d$. We show that the equal-temperature (equilibrium) Ising critical point is a bicritical point where two nonequilibrium critical lines meet a first-order line separating two distinct ordered phases. The shape of the nonequilibrium critical lines is described by a crossover exponent, $\varphi$, which we find to be equal to the susceptibility exponent, $\gamma$, of the Ising model.

Quantum integrable particle systems with inverse square interactions in one-dimensional space are investigated by use of the quantum inverse scattering method. For the case of particles with $\mathrm{SU}\left(\nu \right)$ spins, a hidden symmetry is the $\mathrm{SU}\left(\nu \right)\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}\simeq \mathrm{U}\left(\nu \right)$ current algebra. The system has a higher symmetry, the $W_{1+\infty }$ algebra. This $W$ algebra structure unifies the Calogero type ($\frac{1}{x^2}$ interactions) and the Sutherland type ($\frac{1}{{sin}^{2}x}$ interactions). The energy spectra of the systems are obtained in a simple manner based on the fermion representation of the algebra.

An analytical stability criterion for discrete solitons is presented. Its evaluation proves that discreteness reduces (in comparison with the continuum results) the critical nonlinearity parameter (which separates stable and unstable regimes). Unstable discrete solitons may "collapse" into the more stable intrinsically localized states. The theory applies to a discrete nonlinear Schrödinger equation, but can be generalized to other systems.

The reduced dynamics of a quantum system in contact with a reservoir is generally thought to be "completely positive"; this is certainly true if product initial conditions are used to define the dynamics. We show that with correlated initial conditions it need not be so. In this case the dynamics can properly be defined only on a subset of initial system states; extension, by linearity, to all possible initial states is trivially possible, but the extension may not be physically realizable and may not even be positive, let alone completely positive.

An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling macroscopic limit. Some implications for the quantum measurement problems are discussed, in particular in connection with dissipation.

A measurement procedure on a spin 1/2 system is described, whose effect on the (possibly unknown) state of the system can be reversed, by means of other similar measurements, with a sizable probability of success $P^{\mathrm{rev}}$ (e.g., $\frac{1}{2}<P^{\mathrm{rev}}<1\mathrm{}$, depending on the state). Repeated such measurements followed by reversal, on a single system, allow us to determine its (a priori unknown) state operator with a probability of success which is nonzero, though extremely small (because $P^{\mathrm{rev}}<1\mathrm{}$).

We investigate the phase accumulated by a charged particle in an extended quantum state as it encircles one or more magnetic fluxons, each carrying half a flux unit. A simple, essentially topological analysis reveals an interplay between the Aharonov-Bohm phase and Berry's phase.

We derive the occupation-number distribution in a generalized ideal gas of particles obeying fractional statistics, including mutual statistics, by adopting a state-counting definition. When there is no mutual statistics, the statistical distribution interpolates between bosons and fermions, and respects a fractional exclusion principle (except for bosons). Anyons in a strong magnetic field at low temperatures constitute such a physical system. Applications to the thermodynamic properties of quasiparticle excitations in the Laughlin quantum Hall fluid are discussed.

We examine and explain the Luttinger-liquid character of models solvable by the Bethe ansatz by introducing a suitable bosonic operator algebra. In the case of the Hubbard chain, this involves two bosonic algebras which apply to all values of U, electronic density, and magnetization. Only at zero magnetization does not lead to the usual charge-spin separation. We show that our ‘‘pseudoparticle’’ operator approach clarifies, unifies, and extends several recent results, including the existence of independent right and left equations of motion and the concept of ‘‘pseudoparticle’’ (also known as ‘‘Bethe quasiparticle’’).

A repeatedly discussed gedanken experiment, proposed by Fermi to check Einstein causality, is reconsidered. It is shown that, contrary to a recent statement made by Hegerfeldt, there appears no causality paradox in a proper theoretical description of the experiment.

We discuss bound state excitation in models where wave function collapse is a physical process. Consequences of a feasible photon counting experiment are spelled out, were an upper limit to be found on the rate of anomalous photon emission from solid matter that is better than 1 photon/sec cc. It is also pointed out that experiments already performed, which give an upper bound on the rate of nucleon decay, can have significant consequences for such models. We show how these experimental results could be considered to rule out the original version of the collapse models, and support a version in which the rate of collapse is proportional to the mass, indicative of a gravitational mechanism.

We construct large-$n$ (spherical) limits for a series of interesting quantum phase transitions in disordered systems, including quantum ferromagnets and spin glasses, superconducting thin films with and without an external magnetic field, the dirty boson problem, the fractional quantum Hall effect, and Nelson's model of flux lines in high-temperature superconductors. The spherical limit always produces a random matrix inversion problem with self-consistency conditions, which then must be solved numerically. We present preliminary results for the dirty boson problem in two spatial dimensions.

The temporal evolution of two-dimensional soap froth, starting from a particle initial state, is studied. The initial state is a hexagonal array of bubbles in which a single defect is introduced. A cluster of transformed bubbles grows; the time dependence of the number of bubbles in this cluster in investigated and the distribution of the topological classes in the evolving part of the system is calculated. The distribution appears to approach a fixed limiting one, which differs from that obtained for the usual scaling state of the froth.

The concept of geometric phase is demonstrated in a nuclear gyroscope using ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ nuclear spins (I=3/2) as sensors for quantum-phase accumulation. By spatial rotation sub-Hertz splittings due to geometric phases are resolved in nuclear-quadrupole spectra. Deviations from Berry’s adiabatic geometric phase appear in the regime of nonadiabatic rotation. The observed frequency splittings are no longer linear in the rotational frequency, as expected from adiabatic rotations, and all possible transitions, namely, six in this partially degenerate spin-3/3 system, are observed experimentally.

In the original two-potential formalism the potential was split into two parts which were treated at different dynamical levels. In the present Letter a multichannel generalization of the method is proposed that also allows various groups of channels to be treated differently. The new formalism is used to devise a dynamically consistent way of treating breakup processes in the framework of coupled-channel calculations.

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. Considering domain boundaries in critical systems and the invariance of the hyperbolic length allows a new interpretation of the basic equation of conformal covariance. The scale factors gain a physical interpretation. We exhibit a fully factored form for the three-point function. An infinite series of minimal models with limit point $c=-2\mathrm{}$ is discovered. A correspondence between the anomalous dimension and the angle of certain hyperbolic figures emerges.