We find static, self-dual solutions to the SU(N) gauged, nonlinear Schrödinger equation in two spatial dimensions with scalar matter in the adjoint representation. The gauge field is determined dynamically by the Chern-Simons interaction with nonrelativistic scalar matter. The hierarchy is associated with the Toda hierarchy, which can be solved explicitly. The N=2 case reduces to the Liouville equation found by Jackiw and Pi, when looking at the nonlinear Schrödinger equation gauged by U(1).

Degenerate perturbation theory, without geometrical tools, directly yields vector potentials in the Born-Oppenheimer approximation. The derivation uses only the algebra of the dynamical operators, and the slow variables need not commute.

It is shown that the pair connectedness for percolation on an arbitrary directed graph may be obtained by setting λ=1 in the transmissivity function for a λ-state chiral Potts model, the odd-flow model, and that the pair connectedness of the dual percolation model is expressible in terms of the correlation function of a second chiral Potts model, the odd potential difference model. There is an important distinction between odd and even λ and only those models with odd λ exhibit chirality. The duality relation between the transmissivity and correlation functions leads to a duality relation for pair connectedness of directed percolation theory which extends the result of Dhar, Barna, and Phani for percolation probabilities.

Reflection of microwaves from a cavity is measured in a frequency domain where the underlying classical chaotic scattering leaves a clear mark on the wave dynamics. We check the hypothesis that the fluctuations of the S matrix can be described in terms of parameters characterizing the chaotic classical scatteirng. Absorption of energy in the cavity walls is shown to significantly affect the results, and is linked to time-domain properties of the scattering in a general way. We also show that features whose origin is entirely due to wave dynamics (e.g., the enhancement of the Wigner time delay due to time-reversal symmetry) coexist with other features which characterize the underlying classical dynamics.

We study quantized classically chaotic maps on a toroidal two-diensional phase space. A discrete, topological criterion for phase-space localization is presented. To each eigenfunction an integer is associated, analogous to a quantized Hall conductivity, which when nonzero reflects phase-space delocalization. A model system is studied, and a correspondence between delocalization and chaotic classical dynamics is discussed.

The bulk conductivity ${\mathrm{\sigma }}^{\mathrm{*}}$(p) of the bond lattice in ${\mathit{openZ}}^{\mathit{d}}$ with a fraction p of conducting bonds is analyzed. Assuming a hierarchical node-link-blob (NLB) model of the conducting backbone, it is shown that ${\mathrm{\sigma }}^{\mathrm{*}}$(p) (for this model) is convex in p near the percolation threshold ${\mathit{p}}_{\mathit{c}}$, and that its critical exponent t obeys the inequalities 1≤t≤2 for d=2,3, while 2≤t≤3 for d≥4. The upper bound t=2 in d=3, which is realizable in the NLB class, virtually coincides with two very recent numerical estimates obtained from simulation and series expansion.

The Husimi distribution is computed for a particle in a double-well potential and an oscillatory driving force. The extended phase space of the classical system contains two disjoint stable tubes of regular orbits, embedded in a chaotic sea. For the quantum system we find coherent oscillatory tunneling between these stability tubes, at a rate many orders of magnitude greater than the rate of ordinary undriven tunneling.

Measurement of the free precession of nuclear spins in optically pumped ground-state ${}_{}{}^{201}{}_{}{}^{}\mathrm{Hg}$ atoms has allowed a test of Weinberg’s nonlinear generalization of quantum mechanics. Shifts among the three resolved precession frequencies in the spin-3/2 system were studied as a function of the projection of spin polarization along the precession axis. Our results set an upper limit on ε, Weinberg’s nonlinearity parameter, of ‖ε‖/2πħ<3.8μ Hz, which corresponds to 2.0×${10}^{\mathrm{-}27}$ of the binding energy per nucleon. This is the most stringent such limit to date.

We study the transition to chaos for random dynamical systems. Near the transition, on the chaotic side, the long-time particle distribution (which is fractal) that evolves from an initial smooth distribution exhibits an extreme form of temporally intermittent bursting whose scaling we investigate. As a physical example, the problem of the distribution of particles floating on the surface of a fluid whose flow velocity has a complicated time dependence is considered.

We have found the presence of at least one family of stable periodic orbits in the system H=1/2(${\mathit{p}}_{\mathit{x}}^2$+${\mathit{p}}_{\mathit{y}}^2$+${\mathit{x}}^2$${\mathit{y}}^2$). This counterproves earlier claims that the ${\mathit{x}}^2$${\mathit{y}}^2$ potential gives fully ergodic motion.

We evaluate the Fourier path integral for an optical polaron by the method of partial averaging. Higher Fourier coefficients are taken into account by averaging with Feynman’s trial action, whereas the first N coefficients are treated explicitly by numerical integration. This method removes the Coulomb singularity in the effective action, yields lower bounds to the partition function, and systematically improves Feynman’s variational results. We present numerical results for the exact ground-state energy for small and intermediate values of the coupling constant.

Transient order→chaos transitions of two ${\mathrm{Ba}}^{+}$ ions are observed where the duration of the chaotic state increases smoothly with an increasing Mathieu control parameter q. The transient regime precedes the transition point ${\mathit{q}}_{\mathit{c}}$ for stationary chaos, which is well defined and reproducible. The perturbative step that initiates chaos takes place on a time scale of 1 min, far longer than previous estimates, and is due to a single ${\mathrm{H}}_2$-${\mathrm{Ba}}^{+}$ collision (${\mathrm{H}}_2$ pressure 5×${10}^{\mathrm{-}11}$ Torr). In contrast to random collision events, chaos can be initiated deterministically by a new pulse technique. These observations resolve earlier anomalies and challenge computer simulations.

We derive the exact distribution of times spent in the classically forbidden region by a particle as it tunnels through a square barrier potential. We find that the integrated distribution has a simple interpretation. If one restricts the time spent in the barrier to be ⩽τ, then an effective uncertainty ΔV is introduced in the barrier height, such thatΔVτ≃1. This uncertainty leads to unusual interference effects in the distribution. These interference effects explain why the average speed of a particle traversing a very opaque barrier may exceed the speed of light. © 1990 The American Physical Society

Dyson’s Brownian-motion model is recovered as a rigorous description of the dependence of Hamiltonians H=${\mathit{H}}_0$+λV on the control parameter λ when ${\mathit{H}}_0$ and V belong to different universality classes. For instance, time-reversal invariance may hold for ${\mathit{H}}_0$ but not for V. The clue to our result lies in (i) a certain rescaling of the energy, H→ √f(λ) (${\mathit{H}}_0$+λV), and (ii) not individual Hamiltonians but suitable families.

The thermodynamics of a gas of order two (Q=2) parabosons or parafermions is shown to be equivalent to that of a mixture of two gases of ordinary bosons or fermions, which either contain equal numbers of particles or the particle numbers of which differ by one.

We study the decay of classical systems with regular and chaotic dynamics by investigating the escape of a particle from a container with a small hole. For the case of ergodic motion, we find an exponential decay law, whereas the nonchaotic system decays according to a power law.

An experiment, analogous to that of Cimmino et al., is proposed to measure the phase shift induced by static electric fields on the passage of neutrons through an interferometer when the path-enclosed linear charge density is zero. A finite shift is predicted and discussed in light of the Aharonov-Casher result.

The flow under gravity of a granular material can exhibit either intermittent avalanches or a steady regime. The transition from the discrete to the steady regime is shown experimentally to display hysteresis. Next, a relationship between the current and the slope is established and interpreted.

We propose a new method for evaluating the decay rates of time correlations in chaotic dynamical systems, based on averaging over periodic orbits. We use a cycle expansion of a Fredholm determinant which is in practice superior to the corresponding expansion for the Ruelle ζ function. The method is tested in one-dimensional expanding maps with the resulting decay rates compared to those obtained in two other independent ways: By a perturbative calculation of the spectrum of the transfer operator and by direct numerical computations of time correlations. Moreover, we show that in general the decay rates are not simply related to generalized Lyapunov exponents.

We show that the criticality of integrable lattice models based on the Lie algebras ${\mathit{A}}_{\mathit{n}}$,${\mathit{D}}_{\mathit{n}}$,${\mathit{E}}_{\mathit{n}}$ can be understood as the product of certain numbers of bosonic fields and a generalized parafermionic (fractional spin) theory (GPT). We compute the central charge of the GPT using the thermodynamic Bethe-ansatz approach. For the model associated with the ${\mathit{A}}_2$ Lie algebra, we propose that the associated GPT can be described by a composition of Ising and tricritical-Ising conformal field theories.