Using transfer-matrix methods, we have investigated numerically the probability distributions that govern geometric and free-energy fluctuations in the (1+1)-dimensional directed polymer subject to quenched, uncorrelated Gaussian disorder. Exhaustive averaging, over many realizations of the random energy landscape, have permitted us to observe scaling of the third cumulant of the free energy as predicted by Kardar [Phys. Rev. Lett. 55, 2235 (1985)], to address issues concerning finite-size effects, and to discern the asymmetric form of the free-energy probability distribution. In addition, we have determined precisely the amplitudes of various transverse moments in order to compare to recent estimates of Bouchaud and Orland [J. Stat. Phys. 61, 877 (1990)].

We show how a template for a dynamical system can be uniquely specified by a framed braid. This leads to a homological classification of strange attractors in terms of an associated linking matrix.

We consider the evolution of waves governed by a periodically perturbed nonlinear Schrödinger equation. The system is a nonlinear generalization of the quantum kicked rotator. We study the soliton chaotic motion, its destruction and reversibility properties. It is found that nonlinearity does not destroy the quantum suppression of chaotic diffusion.

We estimate the two largest Lyapunov exponents in a three-dimensional simulation of hydromagnetic convection in which there is dynamo action. It turns out that these first two exponents (from a total of 8×${63}^3$) are positive and of similar magnitude. Thus we conclude that the dynamo is chaotic. Furthermore, the consideration of local exponents helps in our understanding of the relevant dynamics. We find that the downdraft flows are more chaotic than the upward motions. Likewise, the velocity and magnetic fields have more chaotic dynamics than the temperature and density fields.

It is shown that the transient response of a helicoidal phase cholesteric liquid crystal to an applied field described by a step function is governed by two relaxation constants. The shorter one characterizes the local rotation of the director field and the longer the change in the overall twist angle between the bounding surfaces. For typical thermotropic liquid crystals, the ratio between these two time constants is of the order of ${10}^4$, the shorter time being tens of microseconds and the longer a few seconds. It is suggested that these results are general and can be used to interpret recent studies of the dynamic response of cubically ordered cholesteric blue phases.

Measurements of discharging current transients in pentyl cyanobiphenyl liquid crystals have been made at various applied voltages and temperatures. A well-characterized peak in the discharging transient is observed in both nematic and isotropic phase. A computer simulation based upon a random-walk method has been also carried out in order to explore the origin of such an anomalous peak. It is concluded that the occurrence of the anomalous peak is ascribed to a relaxation of an applied-electric-field-induced nonuniform distribution of space charges due to impurity ions incorporated in the liquid crystals.

We present an equation to trace the laser pulse traveling in a wake field, including the phase-slippage effect. An analytical formalism to find the maximum possible acceleration and corresponding extraction point for a given set of initial conditions is presented for a specific plasma wake-field density distribution. This formalism is also useful to find the divergence of the pulse in different regions of acceleration.

We demonstrate analytically and numerically superradiant spiking behavior in the leading and trailing regions of a radiation pulse propagating within a long electron pulse in a single-pass, high-gain free-electron laser (FED). A single superradiant spike is observed when the radiation pulse is shorter than a cooperation length ${\mathit{L}}_{\mathit{c}}$. We show this work may be relevant to the understanding of the spiking behavior in the FEL oscillator, and to possible spiking mechanisms in a perturbed steady-state amplifier.

An interferogram of synchrotron radiation emitted from a train of bunched electrons accelerated by an S-band linac has been observed in the far-infrared region using a polarizing interferometer whose maximum optical path difference covers a distance between adjacent bunches. The interferogram shows that radiation emitted from successive bunches is coherent, and that coherent synchrotron radiation emitted from periodic bunches has a spectrum of a line series, i.e., higher harmonics of the radio frequency of the linac.

Spectra of synchrotron radiation (SR) and Čerenkov radiation (CR) in air have been observed in the wavelength range of 1.15–8 mm using bunched electrons accelerated by an L-band linac, whose energy and radio frequency are 40 MeV and 1300 MHz. The observed intensities of SR and CR at λ=4 mm are enhanced by factors of 9×${10}^7$ and 1×${10}^7$ in comparison with calculated intensities of ordinary SR and CR, respectively. Radiation of the rf wake induced in a chamber has also been observed. Bunch form factors are derived from the observed spectra, and the electron distribution in a bunch is discussed.

Itano and co-workers [Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A 41, 2295 (1990)] have recently reported the experimental verification of the quantum Zeno effect, which is the inhibition of a quantum transition by frequent measurements. In this article, we offer an alternative interpretation of the quantum Zeno effect. We show that an analysis of the dynamics of the full three-level system gives the same result. There is no need to assume explicitly that the wave function has collapsed, nor even to assume that an ideal measurement has been made. In addition, we differentiate between what has been referred to as the quantum Zeno effect and what has been termed the quantum Zeno paradox. The former is the inhibition of induced transitions, and the latter is the, as yet experimentally unobserved, inhibition of spontaneous decay. Our interpretation, which emphasizes the ‘‘measurement’’-induced interruption of atomic-state coherences as the cause of inhibited quantum transitions, suggests a resolution to the quantum Zeno paradox. The theoretical limit of continuous observation is discussed.

According to Pancharatnam [S. Pancharatnam, in Geometric Phases in Physics, edited by A. Shapere and F. Wilczek (World Scientific, Singapore, 1989)], two light beams of differing elliptical polarization can be said to be ‘‘in phase’’ if their interference is maximally constructive. In the same spirit, the relative phase between two beams a and b is the amount by which the phase of beam b needs to be changed to put it in phase with beam a. Berry has established a simple relation between Pancharatnam’s concept and a phase relation between two quantum-mechanical states: If two nonorthogonal states ‖${\mathrm{\psi }}_{\mathit{a}}$〉 and ‖${\mathrm{\psi }}_{\mathit{b}}$〉 are phased in such a way that ‖${\mathrm{\psi }}_{\mathit{a}}$〉+‖${\mathrm{\psi }}_{\mathit{b}}$〉 has maximum norm, i.e., such that 〈${\mathrm{\psi }}_{\mathit{a}}$‖${\mathrm{\psi }}_{\mathit{b}}$〉 is real and positive, they can be said to be in phase or parallel, and in general the relative phase between them is the phase angle of 〈${\mathrm{\psi }}_{\mathit{a}}$‖${\mathrm{\psi }}_{\mathit{b}}$〉. This concept plays a role in the theory of the Abelian geometric phase. In the non-Abelian case, one has two n-dimensional subspaces instead of two single states, and instead of choosing the phase of each state one has to choose an orthonormal basis (including phase) in each subspace. We show that the concept of ‘‘block diagonalization’’ introduced by Cederbaum, Shirmer, and Meyer [J. Phys. A 22, 2427 (1989)] in the context of a molecular problem provides a natural generalization of the Pancharatnam-Berry phase relation.

Many aspects of a model problem, the Lagrangian of which contains a term depending quadratically on the acceleration, are examined in the regime where the classical solution consists of two independent normal modes. It is shown that the techniques of conversion to a problem of Lagrange, generalized mechanics, and Dirac’s method for constrained systems all yield the same canonical form for the Hamiltonian. It is also seen that the resultant canonical equations of motion are equivalent to the Euler-Lagrange equations. In canonical form, all of the standard results apply, quantization follows in the usual way, and the interpretation of the results is straightforward. It is also demonstrated that perturbative methods fail, both classically and quantum mechanically, indicating the need for the nonperturbative techniques applied herein. Finally, it is noted that this result may have fundamental implications for certain relativistic theories.

In this paper, the exact solution and time-evolution operator for the system with a su(1,1)${\mathrm{?}}_{\mathit{s}}$h(4) Hamiltonian are found by making use of Lewis-Riesenfeld quantum theory. The time-evolution operator is then used to derive the Aharonov-Anandan phase. Finally, the noncyclic evolution is discussed with the help of the Aharonov-Anandan phase and the Berry phase is calculated by taking the adiabatic limit.

A noncompact chaotic billiard on a two-dimensional space of constant negative curvature, the infinite equilateral triangle describing anisotropy oscillations in the very early universe, is studied quantum mechanically. A Weyl formula with a logarithmic correction term is derived for the smoothed number of states function. For one symmetry class of the eigenfunctions the level spacing distribution, the spectral rigidity ${\mathrm{\Delta }}_3$, and the ${\mathrm{\Sigma }}_2$ statistics are determined numerically using the finite matrix approximation. Systematic deviations are found both from the Gaussian orthogonal ensemble (GOE) and the Poissonian ensemble. However, good agreement with the GOE is found if the fundamental triangle is deformed in such a way that it no longer tiles the space.

We have solved the problem of determining the traversal time distribution for a quantum transition between arbitrary initial and final states. This distribution is given by a Fourier transform of the Feynman averaged characteristic function for the classical traversal time functional ${\mathit{t}}_{\mathrm{ab}}^{\mathrm{cl}}$[x(t)]. For one-dimensional tunneling, the distributions for the dwell, reflection, and transmission times are determined for an arbitrary potential V(x). All three distributions are complex valued and require the concept of negative probability.

The eigenvalue moment method (EMM), a linear-programming (LP) based technique for generating converging bounds to quantum eigenenergies, is reformulated as an iterative dynamical system (DS). Important convexity properties are uncovered significantly impacting the theoretical and computational implementation of the EMM program. In particular, whereas the LP-based EMM formulation (LP-EMM) can require the generation and storage of many inequalities [up to several thousand for a 10-missing moment problem (${\mathit{m}}_{\mathit{s}}$=10)], the dynamical-system formulation (DS-EMM) generates a reduced set of inequalities [of order O(${\mathit{m}}_{\mathit{s}}$+1)]. This is made possible by replacing the LP generation of deep interior points (DIP’s) by a Newton iteration process. The latter generates an optimal set of DIP’s sufficient to determine the existence or nonexistence of the relevant missing moment polytopes. The general DS-EMM theory is presented together with numerical examples.

For a many-particle system with a spherically averaged single-particle density ρ(r) of a kth-order monotonic nature (i.e., a function whose successive derivatives up to that of order k alternate in sign), rigorous inequalities that involve the central values of ρ(r) and its derivatives as well as the radial expectation values are derived. These inequalities become optimal in the completely monotonic case, that is for k→∞. Then, it is argued that for atomic systems the electron density is completely monotone to quite a good approximation except in hydrogen, where it is rigorous. In this approximation, the corresponding atomic inequalities produce the following: (i) the famous tight upper bound to the electron density at the nucleus ρ(0)≤(Z/2π)〈${\mathit{r}}^{\mathrm{-}2}$〉 obtained by Hoffmann-Ostenhof, Hoffmann-Ostenhof, and Thirring [J. Phys. B 11, L571 (1978)] by assuming an infinite nuclear mass, (ii) the lower bound ρ(0)≥〈${\mathit{r}}^{\mathrm{-}2}$${\mathrm{〉}}^2$/(4π〈${\mathit{r}}^{\mathrm{-}1}$〉), (iii) lower bounds to the values of any kth-order derivative of the electron density at the nucleus, and (iv) some inequalities involving two and/or three radial expectation values. These bounds and/or inequalities improve all the corresponding ones known at present. Finally, for completeness, the accuracy of these atomic bounds and/or inequalities are analyzed in the framework of the Hartree-Fock approximation.

The atomic-beam laser-rf double-resonance technique has been used to obtain precise values for the hyperfine structure (hfs) splittings in ten 4${\mathit{f}}^7$5d6s ${}_{}{}^{10}{}_{}{}^{}$${\mathit{D}}_{\mathit{J}}$ and ${}_{}{}^8{}_{}{}^{}$${\mathit{D}}_{\mathit{J}}$ levels of ${}_{}{}^{151,153}{}_{}{}^{}\mathrm{i}$. Detailed studies of the second-order hfs lead to the isotopic ratios of the hfs constants, and reveal surprisingly strong hfs interactions between the two multiplets. The dipole ratios, when compared with the known ratio of the nuclear dipole moments, reveal striking J- and term-dependent hyperfine anomalies. The quadrupole ratios (after corrections for the second-order hfs) are consistent with the atomic ground-state value and self-consistent among the ten levels studied. The precision of the measurements allows evaluation of the ratio of the magnetic octupole hfs interaction constants between the two isotopes. The result, which is taken to be the ratio of the nuclear ground-state magnetic octupole moments Ω, is found to be Ω${(}^{151}$Eu)/Ω${(}^{153}$Eu)=0.87(6).

Relativistic many-body theory is applied to determine amplitudes for 4p→4s, 4p→3d, and 3d→4s transitions in ${\mathrm{Ca}}^{+}$; 5p→5s, 5p→4d, and 4d→5s transitions in ${\mathrm{Sr}}^{+}$; and 6p→6s, 6p→5d, and 5d→6s transitions in ${\mathrm{Ba}}^{+}$. The calculations, which are carried out through third order in perturbation theory, give lifetimes for excited p states that agree with measured values to better than 10%. The agreement improves to the 2% level after semiempirical corrections are included. The lifetimes predicted for the metastable 4${\mathit{d}}_{3/2}$ and 4${\mathit{d}}_{5/2}$ states in ${\mathrm{Sr}}^{+}$ and for the 5${\mathit{d}}_{3/2}$ state in ${\mathrm{Ba}}^{+}$ also agree well with measurement, but the theoretical lifetime of the 5${\mathit{d}}_{3/2}$ state in ${\mathrm{Ba}}^{+}$ is a factor of 4 larger than the measured lifetime.