A ready comparison of the two methods noted in the title is obscured by the very different formalisms that they employ. Our sojourn-time approach [Jaworski and Wardlaw, Phys. Rev. A 45, 292 (1992)] is based on a Hermitian sojourn-time operator in the framework of time-dependent scattering theory whereas Sokolovski and co-workers [Sokolovski and Baskin, Phys. Rev. A 36, 4604 (1987); Sokolovski and Connor, ibid. 42, 6512 (1990)] have developed an approach based on the Feynman path-integral formulation of quantum mechanics. By translating the path-integral approach into the language of wave functions and linear operators, we reveal the similarities of the two approaches and show that the results for the interaction times are closely related, becoming equivalent in the asymptotic limit.

We formulate stochastic noncontextual hidden-variable theories. In such theories the hidden state λ specifies not definite values, but expectation values A¯(λ), . . . of observables A, . . . and noncontextuality means that A¯(λ) is independent of which other commuting observables commuting with A are measured together with A. We show via Bell inequalities that such theories conflict with quantum theory and propose a two-photon experimental test. We also show that for a single particle of spin ($2^{\mathit{n}}$-1)/2, quantum violation of classical noncontextuality grows exponentially with n.

A simple but rigorous relation is derived that provides uniform lower bounds on the equilibrium internuclear distance ${\mathit{R}}_{\mathit{e}}$ where the potential-energy curves of diatomic molecules in the Born-Oppenheimer approximation have a minimum. By employing monotonicity properties and explicit lower bounds on electronic energies, the applications of these ${\mathit{R}}_{\mathit{e}}$ bounds to systems with one or two electrons are discussed in detail.

The D-wave (L=2) phase shifts and the D-wave elastic and positronium-formation cross sections for positron scattering from hydrogen at energies below the first excitation threshold are calculated in the close-coupling approximation, using an algebraic variational method. Four target-state coupling schemes (H 1s–Ps 1s, H 1s–H 2s–Ps 1s, H 1s–H 2s–H 2p–Ps 1s, and H 1s–H 2s–H 2p¯–Ps 1s) have been considered for the calculation. The algebraic approach again proved to be convenient in handling the positronium-formation channel in the close-coupling calculation, even for a higher-wave scattering.

Through numerical examples, we show that the complex-scaling method is suited to explore the pole structure in multichannel scattering problems. All poles lying on the multisheeted Riemann energy surface, including shadow poles, can be revealed and the Riemann sheets on which they reside can be identified.

We study the phase properties of quantum superpositions of two coherent states (Schrödinger-cat states) amplified by phase-sensitive (squeezed) amplifiers. We show that a phase-sensitive amplifier with a properly chosen phase can preserve the phase distribution of the Schrödinger-cat-state input.

We discuss a recently proposed method [R. Jáuregui and J. Récamier, Phys. Rev. A 46, 2240 (1992)] based on the application of iterative Bogoliubov transformations to anharmonic oscillators and show that, if the algorithm converges, one easily obtains the final result directly in one step. We prove that the Bogoliubov transformation can be written in terms of scaling and translation parameters and present exact results for the coefficients of the Bogoliubov transformation for some selected examples.

We report experimental measurements of electron spectra resulting from the scattering of 9.5-eV electrons by helium atoms through an angle of 9° in the presence of a high-intensity (∼${10}^8$ W ${\mathrm{cm}}^{\mathrm{-}2}$) ${\mathrm{CO}}_2$ laser. The intensities of the additional peaks which occur separated from the elastic scattering peak by multiples of the photon energy in the presence of the laser are much greater than expected. These data suggest that calculations based on the Kroll-Watson approximation, usually applied to this type of experiment, are inappropriate for these scattering conditions.

We have carried out a series of calculations, the results of which demonstrate the breakdown of the isolated-resonance approximation for the electron-impact excitation of positive ions. The specific results presented here, namely for the 3${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S→3s3p ${}_{}{}^3{}_{}{}^{}$P transition in ${\mathrm{Fe}}^{14+}$, are not unique. All of the Mg-like ions that we have investigated so far exhibit the same breakdown. There is no reason to believe either that the Mg-like sequence is unique. This has important implications for the description of resonant processes that are strongly radiation damped, for which the isolated-resonance approximation is widely used and the standard formulation of the close-coupling approximation is not applicable.

We report here measurements of two-body associative-ionization collisions between sodium atoms confined in a magneto-optic trap. These collisions represent a kind of ‘‘open’’ or dissipative collision for which the energy of the atom plus applied light field subsystem need not be conserved due to spontaneous-emission coupling to the vacuum modes of the radiation field. The experiment measures the photoassociative-ionization-rate constant as a function of the optical field intensity from about 40 to 260 mW ${\mathrm{cm}}^{\mathrm{-}2}$. These results are in reasonable agreement with the predictions of an optical-Bloch-equation theory [Y. B. Band and P. S. Julienne, Phys. Rev. A 46, 330 (1992)], but differ strongly from the predictions of a local-equilibrium theory [A. Gallagher, Phys. Rev. A 44, 4249 (1991)].

We investigate numerically the stabilization of Rydberg states of atomic hydrogen in superintense laser light. No stabilization could be observed at frequencies comparable with the Rydberg energies. We show that the stabilization observed at higher frequencies is governed by the spreading and decrease of the coupling potentials at high intensities rather than by a reduction of the wave-function amplitude in the interaction region.

An enhancement of the ${\mathrm{He}}^{2+}$ yield near the appearance intensity was not observed by linearly polarized KrF laser light (248 nm), whereas a significant enhancement was observed by linearly polarized Ti:sapphire laser light (745 nm). These results are consistent with the quasistatic model proposed by Corkum [Technical Digest of Short Wavelength V: Physics with Intense Laser Pulses (Optical Society of America, Washington, DC, 1993), p. 25].

An alternative scheme for the generation of sub-Poissonian photons based on population-dependent spontaneous-emission lifetime in semiconductor microcavities is proposed and discussed theoretically. In the proposed scheme, the lifetime decreasing with electron population antibunches the emission events and, as a result, expands remarkably the frequency range for the suppression of spontaneous photon number fluctuation noise far beyond the inverse of the lifetime. The negative derivative of the lifetime is caused by a resultant effect of field screening due to populated electron-hole pairs and of quantum-confined Stark effect in biased quantum wells embedded in the microcavities. The proposed scheme may open up a new opportunity in extremely low-power (several photons) high-speed photonics.

The parameters of the quantum-defect theory are obtained for the Dirac equation with a zero or a Coulomb field. The regular solution is adjusted to make it real when either E=${\mathit{mc}}^2$+ɛ>${\mathit{mc}}^2$ or ɛ>0, where ɛ is used in the Schrödinger equation. The Jost functions used are similar for both equations and are organized into amplitude and phase so that the forms of the radial wave functions are transparent. The local short-range potential just contributes a phase that is added in the radial wave functions. The ‘‘smooth’’ Green’s function used, which is free of any singularity at the pole, can be used to solve the multichannel nonlocal-inner-field problem.

The motion of a classical or quantum-mechanical charged particle in the unit square (with periodic boundary conditions) is investigated under the influence of periodic electromagnetic fields. It is shown that the external fields can be chosen in such a way that the configuration space of the particle is mapped periodically to itself according to Arnold’s cat map. The time evolution of the quantum system shows the same degree of irregularity as does the classical time evolution which is completely dominated by the properties of the hyperbolic map. In particular, the eigenfunctions of the Floquet operator are determined analytically, and, as an immediate consequence, the spectrum of quasienergies in this system is seen to be absolutely continuous. Furthermore, spatial correlations decay exponentially. The observed features are in striking similarity to properties of classically chaotic systems; for example, long-time predictions of the future behavior of the system turn out to be extremely sensitive to the specification of the initial state. In other words, the time evolution of the quantum system is algorithmically complex. These phenomena, based on the formation of arbitrarily fine structures in the two-dimensional configuration space, require that the system absorb energy (provided by the external kicks) at an exponential rate.

A phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space is known as the scalar Aharonov-Bohm (AB) effect. Unlike the more familiar AB effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. We have performed an analogous interferometric experiment with thermal neutrons subject to pulsed magnetic fields. The observations were carried out at the University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. The expected phase shifts have been observed to a high degree of accuracy. A detailed description of the experiment and its interpretation is given in this paper.

An interpretation of quantum mechanics in terms of classical concepts, ‘‘beables,’’ due to de Broglie, Bohm, and Bell (BBB) is generalized and further developed. By assuming that all physical quantities take discrete values on sufficiently small scales, we can use this interpretation to give trajectories for all possible quantities, including the position of a particle, its spin, etc. When applied to position, it is shown that, in the continuum limit, this interpretation reduces to the causal one of Bohm. As an illustration, the BBB trajectories are computed explicitly in two simple models.

Gutzwiller’s semiclassical approximation is applied to systems of identical particles. The special case of antisymmetry under particle exchange is treated as an example. The Pauli principle is shown to cause a modification of Gutzwiller’s periodic-orbit sum: The amplitude with which a periodic orbit contributes to the sum is changed, but new orbits do not arise in the sum. The case of noninteracting particles is used for purposes of illustration of the procedure.

The Heisenberg equations describing the dynamics of coupled Fermion photon operators are solved self-consistently. Photon modes, for which ω≊kc, and particlelike Bohr modes with frequencies ${\mathrm{\omega }}_{\mathit{n}\mathit{I}}$≊(${\mathit{E}}_{\mathit{n}}$-${\mathit{E}}_{\mathit{I}}$)/ħ are both approximate solutions to the system of equations that results if the current density is the source in the operator Maxwell equations. Current fluctuations associated with the Bohr modes and required by a fluctuation-dissipation theorem are attributed to the point nature of the particle. The interaction energy is given by the Casimir-force-like expression ΔE=1/2ħtsum(Δ${\mathrm{\omega }}_{\mathit{n}\mathit{I}}$+Δ${\mathrm{\omega }}_{\mathit{k}\mathit{c}}$) or by the expectation value of 1/2(qcphi-qp^⋅A^/mc+${\mathit{q}}^2$${\mathit{A}}^2$/${\mathit{mc}}^2$). It is verified that the equal-time momentum-density and vector-potential operators commute if the contributions of both the Bohr modes and vacuum fluctuations are included. Both electromagnetic and Bohr or radiation-reaction modes are found to contribute equally to spontaneous emission and to the Lamb shift.

An approximate analytical solution is developed for the Floquet states of a quantum-mechanical rigid rotor subject to an arbitrary periodically-time-dependent driving force. The rotor Hamiltonian is expanded in powers of the rotational ‘‘anharmonicity’’ about the angular-momentum state ‖${\mathit{j}}_0$〉 and a perturbative Lie algebraic form of the evolution operator is derived. Except in special cases, the resulting Floquet states are localized. The localization length shows a sharp transition from narrow to broad for those Floquet states in the vicinity of a resonance with one of the Fourier components of the driving field. The special case of the periodically kicked rotor is also discussed, which, because of its unbounded frequency spectrum, can lead to delocalized Floquet states.