An expression for the differential probability of transition radiation in our paper [Glauber and Lewenstein, Phys. Rev. A 43, 467 (1991)] is corrected. It is shown further that interference effects cancel from the sum of two suitably defined intensities measured in the forward and backward hemispheres.

In this work we study the quantum deformation of the three-level Lipkin model. The exact spectra are obtained. The reliability of the mean-field approximation is discussed in the framework of the model. Using adequate coherent states, the mean-field ground-state and the random-phase-approximation modes are calculated. The Dyson realization of ${\mathrm{su}}_{\mathit{q}}$(3) in the Bargmann representation is derived. The effect of the quantum deformation on the ground-state energy and on the phase transitions of the model is discussed. The simulation of temperature effects by the quantum deformation is investigated.

Ab initio cross-section calculations of low-energy ${\mathit{e}}^{\mathrm{-}}$-molecule scattering have been limited to molecular targets composed of atoms with few electrons. We use soft norm-conserving pseudopotentials in both the target description and the scattering calculations to study molecules with hundreds of electrons. Comparison with all-electron calculations and crossed-beam experiments for the smallest molecule proves the high quality of the combined pseudopotential–ab initio technique. Our results for all other molecules compared to experimental data indicate that we have a very promising technique.

A neutral atom with a magnetic moment can be bound to a current carrying wire. The atom is trapped in the high-field-seeking state and stabilized by angular momentum. In an atomic-beam experiment the guiding of Na atoms along a 1-m-long, 150-μm-diam, current carrying, tungsten wire is demonstrated. By adding a charged ring around the wire one can create a three-dimensional microscopic trap for neutral atoms. These traps confine the atoms in the lowest-energy spin state.

We develop an optimal control technique (OCT) in order to design a secondary optical pulse that can control the propagation of an arbitrary primary optical pulse in a medium consisting of three-level systems. The output primary pulse shape can be manipulated by designing the shape of the secondary pulse. The OCT is shown to be better than the earlier proposed pulse schemes for protecting the magnitude and shape of the primary pulse from reshaping by the medium.

A process for coherent hard-x-ray generation is suggested, which is based on the idea that high-intensity, ultrashort laser pulses can be coupled into a crystal before the lattice structure is destroyed. In the presence of the lattice periodicity, additional momentum can be transferred to the electrons that are moving in the strong light field. This additional momentum supplied by the crystal results in a substantial decrease of the threshold pump laser intensity required for hard-x-ray generation as compared to free electrons. The lattice is also utilized to select the frequency of the emitted x rays via Bragg coupling. A numerical estimation for the yield of the proposed mechanism gives an output power of some 10 W in the range of 1–10 keV of photon energies by using a state-of-the-art optical pulse with a peak intensity of about ${10}^{17}$ W/${\mathrm{cm}}^2$ and a pulse duration of 30 fs.

The interaction of intense ultrashort laser pulses from a chirped pulse amplification titanium sapphire laser system with dielectric and metallic surfaces was studied. With a p-polarized incident beam and a large angle of incidence we have observed odd and even harmonics of high order with relatively smooth roll-off in the harmonic spectra. The shortest wavelength was 55.3 nm, corresponding to the 15th harmonic order.

Dispersive quadratic media with wave mixing between the first- and second-harmonic modes due to a ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ nonlinearity are shown to inhibit wave collapse and to support stable solitons. The stability of this coupled-soliton family is demonstrated by means of a Lyapunov analysis based on the energy integral of the wave-coupling equations. The dynamics of the coupled modes is finally studied using a virial identity, which predicts either a stable propagation of the mutually trapped solitons or a spreading of both waves, depending on the incident-beam power.

The quantum-mechanical traversal- (tunneling) time problem is reformulated in terms of a square-integrable amplitude distribution (wave function) whose evolution is governed by a generalized Schrödinger equation. The method uses an analogy between quantum mechanics and classical Brownian motion. Brownian and quantum traversal-time distributions are evaluated by the direct integration of corresponding equations of motion. The general relation between Feynman and Schrödinger quantum mechanics is discussed.

The longitudinal recoil-ion momentum distributions of single ionization in collisions between fast heavy ions and atoms are analyzed by exploring the three-body kinematics and its relation to dynamic processes. It is found that there is a kinematic threshold for the longitudinal recoil-ion momentum distributions that can be ascribed to electron capture to the continuum (ECC). The finite cross section at threshold provides unambiguous evidence of the divergence of the ECC peak when the electron velocity is equal to the projectile velocity. Other aspects associated with the ionization process, such as soft-electron emission and binary-encounter collision, are also studied. Theoretical longitudinal recoil-ion momentum distributions are also compared to existing experiments.

A class of complex solutions to the time-independent Hamilton-Jacobi equation in the real-valued configuration space that represent multidimensional nonclassical motions such as dynamical tunneling, namely, energetically allowed but dynamically forbidden transition, as well as the ordinary tunneling are shown. We introduce a quantity called ‘‘parity of motion’’ into each coordinate in configuration space for the Hamilton-Jacobi equation and thereby construct the solutions. Positive parity induces merely ordinary classical motion, while negative parity allows nonclassical motion such as tunneling. These solutions are classified by a given set of parities, each class of which forms a sheet in the entire solution space. New canonical equations of motion are derived with which nonclassical paths are generated in each sheet. Furthermore, it is shown that each sheet is associated with two kinds of action integrals: One, which is real valued, satisfies the principle of least action, thereby generating both ordinary and tunneling trajectories, but is not a solution to the Hamilton-Jacobi equation, while the other action is a solution to the time-independent Hamilton-Jacobi equation, and is complex valued in a tunneling region. Only in Newtonian mechanics, which forms an extreme sheet having all the parities positive, do these two actions happen to coincide with each other. Numerical examples for dynamical tunneling among tori in the Hénon-Heiles system and ordinary potential tunneling in a three-dimensional system are presented.

A direct integration of the Heisenberg equations of motion yields expansions of the position and momentum operators x(t) and p(t), each as an infinite series in terms of the initial Weyl-ordered basis set {${\mathit{S}}_{\mathit{m},}$n} formed from x(0) and p(0), with c-number time-dependent coefficients. This method is applied to the problem of tunneling in a symmetric and an asymmetric quartic potential. The expectation values of the position and momentum operators with minimum uncertainty wave packet 〈0‖x(t)‖0〉 and 〈0‖p(t)‖0〉 can be calculated accurately for a maximum time that is short compared to the period of oscillation of the wave packet. From the result of this calculation, with the help of Prony’s method one can determine the level spacings for the low-lying states. In addition, in this formulation the wave packet retains its shape; therefore, one can study the trajectory 〈0‖x(t)‖0〉 and 〈0‖p(t)‖0〉 as the quantal analogue of the motion of the system in phase space.

We examine some surprising results that have been obtained for pre- and postselected quantum systems. We show that these results depend on a counterfactual interpretation of the rule of Aharonov, Bergmann, and Lebowitz [Phys. Rev. 134, B1410 (1964)] (the ABL rule) and that this interpretation is not valid in general. We then argue, with the help of the consistent histories interpretation of quantum mechanics, that there is a special class of situations where application of the counterfactual interpretation of the ABL rule can be justified. We then reexamine the aforementioned surprising results.

It has been recently proven that the bound states of the one-dimensional Schrödinger equation H${\mathrm{\psi }}^{\left(\mathit{i}\right)}$=${\mathit{E}}^{\left(\mathit{i}\right)}$${\mathrm{\psi }}^{\left(\mathit{i}\right)}$ in [0,∞) can be approximated by those of the corresponding Dirichlet eigenproblem ${\mathit{H}}_{\mathit{R}}$${\mathrm{\psi }}_{\mathit{R}}^{\left(\mathit{i}\right)}$=${\mathit{E}}_{\mathit{R}}^{\left(\mathit{i}\right)}$${\mathrm{\psi }}_{\mathit{R}}^{\left(\mathit{i}\right)}$ in a finite box [0,R] when R→∞. In this paper, we use a set of mathematical criteria that guarantee the correct calculation of expectation values in the frame of Hilbert spaces, to show that correct expectation values of most physical operators S are obtained by using the equation ${\lim }_{\mathit{R}\to \mathrm{\infty }}$〈${\mathrm{\psi }}_{\mathit{R}}^{\left(\mathit{i}\right)}$,S${\mathrm{\psi }}_{\mathit{R}}^{\left(\mathit{j}\right)}$〉= 〈${\mathrm{\psi }}^{\left(\mathit{i}\right)}$,S${\mathrm{\psi }}^{\left(\mathit{j}\right)}$〉, which includes operators not relatively form bounded by the Hamiltonian H. It is shown that standard numerical methods supply approximate wave functions ${\mathrm{\psi }}_{\mathit{R}\mathit{m}}^{\left(\mathit{i}\right)}$ for which the equation ${\lim }_{\mathit{m}\to \mathrm{\infty }}$〈${\mathrm{\psi }}_{\mathit{R}\mathit{m}}^{\left(\mathit{i}\right)}$,S${\mathrm{\psi }}_{\mathit{R}\mathit{m}}^{\left(\mathit{j}\right)}$〉= 〈${\mathrm{\psi }}_{\mathit{R}}^{\left(\mathit{i}\right)}$,S${\mathrm{\psi }}_{\mathit{R}}^{\left(\mathit{j}\right)}$〉 holds true. Thus, combining the previous limits we obtain a general approach to compute correct expectation values. It is shown how this approach agrees with the results found by other authors in special cases. In the particular case of computing approximate wave functions ${\mathrm{\psi }}_{\mathit{R}\mathit{m}}^{\left(\mathit{i}\right)}$ with the Ritz method, we show, analytically and numerically, that correct convergence toward the expectation values of high power of moment operators ${\mathit{r}}^{\mathit{k}}$ holds even when the basis functions have an analytic structure that substantially differs from that of the exact wave function.

We have formulated the quantum inverse problem for the unstable nonlinear Schrödinger equation that forms the basis of nonlinear optics, following the modified approach of Sklyanin. Due to the nonexistence of the vacuum for the corresponding Lax L operator, the algebraic Bethe ansatz cannot be formulated. This difficulty is removed by recourse to the functional Bethe ansatz. The whole analysis is performed by considering different boundary conditions at the two ends of the interval on the x axis. Both signs of the nonlinearity are treated, corresponding to ‘‘bright’’ and ‘‘dark’’ solitons.

Two-photon polarization-correlation measurements have been performed in order to test local realism under conditions in which the two photons pass through quarter-wave plates before reaching the polarizers. The motivation for this experiment is the fact that two previous experiments with quarter-wave plates preceding the polarizers failed to observe statistically significant violations of locality [J. F. Clauser, Nuovo Cimento 338, 740 (1976); A. J. Duncan, H. Kleinpoppen, and Z. A. Sheikh, in Bell’s Theorem and the Foundations of Modern Physics, edited by A. van der Merwe, F. Selleri, and G. Tarozzi (World Scientific, Singapore, 1992), p. 161]. We find that the Clauser-Horne type of Bell inequality is violated by about 40 standard deviations. Possible reasons for the failure of earlier experiments are discussed.

We study the time evolution of a linear superposition of two spatially separated wave packets, and we focus on the entanglement of the two distinct branches of the state vector with the environment. We focus in particular on the dynamics of a dissipative oscillator under the influence of objective processes of wave-function collapse, the continuous spontaneous localizations (CSL) recently proposed by Ghirardi et al. [G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990)]. We prove that the entanglement of the system of interest with the environment induces an accumulation of spontaneous wave-function collapses denoted by us as the environment-enhanced CSL process. This process of CSL accumulation is triggered by the same mechanism of interaction between the quantum system and the environment as that responsible for relaxation and dissipation. In agreement with the predictions of a preceding paper of our group [D. Vitali, L. Tessieri, and P. Grigolini, Phys. Rev. A 50, 967 (1994)], the CSL processes are shown to produce negligible effects at the statistical level. However, if we assume the attitude stimulated by the recent literature on optical quantum jumps, which is forcing us to adopt individual-system pictures, we show that the single runs are characterized by processes of wave-function collapses occurring at times compatible in principle with the experimental observation.

The intimate connection between the Berry phase and the nonstationarity of a quantum state is discussed. For a quantum system with time-independent Hamiltonian $H$, there may exist stationary states. It is shown that for a stationary state, the Berry phase always vanishes, and only for a nonstationary state after a cyclic evolution might the Berry phase appear. For time-dependent $H$, there exists no exactly stationary state, hence the Berry phase may appear.