The expression for the exact ground-state energy as given by Horn and Weinstein [Phys. Rev. D 30, 1256 (1984)] is approximated using a probability distribution function having a δ function and a uniform distribution. The expression obtained up to second order does not have the singularity that one encounters in the connected-moment expansion. It also gives the same kind of expression for the ground-state energy that recently has been given by Mancini, Zhou, and Meier [Int. J. Quant. Chem. 50, 101 (1994)] when the third moment becomes negative.

The wave functions with the most general boundary conditions consistent with the conservation of probability for a free particle inside a box [Phys. Rev. D 42, 1194 (1990)] are calculated. The exact Green’s functions and propagators for some special cases are obtained and a semiclassical approach for the propagators is considered. Finally, the influence of the boundary conditions over the path integral’s formalism is briefly discussed.

We study the evolution of statistical distance on the Bloch sphere under unitary and nonunitary dynamics. This corresponds to studying the limits to clock precision for a clock constructed from a two-state system. We find that the initial motion away from pure states under nonunitary dynamics yields the greatest accuracy for a ‘‘one-tick’’ clock; in this case the clock’s precision is not limited by the largest frequency of the system.

A semiclassical approximation is derived from the autocorrelation function describing the excitation and detection of Rydberg wave packets by pairs of phase-locked laser pulses. The resulting expression is in terms of a sum over Kepler trajectories, and provides a direct explanation of the periodicity and spreading of the wave packet at short times when the evolution is classical. More surprisingly, this solution also provides an accurate description of the complex revival behavior of the wave packets, which is nonclassical. The phases of the wave packets, which are detected by the pulse-locking scheme, are also accurately given by analytical expressions derived from the semiclassical sum. The phase of the wave packets at short times have a simple interpretation as the phases of Bohr-Sommerfeld, and are related to Berry’s phase. The semiclassical expression for the phases of the nonclassical revival wave packets is simpler than the corresponding quantal solution.

In relativistic heavy-ion collisions, the strong Lorentz-contracted electromagnetic fields are capable of producing copious numbers of lepton pairs through the two-photon mechanism. Monte Carlo techniques have been developed that allow the exact calculation of production by this mechanism when a semiclassical approximation is made for the motion of the two ions. Here, we develop a hybrid Monte Carlo technique that enables us to calculate the impact-parameter dependence of the two-photon mechanism for lepton-pair production, and by using this result we obtain the probability distribution for multiple-pair production as a function of impact parameter. Computations are performed for S+Au and Pb+Pb systems at 200 and 160 A GeV, respectively. We also compare our results with the equivalent-photon approximation and elucidate the differences.

We study the quantum dynamics of the simplest dissipative system, a particle moving in a constant external field and interacting with a bath of harmonic oscillators with Ohmic spectral density. Applying the main idea and methods developed in our recent work [L. H. Yu and C. P. Sun, Phys. Rev. A 49, 592 (1994)] to this system, we obtain the simple and exact solutions for the coordinate operator of the system in the Heisenberg picture and the wave function of the composite system of the system and the bath in the Schrödinger picture. An effective Hamiltonian for the dissipative system is explicitly derived from these solutions. The meaning of the wave function described by this effective Hamiltonian is clarified by analyzing the effect of the Brownian motion. In particular, the general effective Hamiltonian for an arbitrary potential is directly derived with this method for the case when the Brownian motion can be ignored. Using this effective Hamiltonian, we show an interesting result that the dissipation suppresses the wave-packet spreading.

The pure recoil correction to hydrogenlike energy levels is revisited. An alternative method for its evaluation is presented. We confirm that the previous result [Doncheski et al., Phys. Rev. A 43, 2125 (1991)] of the ${\mathit{m}}^2$/M(Zα${)}^6$ contribution was missing some important terms. Our result is ΔE=(${\mathit{m}}^2$/M)(Zα${)}^6$/${\mathit{n}}^3$[4 log(2)-7/2]. A new value of the deuteron radius is obtained by comparing theory to the measurement of the hydrogen-deuterium isotope shift.

The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a system, based on a symbiosis of two existing systems, for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible experimental implementation.

The estimation of phase shift in realistic experiments is addressed here. Provided that the phase concept is not ideal, the phase shift should always be inferred from the performed measurement. Particulary, two different estimations are suggested. The conditional probability is given by the experimentally observable dependence of the measured probability on the phase shift. As an explicit example, the accuracy of the phase measurement on the Mach-Zehnder interferometer is evaluated using different methods for comparison.

We calculate the impact-parameter-dependent total probability ${\mathit{P}}_{\mathrm{total}}$(b) for the electromagnetic production of electron-positron pairs in relativistic heavy-ion collisions in lowest order. We study expecially impact parameters smaller than the Compton wavelength of the electron, where the equivalent-photon approximation cannot be used. Calculations with and without a form factor for the heavy ions are done; the influence is found to be small. The lowest-order results are found to violate unitarity and are used for the calculation of multiple-pair production probabilities with the help of the approximate Poisson distribution already found in earlier publications.

We develop a nonequilibrium time-dependent functional theory of coupled interacting fields in terms of the Liouvillian quantum field dynamics. In this theory the expectation values of the appropriate field operators are treated as the functional variables. Thus, the formalism proposed here goes beyond the existing time-dependent density-functional method, in that we now have a mixed-state multivariable dynamical theory. A large class of condensed matter problems, with the given initial condition that the system be in thermodynamic equilibrium and subjected to time-dependent external forces, can now be examined. In particular, we formulate the self-consistent coupled equations for the electron, ion, and the electromagnetic fields. The above formalism provides a firm physical and mathematical basis for time-dependent dynamical simulation procedures such as those envisaged in the Car-Parrinello approach by replacing the fictitious Lagrangian by a precise action principle. The theory involves a certain functional representing the mutual interactions and correlations among these fields. In parallel with this, we also generalize the Baym Φ-derivable method in many-body theory to investigate the class of problems mentioned above. This involves a functional of the exact one-particle Green functions. We compare the two methods and suggest the use of the latter in the former scheme as a way of going beyond the simple mean-field schemes. We illustrate the utility of the framework by citing a variety of illustrative examples.

Relativistic corrections to the ground-state energies of the He, ${\mathrm{Be}}^{2+}$, ${\mathrm{Ne}}^{8+}$, Be, and Ne atoms are calculated using first-order perturbation theory, yielding results accurate to order 1/${\mathit{c}}^2$, where c is the velocity of light. Accurate nonrelativistic wave functions and variational and diffusion quantum Monte Carlo techniques are used to calculate the required expectation values. Our results agree with previous work for the two-electron cases, and in all cases we obtain excellent agreement with the experimental total energies. Our values for the expectation values of the relativistic correction to the Coulomb interaction (the Breit interaction) are considerably smaller than those calculated within Dirac-Fock theory, and therefore our calculations give a quantitative estimate of the importance of correlation effects in determining this contribution.

We have measured the 1s2s ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$–1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ and 1s2s ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$–1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ fine-structure transition wavelengths in the heliumlike ${\mathrm{Ar}}^{16+}$ ion using the beam-foil spectroscopy technique with position-sensitive photon detection. The wavelength results are 559.944(16) Å for the J=1–2 transition and 661.533(18) Å for the J=1–0 transition, which correspond to measurement precisions of about 2×${10}^{\mathrm{-}5}$ a.u. in the transition energies. These values are sensitive to the relativistic contributions in the transition energies to <500 ppm and to the total QED corrections to <0.5%. The measurements confirm the significance of (Zα${)}^4$-dependent relativistic corrections to the n=2 state fine structures suggested by recent calculations. The small remaining discrepancies between these measurements and the accurate theoretical values suggest that the magnitude of uncalculated higher-order QED terms is about 0.15(Zα${)}^4$ a.u. Our experimental results disagree with an earlier recoil-ion measurement for the ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$– ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ transition wavelength.

A model is developed that permits the calculation of the radiation emitted by complex or highly charged ions in a plasma. The model is based on the usual separation of the plasma-emitter interaction into the homogeneous broadening effects of the fast electrons and the inhomogeneous broadening arising from slow ions. For plasma conditions where the ion motion can be neglected, the spectrum is the usual static line shape. To account for ion dynamics, the frequency-fluctuation model is introduced by decomposing the line shape of each radiative transition into a sum of radiative channels that are associated with the smallest observable inhomogeneities that form the static profile. The fluctuations of the ion microfield, the ion dynamics effect, is modeled by an exchange process between the static radiative channels. This results in both a smoothing and an overall coalescence of the radiative channels and depends strongly on an averaged characteristic fluctuation rate associated with the dynamics of the interaction of the local plasma microfield with the ion. This rate is formally related to the double-time field-field correlation function behavior. This stochastic model of the observed frequency fluctuations permits fast and accurate calculations of the emitted spectral profiles, including ion dynamics emitted by complex ions in a wide range of plasma conditions.

Spectroscopic properties of all excited states of KRb dissociating into 4s(K)+5s(Rb), 4s(K)+5p(Rb), and 4p(K)+5s(Rb) are studied, using quantum chemical calculations. Only the 1 and 2 ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$ states showed a weak coupling between the 4s(K)+5p(Rb) and the 4p(K)+5s(Rb) components. The dipole moments, atomic orbital populations, and transition dipole moments of those two states showed a twin nature. Calculated Einstein coefficients for the 1 ${}_{}{}^1{}_{}{}^{}\mathit{X}$ and 2 ${}_{}{}^1{}_{}{}^{}\mathit{X}$ dipole transitions predict unusually rich band spectra. The intensity distributions of those two transitions showed a remarkable difference.

In the asymmetric (or planetary) doubly excited states of the helium atom, one of the electrons is excited much more than the other. The motion of the electrons is strongly correlated: both of them reside mostly on the same side of the atomic nucleus. An adiabatic theory for such states is based on the approximate separation of rapid and slow motion. The rapid motion is that of the inner electron along its elliptic orbit. The parameters of the orbit (eccentricity and the aphelion vector) slowly evolve in time. The other slow motion is the radial vibrations of the outer electron. The effective Hamiltonian is constructed as the average of the exact Hamiltonian over the rapid motion. In the quadratic approximation two types of slow motion are separated and reduced to two harmonic oscillators. The unexpected feature is that the ratio of the related frequencies is very simple: 1:2. The ratio is changed when the outer electron is replaced by the particle with an arbitrary mass. The slow motions are quantized and the series of the energy levels are obtained. In the case of infinite mass of the outer particle, the potential curves of the quasimolecule are calculated. The present purely analytic results are compared with the numerical data.

A scheme of approximation of the Kohn-Sham exchange potential ${\mathit{v}}_{\mathit{x}}$ is proposed, making use of a partitioning of ${\mathit{v}}_{\mathit{x}}$ into the long-range Slater ${\mathit{v}}_{\mathit{S}}$ and the short-range response ${\mathit{v}}_{\mathrm{resp}}$ components. A model potential ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ has been derived from dimensional arguments. It possesses the proper short-range behavior and the atomic-shell stepped structure characteristic for ${\mathit{v}}_{\mathrm{resp}}$. When combined with the accurate ${\mathit{v}}_{\mathit{S}}$, ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ provides an excellent approximation to the exchange potential of the optimized potential model ${\mathit{v}}_{\mathit{x}}^{\mathrm{OPM}}$. With the generalized-gradient approximation to ${\mathit{v}}_{\mathit{S}}$ ${\mathit{v}}_{\mathrm{resp}}^{\mathrm{mod}}$ provides an efficient density-functional-theory approach that fits closely the form of the accurate exchange potential and yields reasonably accurate exchange and total energies as well as the energy of the highest occupied orbital.

The dynamics of the wave packet generated by a short-pulse laser can be characterized by an autocorrelation function. The autocorrelation function is an experimentally measurable quantity. This paper shows that the autocorrelation function can be written as a sum of modified Gaussian functions that correspond to the closed orbits of the system. The autocorrelation function can be calculated by using existing algorithms in closed-orbit theory. As an application of the theory, the autocorrelation function is obtained for a system that consists of an ${\mathrm{H}}^{\mathrm{-}}$ ion in a static electric field.

A theory of selective reflection and transmission is developed for a system consisting of a thin layer of a dilute atomic vapor sandwiched between two transparent solids with parallel interfaces. Strong effects of spatial dispersion due to the atomic motion and electronic quenching on gas-solid interfaces are accounted for. It is shown that both even and odd Doppler-free resonances may occur in selective reflection, depending upon the thickness of the vapor layer. It is also found that the amplitude of selective reflection is a result of the interference between reflections from the two boundaries of the vapor-solid interfaces and, hence, may be greatly enhanced under certain conditions.

The previously unmeasured neutron time-of-flight distributions for the reaction ${\mathrm{\pi }}^{\mathrm{-}}$p→${\mathrm{\pi }}^0$n in gaseous targets at pressures of 17 and 40 bar have been measured. The kinetic energy of the ${\mathrm{\pi }}^{\mathrm{-}}$p atoms at the instant of the nuclear reaction has been evaluated from the Doppler broadening of the neutron time-of-flight spectra. Evidence was found for ${\mathrm{\pi }}^{\mathrm{-}}$p atoms with kinetic energies of 75 eV. The present experimental data were interpreted within a cascade model that takes the evolution of the kinetic-energy distribution during the cascade into account. The parameters of the model were determined from experiments measuring neutron time of flight in liquid hydrogen and x-ray yields in gas. Coulomb deexcitation is responsible for the significant fraction of the high-energy component, whose intensities are compatible with the calculations of Bracci and Fiorentini [Nuovo Cimento 43A, 9 (1978)]. Stark mixing is found to be significantly stronger than in the commonly used straight-line approximation; the initial mean kinetic energy of 1–2 eV is consistent with the results of muonic hydrogen. The model therefore describes the cascade of pionic hydrogen over a range of pressures of three orders of magnitude. The implications for high-resolution x-ray measurements of the 1S-level nuclear width are discussed.