Recently, there has been some controversy about the results of two papers, one by Liu and Parr [Chem. Phys. Lett. 278, 341 (1997)] and one by Nesbet [Phys. Rev. A 58, R12 (1998)]. It is pointed out that the two problems have the same origin, which is the fact that the wave-function–density–wave-function mapping in density-functional theory is not an identity.

Measurements are ordinarily described with respect to absolute “Newtonian” time. In reality, however, the switching-on of the measuring device at the instance of the measurement requires a timing device. Hence the classical time t must be replaced by a suitable quantum time variable τ of a physical clock. The main issue raised in this paper is that while doing so, we can no longer neglect the back reaction due to the measurement on the clock. For a von Neumann measurement model, this back reaction yields a bound on the accuracy of the measurement. When this bound is violated the result of a measurement is generally not an eigenvalue of the observable, and furthermore, the state of the system after the measurement is generally not a pure state. We argue that as a consequence, a subclass of observables in a closed system cannot be realized by a von Neumann–like measurement.

We present the quantum theory of a Stern-Gerlach system in contact with a linearly dissipative environment at an arbitrary temperature. The dynamics of the reduced density matrix of the system is calculated using the path integral technique, under a general condition when the system and its environment may not be decoupled initially. We analyze the behavior of the density matrix in the long-time limit and compute the time scales of decay of the elements off-diagonal in the coordinate and the momentum space, for the cases of high temperature, zero temperature, and intermediate temperature baths.

Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these two bases and to emphasize its interpretation as a Fourier transform. We then prove a general sufficient condition for complete separability in terms of the spin coefficients and give necessary and sufficient conditions for the complete separability of a class of generalized Werner densities. As a further application of the theory, we give necessary and sufficient conditions for full separability for a particular set of n-qubit states whose densities all satisfy the Peres condition.

Positron binding to silver and gold atoms was studied using a fully ab initio relativistic method, which combines the configuration-interaction method with many-body perturbation theory. It was found that the silver atom forms a bound state with a positron with binding energy 123 (±30%) meV, while the gold atom cannot bind a positron. Our calculations reveal the importance of the relativistic effects for positron binding to heavy atoms. The role of these effects was studied by varying the value of the fine-structure constant $\alpha .$ In the nonrelativistic limit, $\alpha =0,$ both systems $e^{+}\mathrm{Ag}$ and $e^{+}\mathrm{Au}$ are bound with binding energies of about 200 meV for $e^{+}\mathrm{Ag}$ and 220 meV for $e^{+}\mathrm{Au}.$ Relativistic corrections for a negative ion are essentially different from that for a positron interacting with an atom. Therefore the calculation of electron affinities cannot serve as a test of the method used for positron binding in the nonrelativistic case. However, it is still a good test of the relativistic calculations. Our calculated electron affinities for silver (1.327 eV) and gold (2.307 eV) atoms are in very good agreement with corresponding experimental values (1.303 and 2.309 eV, respectively).

Using hyperspherical close-coupling method cross sections for charge-transfer reaction for $\mathrm{H}\mathrm{}\left(1s\right)+{\mu }^{+}$ collisions are calculated from threshold up to 2 eV. It is shown that partial-wave cross sections can be obtained using a rotor model which is similar to the standard perturbed stationary-state approximation for ion-atom collisions. The results are compared to ${\mathrm{D}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions to examine the dependence of transfer cross sections on the masses of the collision partners. Feshbach and some shape resonances are also examined.

The ground-state energies of interacting bosons are computed beyond the mean-field approximation by a new method known as reduced Hamiltonian interpolation (RHI) [D. A. Mazziotti and D. R. Herschbach, Phys. Rev. Lett. 83, 5185 (1999)]. In the RHI, the N-particle Hamiltonian is represented through a sequence of p-particle expanded and reduced Hamiltonians that give upper and lower bounds on the true energy. Assimilating ideas from N representability and dimensional interpolation, the RHI technique interpolates over the number p of quasiparticles to determine the N-particle energy with close upper and lower bounds. With the Hellmann-Feynman theorem, we extend the RHI to compute the two-particle reduced density matrix (2RDM) as well as the energy. We examine both the computational advantages of RHI in comparison with traditional methods and the possibility of extending the RHI to treat fermion correlation. Applied to bosons with harmonic interactions as well as a two-level system, the RHI technique yields more than 99% of the correlation energy and an accurate correlation correction for the elements of the 2RDM.

Demonstrating that, despite loss processes, Bose-Einstein condensates can be formed in steady state is a prerequisite for obtaining a coherent beam of atoms in a continuous-wave atom laser. In this paper we propose a method for loading atoms into the thermal component of a Bose condensed cloud confined in a magnetic trap. This method is aimed at allowing steady-state dynamics to be achieved. The proposed scheme involves loading atoms into the conservative magnetic potential using the spontaneous emission of photons. We show that the probability for the reabsorption of these photons may be small.

The photon-photon scattering in vacuum can give rise to the second-harmonic generation of intense laser radiation in a dc magnetic field in the “box” diagram approximation of quantum electrodynamics if the symmetry of interaction is broken by modulation or/and nonuniformity of optical wave +dc field system in time or/and space. Specific examples considered here are: an optical pulse plane wave or a Gaussian laser beam propagating in uniform or nonuniform dc fields.

The energy dependence of the total cross section for electron scattering by methane and its chloride compounds has been studied by considering the latest experimental results and those predicted by the Born-Bethe theory. A simple analytical expression depending on the number of electrons and the polarizability of the target is proposed for these molecules. The energy dependence given by this formula shows an asymptotic behavior for increasing energy in better agreement with the Born-Bethe theory. The inconsistency with the Born-Bethe theory of the two-parameter formula given recently by Karwasz et al. has also been shown.

The second-sideband Raman excitation of the motional ground state of a single ion trapped in a harmonic potential is analyzed in the strong Raman coupling regime. Appropriate Raman motional excitations driven by strong standing-wave lasers can be used to split the motional ground state to a macroscopic motional wave-packet state with spatial separation between the split parts comparable to the dimension of the involved ionic transition wavelengths. A spatial flat wave-packet with coherence persisting in a wide spatial range can also be excited. The spatial spread of such a spatial flat macroscopic motional wave-packet oscillates periodically during the free-time evolution in the harmonic trap, with a spatial flat distribution persisting at most of the oscillating times.

It is proven that the phase shift of a polarized neutron interacting with a spatially uniform time-dependent magnetic field demonstrates the same physical principles as the magnetic Aharonov-Bohm effect. The crucial role of inert objects is explained, thereby proving the quantum-mechanical nature of the effect. It is also proven that the nonsimply connectedness of the force-free region is not a profound property of the system, and that it cannot be regarded as a sufficient condition for a nonzero phase shift.

We consider the interaction of an harmonic oscillator with the quantum field via radiation pressure. We show that a “Schrödinger cat” state decoheres in a time scale that depends on the degree of “classicality” of the state components, and which may be much shorter than the relaxation time scale associated to the dynamical Casimir effect. We also show that decoherence is a consequence of the entanglement between the quantum states of the oscillator and field two-photon states. With the help of the fluctuation-dissipation theorem, we derive a relation between decoherence and damping rates valid for arbitrary values of the temperature of the field. Coherent states are selected by the interaction as pointer states.

We investigate theoretically the speed limit of quantum gate operations for ion trap quantum information processors. The proposed methods use laser pulses for quantum gates that entangle the electronic and vibrational degrees of freedom of the trapped ions. Two of these methods are studied in detail and for both of them the speed is limited by a combination of the recoil frequency of the relevant electronic transition, and the vibrational frequency in the trap. We have experimentally studied the gate operations below and above this speed limit. In the latter case, the fidelity is reduced, in agreement with our theoretical findings.

Absolute measurements of the energies of resonance lines in heliumlike vanadium on an electron-beam ion trap are reported. The $1s2p{}^1{P}_1\to {1s}^2,$ $1s2p{}^3{P}_2\to {1s}^2$ $(1s2p{}^3{P}_1\to {1s}^2$ and $1s2p{}^3{P}_0\to {1s}^2)$ blend and $1s2s{}^3{S}_1\to {1s}^2$ transitions are $5205.10\pm 0.14\mathrm{eV},$ $5189.12\pm 0.21\mathrm{eV},$ $5180.22\pm 0.17\mathrm{eV},$ and $5153.82\pm 0.14\mathrm{eV},$ respectively. This agrees with recent theoretical calculations and the experimental precision lies at the same level as the current uncertainty in theory (0.1 eV). These measurements represent a 5.7–8% determination of the QED contribution to the transition energies and are the most precise measurements of heliumlike resonance lines in the $Z=19\mathrm{}–31$ range. The measurement of the $1s2s{}^3{S}_1\to {1s}^2$ transition is also sensitive to the $1s2s{}^3{S}_1$ QED contribution at the 40% level. The intensity of the strong $1s2p{}^3{P}_1\to {1s}^2$ component of the blend compared to the total blend intensity is $94\%\pm 12\%.$ This is in accord with current theoretical predictions but disagrees with an earlier reported ratio.

Accurate electronic structure calculations for diatomic molecules have been performed, using the Krieger-Li-Iafrate (KLI) approximation to the optimized potential method (OPM) for the evaluation of the exact exchange potential of density-functional theory. It is found that the KLI scheme provides an excellent approximation to the full OPM for these systems. The deviations between both variants of the OPM are smaller than the differences resulting from the use of different basis sets. Furthermore, it is shown that the spectroscopic constants obtained with the exchange-only KLI approach are very close to Hartree-Fock values.

Measurement of mass-, energy-, and angle-resolved fragment ions reveals that the $\beta$ value for ${\mathrm{C}}^{+}$ with kinetic energy $>~3\hspace{0.5em}\mathrm{eV}$ is $\sim 0.9$ in the region of the $\mathrm{O}\hspace{0.5em}1\overrightarrow{s}2{\pi }_u$ excitation and that the $\beta$ value for ${\mathrm{O}}^{+}$ with kinetic energy $>~4\hspace{0.5em}\mathrm{eV}$ varies from $-0.23$ to $-0.57$ across the O $1\overrightarrow{s}2{\pi }_u$ resonance. These findings postulate that the ${\mathrm{CO}}_2$ molecule excited to the lower branch of the vibronically split O ${1s}^{-1}2{\pi }_u$ excited states deforms into a bent geometry while the molecule excited to the higher branch remains in a linear geometry.

The dominant long-range interaction of an alkali-metal atom with charged particles at low energies is given for large separation R by the dispersive potential $W\simeq -{\alpha }_d{/R}^4$ in terms of the dipole polarizability ${\alpha }_d.$ For atoms prepared initially in Rydberg states of quantum numbers (n, l), the potential assumes a more complicated form due to the complete or near degeneracy of the n manifold. Contributions to the polarizability are treated in two parts, (a) one for the nondegenerate states and (b) the other for the degenerate or near degenerate cases. It is shown that ${\tilde{\alpha }}_d^{\mathrm{}\left(b\right)\mathrm{}}$ for case (b) is in general R dependent, and in the limit of complete degeneracy, diverges as $R^2.$ That is, for a small energy gap Δ between a pair of nearly degenerate states which are dipole coupled, the dispersion potential $W^{\mathrm{}\left(b\right)\mathrm{}}\simeq {D/R}^2$ for $R<\mathrm{}{R}_x$ and $W^{\mathrm{}\left(b\right)\mathrm{}}\simeq -{\alpha }_d^{\mathrm{}\left(b\right)\mathrm{}}{/R}^4$ for $R>\mathrm{}{R}_x,$ where D is the dipole moment, $R_x=[2|D/\Delta |{]}^{1/2},$ and ${\alpha }_d^{\mathrm{}\left(b\right)\mathrm{}}\simeq D^2/\Delta .$ They may also compete with a ${1/R}^3$ potential for Rydberg atoms with $l>\mathrm{}0.\mathrm{}$ The total ${\alpha }_d$ can be very large in magnitude for small Δ and even assume negative values, but the corresponding $R_x$ also increases as Δ decreases. The validity region in R of the $R^{-4}$ behavior of the potential recedes to larger R as the polarizability grows. A general formula for ${\alpha }_d$ is given, taking into account the effects of fine-structure splitting, the Lamb shift, and quantum defects.

Ionization and electron transfer in collisions of bare ions from neutral target atoms with many active electrons are investigated within the independent particle model. We propose a simple model for the inclusion of time-dependent screening effects and discuss the question of how to analyze the solutions of the single-particle equations in order to avoid fluctuating transition probabilities, which normally occur when the effective mean-field potential depends on the propagated orbitals. The basis generator method is used to solve the single-particle equations for the ${\mathrm{He}}^{2+}+\mathrm{Ne}$ collision system in the energy range of 5 to 1000 keV/amu. It is shown that time-dependent screening effects reduce the cross sections for ionization and capture at low and intermediate impact energies significantly. Good overall agreement with experimental data is found except for the higher final charge states of the target ion.

A time-dependent close-coupling method is used to calculate the electron-impact ionization cross section for the outer $2p$ subshell of both carbon and neon atoms. The inner $1s$ and $2s$ subshells are treated using pseudopotentials, while interaction with the remaining $2p$ core electrons is handled in a configuration-average approximation. When the time-dependent ionization cross section for the $2p$ subshell of carbon is combined with distorted-wave ionization cross sections for the $2s$ subshell, the resulting total cross section is in reasonable agreement with previous experimental measurements. However, when the time-dependent ionization cross section for the $2p$ subshell of neon is combined with distorted-wave ionization cross sections for the $2s$ subshell, the resulting total cross section is substantially higher than all previous experimental measurements. Further $\mathrm{LS}$ term-dependent distorted-wave ionization cross sections for the $2p$ subshell of neon suggest the need for extending the time-dependent close-coupling method to include a full Hartree-Fock interaction with the remaining $2p$ core electrons.