We derive the spectrum of fluctuations of the vacuum radiation pressure on a spherical perfectly reflecting mirror. From the fluctuation-dissipation theorem, we obtain the dissipative force exerted upon the mirror when it moves in vacuum. As in the classical problem of scattering by a plane wave, the spectrum presents a resonant behavior at wavelengths of the order of the sphere’s radius. The high-frequency limit agrees with Barton’s general result for a large body of arbitrary shape.

The question of (superluminal) signaling by means of quantum correlations is reconsidered and previous arguments are generalized and completed to yielding conclusive answers to the negative. Statistical analysis of the amplified input on the receiver’s side shows that the state discrimination needed for defining a signal is in conflict with the linearity of quantum dynamics. Connections with fundamental issues of quantum mechanics are pointed out.

It is shown that the evolution of an open quantum system whose density operator obeys a Markovian master equation can in some cases be meaningfully described in terms of stochastic Schrödinger equations (SSE’s) for its state vector. A necessary condition for this is that the information carried away from the system by the bath (source of the irreversibility) be recoverable. The primary field of application is quantum optics, where the bath consists of the continuum of electromagnetic modes. The information lost from the system can be recovered using a perfect photodetector. The state of the system conditioned on the photodetections undergoes stochastic quantum jumps. Alternative measurement schemes on the outgoing light (homodyne and heterodyne detection) are shown to give rise to SSE’s with diffusive terms. These three detection schemes are illustrated on a simple quantum system, the two-level atom, giving new perspectives on the interpretation of measurement results. The reality of these and other stochastic processes for state vectors is discussed.

Shapiro, Shepard, and Wong [Phys. Rev. Lett. 62, 2377 (1989)] suggested that a scheme of multiple phase measurements, using quantum states with minimum ‘‘reciprocal peak likelihood,’’ could achieve a phase sensitivity scaling as 1/${\mathit{N}}_{\mathrm{tot}}^2$, where ${\mathit{N}}_{\mathrm{tot}}$ is the mean number of photons available for all measurements. We have simulated their scheme for as many as 240 measurements and have found optimum phase sensitivities for 3≤${\mathit{N}}_{\mathrm{tot}}$≤120; a power-law fit to the simulated data yields a phase sensitivity that scales as 1/${\mathit{N}}_{\mathrm{tot}}^{0.82\pm 0.01}$. By using a combination of numerical and analytical techniques, we extend our results to higher values of ${\mathit{N}}_{\mathrm{tot}}$ than are accessible to our simulations; we find no evidence for phase sensitivities better than the benchmark 1/${\mathit{N}}_{\mathrm{tot}}$ sensitivity of squeezed-state interferometry. We conclude that reciprocal peak likelihood is not a good measure of phase sensitivity. We discuss other factors that are important to phase sensitivity.

We initiate a study of rates of quantum decoherence in regular and chaotic systems. The system of interest investigated is quite general, and the interaction with the surroundings is via a particular quantum-nondemolition coupling. We find that the averaged coherence, as measured by Tr${\mathrm{\rho }}^2$(t), decays faster asymptotically in chaotic than in regular systems; this is a direct result of the repulsion of energy levels in the former case. We also investigate the phenomenon of self-averaging, providing general conditions that ensure that averaged and unaveraged quantities, such as Tr${\mathrm{\rho }}^2$(t), coincide. We find good agreement between our analytic results and those obtained numerically for the circle and stadium billiards.

Recently Hardy has exhibited a striking new violation of local realism that occurs in a pair of interferometers that have been interconnected so that knowledge about the path chosen by a particle in one interferometer conveys some information about the path or paths chosen by the particle in the other interferometer. It has been demonstrated that particle annihilation and a two-photon interference effect can be exploited to give rise to this local realism violation. Here we show that in the case of fermion interferometers the Pauli exclusion principle can be exploited to give rise to this effect.

The Dirac equation in one dimension with a Lorentz scalar potential is associated with a supersymmetric pair of Schrödinger Hamiltonians ${\mathit{H}}_1$ and ${\mathit{H}}_2$. The ${\mathit{H}}_1$ and ${\mathit{H}}_2$ share the same energy spectrum and scattering phases. The shared spectrum includes the lowest states unless the Dirac equation allows a zero mode (a zero-energy bound state). This situation is unlike the common examples of supersymmetric quantum mechanics. The Dirac equation admits a zero mode only if the scalar potential has certain ‘‘topology.’’ Various such features are illustrated through explicit examples. In particular, the phase equivalence between ${\mathit{H}}_1$ and ${\mathit{H}}_2$ is exploited to construct transparent potentials for the Dirac equation in one dimension.

Electric-dipole polarizabilities of K, Rb, Cs, and Fr are calculated in the framework of the quasirelativistic method based on mass-velocity and Darwin terms in the Pauli Hamiltonian. The electron-correlation contribution due to atomic cores is taken into account at two levels of approximation. The next-to-valence-shell contributions follow from the appropriate complete active-space multiconfiguration self-consistent-field calculations while the remaining core correlation effects are evaluated by using a second-order-perturbation method. Both pure relativistic and mixed correlation-relativistic contributions are evaluated. The present nonrelativistic results for K (44.6 A${\mathrm{̊}}^3$), Rb (60.8 A${\mathrm{̊}}^3$), Cs (72.8 A${\mathrm{̊}}^3$), and Fr (81.8 A${\mathrm{̊}}^3$) are reduced by 0.8 A${\mathrm{̊}}^3$, 11.3 A${\mathrm{̊}}^3$, 11.5 A${\mathrm{̊}}^3$, and 33.5 A${\mathrm{̊}}^3$, respectively, due to relativistic and correlation-relativistic corrections. The quasirelativistic results for K, Rb, and Cs are in good agreement with experimental data. The predicted dipole polarizability of Fr is 48.3 A${\mathrm{̊}}^3$. Additionally, polarized basis sets for Cs and Fr for calculations of molecular electric properties have been generated in this study.

We have done a many-body-perturbation-theory calculation, up to second order, for 6s→6${\mathit{p}}_{1/2}$ and 6s→6${\mathit{p}}_{3/2}$ transitions for Cs using the Dirac-Fock orbitals as single-particle wave functions. The results show that many-body-perturbation-theory calculations for transition amplitudes do not converge well unless some infinite subsets of diagrams are included. A systematic way of including infinite subsets of diagrams based on the Green’s-function formalism that preserves gauge invariance of transition amplitudes in each step is proposed for future work.

A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence.

The 1${\mathit{s}}^2$2${\mathit{s}}^2$ ground-state energies of berylliumlike systems are calculated with a full-core plus correlation method. A partial saturation of a basis-function method is used to extrapolate a better nonrelativistic energy. The 1${\mathit{s}}^2$2${\mathit{s}}^2$ ionization potentials are calculated by including the relativistic corrections, mass polarization, and QED effects. These results are compared with the existing theoretical and experimental data in the literature. The predicted Be i, C iii, N iv, and O v ionization potentials are within the quoted experimental error. Our result for F vi, 1 267 606.7 ${\mathrm{cm}}^{\mathrm{-}1}$, supports the recent experiment of Engström [Phys. Scr. 31, 379 (1985)], 1 267 606(2) ${\mathrm{cm}}^{\mathrm{-}1}$, over the datum in the existing data tables. The predicted specific mass polarization contribution to the ionization potential for Be i, 0.006 88 a.u., agrees with the 0.006 74(100) a.u. from the experiment of Wen et al. [Phys. Rev. A 37, 4207 (1988)]. The calculated relativistic correction to the double ionization of Be i, -0.000 135 0 a.u., also agrees with the recent result, -0.000 135 a.u., of Lindroth et al [Phys. Rev. A 45, 1493 (1992)]. Using the calculated results of Z=4–10, 15, and 20, we extrapolated the results for other Z systems up to Z=25 for which the ionization potentials are not explicitly computed.

A model with all the radial degrees of freedom frozen is used to simulate the intrashell states of four-valence-electron atomic systems. By inspecting the two- and three-body densities, and by inspecting directly the eigenfunctions in appropriate subspaces, the features of geometric structure and of internal motion have been obtained. The effect of the spatial permutation symmetry has been emphasized. Although the interactions are spin independent, the correlations are found to be strongly spin dependent. All odd-parity states under consideration prefer the conjugate circles (CC) structure (two circles have a common diameter and have their planes vertical to each other). Two modes of motion are found in this structure, namely, the four-body head-on collision mode and the double two-body collisions mode. It is confirmed that the modes found in the quantum states are closely related to periodic solutions of classical mechanics.

The method of Ley-Koo and Bunge [Phys. Rev. A 40, 1215 (1989)] to evaluate nonrelativistic atomic two-body integrals without a series expansion of the interaction function is extended to the relativistic case. Explicit and general formulas are obtained for the efficient evaluation or handling of atomic electron-electron integrals over bispinorial one-electron functions, including the electromagnetic interaction with retardation effects and the parity-nonconserving weak interaction in both the Yukawa and contact forms.

The time-independent Hamiltonian version of QED provides a foundation for a relativistic description of atomic structure and scattering, with virtual-pair effects treated in a consistent manner. Since the spectrum of the Hamiltonian is bounded from below, the problem of ‘‘variational collapse,’’ associated with the existence of negative-energy solutions of the Dirac equation, does not arise. For the same reason, extremum principles of the Rayleigh-Ritz type may be applied. These features are illustrated here in the context of a system consisting of two electrons in an external Coulomb field. An effective Hamiltonian describing this system is constructed in a ladder approximation that accounts for the virtual creation and annihilation of electron-positron pairs. It is shown that this pair contribution to the effective Hamiltonian satisfies a maximum principle and that, consequently, a minimax principle is available for the approximate evaluation of the binding energy of the heliumlike ion. The relation between the present treatment of virtual-pair effects and that based on the Bethe-Salpeter equation in the ladder approximation is clarified.

The energies and linewidths of the 7sng autoionizing states of Ba are reported for n=6–22. This series has localized perturbers near n=8 and near n=14. The scaled linewidth of the lower, unperturbed 7sng states is ${\mathit{n}}^{\mathrm{*}3}$Γ=γ=0.035, comparable to the 6${\mathit{p}}_{1/2}$ng states (where γ=0.05). For 15≤n≤22, the linewidth is approximately constant at 2 ${\mathrm{cm}}^{\mathrm{-}1}$, rather than decreasing as 1/${\mathit{n}}^{\mathrm{*}3}$. This may be the result of a shape resonance in the ng electron’s potential located just above the 7s ionic limit.

A formulation within the London approximation of magnetic ring currents is applied to ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{70}$, and their hexa-anions. Contrary to previous approaches, this formulation does not require the identification of closed loops and can therefore be applied to these molecules despite their topological complexity. Knowledge of the ring currents provides a better understanding of their magnetic ring-current susceptibilities. Probe dipoles are used to investigate local spatial variations of the magnetic field induced by the ring currents. In an attempt to evaluate how the carbon chemical shifts are affected by the ring currents, we separate the current into a component circulating above and one below the molecular surface. Assuming a displacement of the negatively charged electronic clouds towards the outside of the molecule, we are able to understand the relative positions of the carbon NMR lines of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{60}^{6\mathrm{-}}$.

We present ab initio calculations of the screened self-energy and vacuum polarization for the resonance transitions of Li-like, Na-like, and Cu-like ions, for a degree of ionization of about 10 or greater. The direct part of the Dirac-Fock potential is incorporated to all orders in the radiative corrections, and exchange effects are added in leading order. When combined with previous calculations of correlation and nuclear effects, our results agree with experiment at the level of experimental uncertainty with only a few exceptions, most notably the low-Z part of the Cu isoelectronic sequence. The calculations agree well at low Z with phenomenological estimates of the QED terms based on scalings of the known hydrogenic values but deviate slightly at high Z. We discuss the leading omitted two-photon QED terms.

The nonlocal weighted-density approximation (WDA) to the exchange- and kinetic-energy functionals of many-electron systems, proposed several years ago by Alonso and Girifalco within the framework of density-functional theory, is used to compute the ground-state electronic density and the total energy of atoms and ions with filled or half-filled electronic shells. The results and the results of analogous calculations using the well-known Thomas-Fermi-Dirac-Weizsäcker (TFDW) approximation for the kinetic (TFW) and exchange (D) energy density functionals are compared with Hartree-Fock values. A striking improvement of the total and exchange energies, of the density at the nucleus, and of the 〈${\mathit{r}}^{\mathrm{-}1}$〉 expectation values is obtained within the WDA scheme. The local behavior of the WDA electronic- and kinetic-energy densities is also analyzed.

The model Coulomb pair-correlation functions proposed several years ago by Gritsenko, Bagaturyants, Kazansky, and Zhidomirov are incorporated into the self-consistent local-density approximation (LDA) scheme for electronic systems. Different correlation functions satisfying well-established local boundary conditions and integral conditions have been tested by performing LDA calculations for closed-shell atoms. Those correlation functions contain a single parameter which can be optimized by fitting the atomic correlation energies to empirical data. In this way, a single (universal) value of the parameter is found to give a very good fit for all the atoms studied. The results provide a substantial improvement of calculated correlation energies as compared to the usual LDA functionals and the scheme should be useful for molecular and cluster calculations.

QED effects associated with the electron self-energy and vacuum polarization are calculated in non-Coulomb potentials for atomic states with principal quantum numbers 1 and 2. We consider the Coulomb potential with finite nuclear size incorporated and using the core-Hartree potential, a local version of the Hartree-Fock potential. The calculations are carried out for ions with nuclear charges in the range Z=60–90. For the Coulomb potential with finite nuclear size, substantial discrepancies with an earlier tabulation are found. Radiative corrections are calculated for lithiumlike uranium using the core-Hartree potential and comparison with experiment is made.