We propose a simple quantum-mechanical equation for n particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton solutions, where the ratio of charge to flux is a constant independent of the specific solution. As an approximation, the charge-flux interaction is described here by the Aharonov-Bohm potential, and the charge-charge interaction by the Coulomb one. The equation for two particles, one with charge and flux $(q,$ $\Phi /Z)$ and the other with $(-Zq,$ $-\Phi )$ where Z is a pure number is studied in detail. The bound-state problem is solved exactly for arbitrary q and $\Phi$ when $Z>\mathrm{}0.\mathrm{}$ The scattering problem is exactly solved in parabolic coordinates in special cases when $q\Phi /2\mathrm{}\pi ħc$ takes integers or half integers. In both cases the cross sections obtained are rather different from that for pure Coulomb scattering.

We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This master equation is diffusive and produces loss of coherence. Moreover, real clocks can be described in terms of effective interactions that are nonlocal in time. Alternatively, they can be modeled by an effective thermal bath coupled to the system.

Generalized coherent states are constructed for the Coulomb problem. Following a construction procedure proposed by Klauder [J. Phys. A 29, L293 (1996)], Rydberg atom coherent states are defined and analyzed. The relationship between decorrelation in time and delocalization in space is elucidated. Keplerian orbits are discussed. The connection with sharp Gaussian wave packets used to explain pump-probe experiments is made. This is achieved by introducing genuine Gaussian Klauder coherent states that are overcomplete, and permit a resolution of the identity operator. They decorrelate comparatively slowly, and remain spatially localized for many Keplerian periods.

A semiclassical theory based on the Maslov-type wave packet is reported. The present approximation constitutes a class of semiclassical theory that brings about a hierarchy of theoretical structures below or equivalent to the standard semiclassical approximation to the Feynman kernel. We first propose a semiclassical wave function; that is, what we call the action-decomposed function (ADF). An ADF is propagated in time semiclassically along a “single action surface,” which is characterized in terms of a given initial momentum, with the phase being proportional to the $F_2\mathrm{}(q,p)\mathrm{}$-type generating function. An arbitrary wave function can be expanded continuously in the ADF’s of different initial momenta, each of which is associated with weighting factors both in configuration and momentum spaces. Depending on the form of the weighting function, the present scheme covers a number of different levels of approximation, ranging from a “single” ADF to a semiclassical kernel. Thus our theory provides a way of connecting the Maslov-type semiclassical wave packet to the WKB theory based on the Feynman kernel. It is generally concluded that the above kernel limit attains the highest accuracy possible within the present scheme, but it requires a large number of classical trajectories to represent it. On the other hand, a single ADF yields a little less accurate results but demands the fewest representing classical trajectories due to the narrowest momentum distribution. In fact, we show numerically that the autocorrelation function represented in terms of a single ADF, from which the energy spectrum is extracted with a Fourier transformation, can be calculated with drastically fewer classical trajectories without losing much accuracy. We also present a limitation in applying the ADF, and show an interesting symptom arising from a pathological use of the approximation. The present theory is quite promising for a spectral analysis of the vibrational states of relatively large molecules, if applied appropriately.

In a recent paper [L. Ferrari, Phys. Rev. A 57, 2347 (1998)], one of the authors has shown that the mean energy of a quantum oscillator with periodic time-dependent frequency diverges exponentially in time, under certain conditions. In the present paper, we study the explicit form of the evolving state, and compare the results obtained with the general expressions developed by other authors for an arbitrary time-dependent frequency. Then we approach the problem of the anharmonic effects. A first-order calculation is performed in the case of a short-range perturbation. The transition rates between different states, evolving with the unperturbed Hamiltonian, are shown to vanish at long times when the unperturbed oscillator’s energy diverges exponentially. A nonperturbative approach must be adopted, in the presence of anharmonic potentials of the form $V\left(q\right)\mathrm{}\propto q^j,\hspace{0.5em}j>\mathrm{}2\mathrm{}$. In the case of weak anharmonicity $(j-2\ll 1)$, a mean-field procedure can be used to show that the mean energy does actually saturate at long times, with the possible exception of periodic peaks, having nonsaturating height, that we call “special quantum effects.”

This paper addresses the question of understanding quantum algorithms in terms of unitary operators. Many quantum algorithms can be expressed as applications of operators formed by conjugating so-called classical operators. The operators that are used for conjugation are determined by the problem and any additional structure possessed by the Hilbert space that is acted upon. We prove many commutative laws for these different operators, and we use those to phrase and analyze old and new problems and algorithms. As an example, we review the Abelian subgroup problem. We then introduce the problem of determining a group homomorphism, and we give classical and quantum algorithms for it. We also generalize Deutsch’s problem and improve the previous best algorithms for earlier generalizations of it.

In contrast to the many-to-one and quadratic nature of correspondence in the conventional representation of quantum channels, such as the operator-sum or the unitary representation, we present a one-to-one and linear (affine) parametrization of quantum channels. This parametrization enables us to visualize the convex structure of the space of quantum channels. To demonstrate its usefulness, we apply it to the analysis of quantum binary channels.

In this paper we investigate the possibility of making complete Bell measurements on a product Hilbert space of two two-level bosonic systems. We restrict our tools to linear elements, such as beam splitters and phase shifters, delay lines and electronically switched linear elements, photodetectors, and auxiliary bosons. As a result we show that with these tools a never failing Bell measurement is impossible.

In this paper I present a protocol for quantum cryptography which is secure against attacks on individual signals. It is based on the Bennett-Brassard protocol of 1984. The security proof is complete as far as the use of single photons as signal states is concerned. Emphasis is placed on the practicability of the resulting protocol. For each run of the quantum key distribution the security statement gives the probability of a successful key generation and the probability for an eavesdropper’s knowledge, measured as change in Shannon entropy, to be below a specified maximal value.

Quantum-information theory is used to analyze various nonlinear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The efficiency of the transformation of nonorthogonal states into orthogonal ones is discussed.

We study the problem of optimizing the Shannon mutual information for sources of real quantum states, i.e., sources for which there is a basis in which all of the states have only real components. We consider in detail the sources ${\mathcal{E}}_M$ of M equiprobable quantum bit (qubit) states lying symmetrically around the great circle of real states on the Bloch sphere and give a variety of explicit optimal strategies. We also consider general real group-covariant sources for which the group acts irreducibly on the subset of all real states and prove the existence of a real group-covariant optimal strategy, extending a theorem of Davies [E. B. Davies, IEEE. Inf. Theory IT-24, 596 (1978)]. Finally, we propose an optical scheme to implement our optimal strategies, simple enough to be realized with present technology.

We show that pure states of multipartite quantum systems are multiseparable (i.e., give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the quantification of multipartite pure-state entanglement are discussed. Further, as an application of the techniques used here, we show that any purification of a bipartite-bound entangled state having a positive partial transpose is tri-inseparable, i.e., has none of its three bipartite partial traces separable.

Coulomb capture and the subsequent muonic x-ray cascade have been measured for a selection of solid-state targets: three allotropic forms of selenium, magnesium chloride with and without crystal water, and single-phase Nb-Ta alloys in three different stoichiometric ratios. Small but statistically significant differences were found in higher-level crossover transition x-ray intensities in Se. A rather large enhancement of crossover transition intensities was observed in magnesium chloride with water, which is ascribed to transfer from hydrogen. No significant variations with composition were found in the Lyman intensity patterns from Nb-Ta; the per-atom capture ratio was measured to be constant within 5%.

Reasoning from known identities arising from scaling considerations, formulas in terms of only the moments of the electron density, $M_k=〈r^k\rho 〉,$ are developed for all energy components in the density-functional theory of the ground states of atoms. In particular, employing Hartree-Fock data for the first 54 atoms and many of their ions, it is demonstrated that formulas of the form $T_S={\sum }_{k=1\mathrm{}}^4{A}_k{(M}_{-2/k}{)}^k$ and $E_x={\sum }_{k=1\mathrm{}}^4{C}_k{(M}_{-1/k}{)}^k$ fit the neutral atoms He through Xe with standard deviations of 0.26% and 0.70%, respectively.

The atomic quadrupole moment, $Q_{\mathrm{zz}},$ and the electric field gradient at the nucleus, $q_{\mathrm{zz}},$ of the ${}^2{P}_{3/2}$ ground state of ${\mathrm{Ar}}^{+}$ have been calculated using a finite-element multiconfiguration Hartree-Fock method. The Hartree-Fock value for $Q_{\mathrm{zz}}\left({\mathrm{Ar}}^{+}\right)$ is $-0.57213\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{}$ The valence-correlation contribution obtained by correlating the valence $3s$ and $3p$ shells is calculated to be 0.048 44 a.u. The core-correlation and relativistic corrections are $-0.00299\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{}$ and $-0.00035\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{},$ respectively, yielding a final atomic quadrupole moment of $-0.5271\left(11\right)\mathrm{}\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{},$ which in absolute value is 1.2% larger than the recently measured value of $-0.5208\left(2\right)\mathrm{}\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{}$ The corresponding values for $q_{\mathrm{zz}}\left({\mathrm{Ar}}^{+}\right)$ are 4.1129 a.u, $-0.2295\hspace{0.5em}\mathrm{a}.\mathrm{u}.\mathrm{},$ 0.4211 a.u., and 0.0187 a.u., respectively, yielding a final value of 4.323(10) a.u. for $q_{\mathrm{zz}}.$

A density-functional theory that treats all states of an electronic system on the same footing is introduced. The corresponding Kohn-Sham formalism can be applied to ground and excited states alike, does not suffer from a $v$-representability problem, and represents a rigorous formal basis for the common, but so far unjustified practice to treat excited states by Kohn-Sham methods. The presented density-functional theory emerges from a generalization of the constrained-search procedure. The new Kohn-Sham formalism is based on generalized adiabatic connections introduced here. The possible topologies of those generalized adiabatic connections are discussed. A density-based stationarity principle and a density theorem that represents a more general counterpart of the Hohenberg-Kohn theorem are presented. A method to take into account exactly exchange interactions in the presented Kohn-Sham formalism is introduced, implemented, and applied to atoms.

Muonic x-ray cascades in B, C, N, O, and Ne following muonic atom formation in ${\mathrm{B}}_2{\mathrm{H}}_6,$ ${\mathrm{CH}}_4,$ ${\mathrm{C}}_2{\mathrm{H}}_6,$ ${\mathrm{C}}_4{\mathrm{H}}_{10},$ ${\mathrm{N}}_2,$ ${\mathrm{O}}_2$, and Ne were investigated. The densities of the different target gases were low enough to prevent any contact of the atom or molecule on which the formation takes place with surrounding atoms or molecules during the cascade. Using semiconductor detectors, the yields of transitions in several series with energies between 1.5 keV and 300 keV were measured. Cascade calculations were performed in order to explain the observed transition yields. The cascades could be reproduced by variation of only two parameters: the number of electrons and the muon angular momentum distribution at the starting point of the calculation. The cascade of $\mu \mathrm{Ne}$ formed in monoatomic neon was described best. Moreover, muonic carbon cascades were found to differ according to the sort of hydrocarbon, demonstrating the influence of the capturing molecule’s structure on the muonic cascade. By varying the number of initially available electrons, the molecular effects could be described with the cascade program.

The carbon $1s$ photoelectron spectrum has been measured for ${\mathrm{CH}}_4$ at photon energies of 302, 320, and 330 eV and for ${\mathrm{CD}}_4$ at 330 eV with an instrumental resolution about half the natural linewidth. These spectra have been analyzed to obtain vibrational spacings, vibrational intensities, and the lifetime of the carbon $1s$ core-hole state. The vibrational intensities vary with photon energy, in agreement with earlier results. At 330 eV, the observed Franck-Condon factors for both ${\mathrm{CH}}_4$ and ${\mathrm{CD}}_4$ can be understood only if anharmonic effects (consistent with the predictions of theory) are included. On the other hand, the vibrational spacings in ${\mathrm{CH}}_4$ show no evidence for anharmonicity (in contrast with theoretical predictions). In ${\mathrm{CD}}_4$ the observed anharmonicity in the vibrational energy spacings is about half of the predicted value, but the experimental and theoretical values differ only by an amount comparable to the experimental uncertainty. The measured values of the lifetime show a dependence on photon energy; this is attributed to failure of the theory of post-collision interaction to predict correctly the observed electron spectrum near threshold. At 330 eV, the measured Lorentzian lifetime, 93–95 meV, agrees with predictions of simple theory, but not with the prediction of more complete theory. It is also observed that there are systematic discrepancies between the observed line shapes and those predicted by the theory of postcollision interaction.

We present variational calculations of the Bethe logarithm for the $1{}^{1}S$ and $2{}^{1}S$ states of helium. The approach is based on the explicit second-order perturbation formula and closely follows the method of Schwartz. The final values are $\ln \left[K_0\right(1\mathrm{}{}^{1}S)/(1\mathrm{}\mathrm{Ry}\left)\right]=4.370\mathrm{}1579\left(5\right)\mathrm{}$ and $\ln \left[K_0\right(2\mathrm{}{}^{1}S)/(1\mathrm{}\mathrm{Ry}\left)\right]=4.366\mathrm{}4091\left(7\right)\mathrm{}$. The latter result reduces the difference between theoretical and experimental values for the ionization potential of the $2{}^{1}S$ state to $0.15$ MHz.

The photoion ${\mathrm{Li}}^{2+}{/\mathrm{L}\mathrm{i}}^{+}$ production cross section ratio of ground-state atomic lithium has been measured for photon energies ranging from 80 to 424 eV. The absolute cross sections for the ${\mathrm{Li}}^{2+}$ and ${\mathrm{Li}}^{+}$ yield are also derived. In this energy region, the ${\mathrm{Li}}^{2+}{/\mathrm{L}\mathrm{i}}^{+}$ ratio reaches a plateau of about 1.0% before reaching a maximum of about 4.5%, then decreases slowly. Good agreement is found between the measured total photoionization cross sections of lithium and theoretical calculations. The ${\mathrm{Li}}^{2+}{/\mathrm{L}\mathrm{i}}^{+}$ ratio is also compared to the ${\mathrm{He}}^{2+}/{\mathrm{He}}^{+}$ ratio from excited $\mathrm{He}\mathrm{}\left(1s2s\right)\mathrm{}$ for photon energies up to 70 eV above threshold. The branching ratio of ${\mathrm{Li}}^{2+}$ to total Li ion production is also compared to the single-ionization cross section of electron impact on ${\mathrm{Li}}^{+}$ ions.