A Lagrangian, moving-with-the-fluid, picture in the quantum Wigner phase space is rigorously defined, introducing a state-dependent current in phase space. Contrary to its classical counterpart, the Lagrangian dynamics in quantum phase space is non-Hamiltonian and elementary phase-space volumes are not conserved. The consequences for the numerical implementation of a fluid trajectory method in quantum phase space are discussed.

We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all bipartite unitary quantum gates, and it is found that the controlled-NOT gate is the most robust two-qubit quantum gate, in the sense that it is the quantum gate which can tolerate the most depolarizing noise and still generate entanglement. Our results enable us to place several analytic upper bounds on the value of the threshold for quantum computation, with the best bound in the most pessimistic error model being $p_{\mathrm{th}}<~\mathrm{0.5.}$

We analyze the entanglement of SU(2)-invariant density matrices of two spins $S_1,$ $S_2$ using the Peres-Horodecki criterion. Such density matrices arise from thermal equilibrium states of isotropic-spin systems. The partial transpose of such a state has the same multiplet structure and degeneracies as the original matrix with the eigenvalue of largest multiplicity being non-negative. The case $S_1=S,$ $S_2=1/2\mathrm{}$ can be solved completely and is discussed in detail with respect to isotropic Heisenberg spin models. Moreover, in this case the Peres-Horodecki criterion turns out to be a sufficient condition for nonseparability. We also characterize SU(2)-invariant states of two spins of length 1.

A detailed quantitative analysis of the system of two protons and one electron (ppe) placed in magnetic field ranging from ${10}^9–4.414\times {10}^{13}\mathrm{G}$ is presented. The present study is focused on the question of the existence of the molecular ion ${\mathrm{H}}_2^{+}$ in a magnetic field. A variational method with an optimization of the form of the vector potential (optimal gauge fixing) is used as a tool. It is shown that in the domain of applicability of the nonrelativistic approximation the (ppe) system in the Born-Oppenheimer approximation has a well-pronounced minimum in the total energy at a finite interproton distance for $B\lesssim {10}^{11}\mathrm{G},$ thus manifesting the existence of ${\mathrm{H}}_2^{+}.$ For $B\gtrsim {10}^{11}\mathrm{G}$ and large inclinations (of the molecular axis with respect to the magnetic line) the minimum disappears and hence the molecular ion ${\mathrm{H}}_2^{+}$ does not exist. It is shown that the most stable configuration of ${\mathrm{H}}_2^{+}$ always corresponds to protons situated along the magnetic line. With magnetic field growth the ${\mathrm{H}}_2^{+}$ ion becomes more and more tightly bound and compact, and the electronic distribution evolves from a two-peak to a one-peak pattern. The domain of inclinations where the ${\mathrm{H}}_2^{+}$ ion exists reduces with magnetic field increase and finally becomes $0°–25°$ at $B=4.414\mathrm{}\times {10}^{13}\mathrm{G}.$ Phase-transition-type behavior of variational parameters for some interproton distances related to the beginning of the chemical reaction ${\mathrm{H}}_2^{+}\leftrightarrow \mathrm{H}+p$ is found.

We report integral and differential cross sections for elastic scattering of electrons by $X{\mathrm{H}}_4$ $(X=\mathrm{C},\mathrm{}\mathrm{S}\mathrm{i},\mathrm{}\mathrm{G}\mathrm{e},\mathrm{}\mathrm{S}\mathrm{n},\mathrm{}\mathrm{Pb})$ molecules for energies between 3 and 10 eV. We use the Schwinger multichannel method with pseudopotentials [Bettega et al., Phys. Rev. A $47,$ 1111 (1993)] at the static-exchange and static-exchange plus polarization approximations. We compare our results with available theoretical and experimental results and find very good agreement. In particular, our results show Ramsauer-Towsend minima for all $X{\mathrm{H}}_4$ molecules.

The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states $N_m^{\mathrm{b}}$ in a given $m\mathrm{th}$ partial wave is related to the phase shift ${\delta }_m\mathrm{}\left(k\right)\mathrm{}$ and the singularity strength of the potential. When the effective potential has an inverse square singularity at the origin of the form ${\nu }^2/{\rho }^2$ and inverse square tail at infinity such as ${\mu }^2/{\rho }^2,$ Levinson’s relation gives ${\delta }_m\mathrm{}\left(0\right)\mathrm{}-{\delta }_m\left(\infty \right)=\pi [N_m^{\mathrm{b}}+(|\nu |-|\mu |)/2\mathrm{}].$

Cs ions with energies ranging from 10 keV to 1.8 MeV are scattered under a grazing angle of incidence from a flat and clean Cu(111) surface. The observed fractions of Cs atoms in the scattered beams and their dependence on projectile velocity are well described by a model of kinematically assisted resonant charge transfer between projectile and two-dimensional surface-state continuum of the target surface. A comparison with calculations for a target represented by the electronic structure of a free-electron metal shows neutral fractions which are enhanced for the Cu(111) by more than one order of magnitude. This is the strongest effect of the projected band gap of a metal surface on the charge transfer observed so far.

Surface light-induced drift (SLID) of a rarefied gas in cells with flat-plate and circular-cylindrical geometries is studied, and exact analytical solutions to the model rate equations are obtained in the limit of large Knudsen number. The model rate equations, which have not appeared before, have been tailored specifically in order to study the roles played in SLID, in a physically realistic setting, by both the tangential momentum and the normal momentum molecule-surface accommodation coefficients. Because the model equations are new (to the best of our knowledge), the results are generally different from those of previous work, although emphasis is placed on obtaining relations between the present and previous results; applications to experiments may be made by means of those relations.

A time-dependent semiclassical lattice solution of the Schrödinger equation is used to calculate charge-transfer processes in proton collisions with lithium atoms. State-selective cross sections are obtained at 5–15 keV incident energy for laser excited $2p\sigma$ states aligned parallel and $2p\pi$ states aligned perpendicular to the ion beam. State-selective cross sections are also obtained at 5 keV for ${1s}^{2}2s$ ground states in which the polarization of a moderately intense pulsed laser is aligned parallel and perpendicular to the ion beam. The addition of a pulsed laser is found to have a strong effect on the charge-transfer cross sections to the $n=3\mathrm{}$ excited states of hydrogen.

We study the ionization of extreme Stark states in sodium by THz electromagnetic half-cycle pulses. The results of our full-quantum calculations reveal the presence of an oscillatory pattern in the ionization spectra of extreme red (downhill) states that have been kicked away from the ion core (downhill with respect to the potential imposed by the Stark field). We find no oscillations in the spectra of extreme blue (uphill) states that have been kicked towards the ion core (also downhill with respect to the Stark potential). The oscillatory pattern in the red state ionization spectra is explained with a one-dimensional semiclassical model in terms of interferences between two classical paths. This model also predicts that the blue state ionization spectra should also show oscillatory behavior. The absence of the oscillations in the full calculations can be regarded as a breakdown of the one-dimensional model in representing the ionization dynamics of these states. We find that the one-dimensional model fails when the duration of the THz pulse is comparable to the classical Kepler orbit time.

A method for quantum-mechanical calculations of cross sections for the Zeeman transitions in collisions of ${}^{3}P$ atoms with structureless targets in a magnetic field is presented and applied to the study of magnetic and electronic relaxation in oxygen-helium and carbon-helium collisions at cold and ultracold temperatures. The rate constants for collisionally induced transitions between Zeeman levels in ground-state oxygen have large magnitudes in a 1 T field. It is shown that magnetic fields induce the forbidden ${}^3{P}_1$ $\to$ ${}^3{P}_0$ transition in ultracold collisions of carbon with helium. The cross section vanishes at zero energy for field-free collisions, but becomes infinitely large in a finite magnetic field, varying with velocity $v$ and magnetic field B as $B^2/v.\mathrm{}$

We consider a possibility to describe the Feshbach resonance in terms of the boson-fermion (BF) model. Using such a model, we show that after a gradual disentangling of the boson from fermion subsystem, the resonant-type scattering between fermions is indeed generated. We decouple the subsystems via (a) the single step and (b) the continuous canonical transformation. With the second one, we investigate the feedback effects effectively leading to the finite amplitude of the scattering strength. We study them in detail in the normal $T>\mathrm{}{T}_c$ and superconducting $T<~T_c$ states.

The density operator of the arbitrary physical system must be positive definite. Employing the general master equation technique which preserves this property, we derive equations of motion for the density operator of an active atom which interacts collisionally with the reservoir of perturber atoms. The obtained general relations applied to the two-level atom yield Bloch-Boltzmann equations (BBE) which, as it is the case with master equation approach, are linear in the matrix elements of the active-atom density operator. The obtained BBE guarantee that positivity is preserved, which needs not to be the case with the results known from literature. We argue that our results are the correct ones and as such should be used in practical applications. Moreover, the structure and the terms which appear in our set of BBE seem to allow simpler and more straightforward physical interpretation.

We were able to arbitrarily control the speed of a light pulse from subluminal to superluminal velocity by changing only the power of the laser for coupling coherently the single transition between $6{}^2{S}_{1/2}F=4\mathrm{}$ and $6{}^2{P}_{3/2}{F}^{\prime }=5\mathrm{}$ in the $D_2$ line of a Cs atomic vapor system. With weak coupling power, a Gaussian light pulse was propagated superluminally with a negative group velocity $v_g=-c/14\mathrm{}400,$ which is caused by a highly anomalous dispersion related to an electromagnetically induced absorption. By increasing the coupling power at the same laser frequency, the pulses were propagated with a vacuum speed at the middle power and a subluminal group velocity $v_g=c/3000\mathrm{}$ at high power, which is caused by a normal dispersion related to an electromagnetically induced transparency. It was also found that group velocities depend largely on polarization combinations.

We propose an experimental setup allowing one to convert an input light of wavelengths about $1–2\mu \mathrm{m}$ into an output light of a lower frequency. The basic principle of operation relies on the nonlinear optical properties exhibited by a microcavity filled with a photonic bandgap material. The light inside this material behaves like an interacting Bose gas susceptible to reach thermal equilibrium and create a Bose-Einstein condensate. Theoretical estimations show that using a fiber grating, a conversion of $1\mu \mathrm{m}$ into $1.5\mu \mathrm{m}$ is achieved with an input pulse of about 1 ns, and characterized by a peak power of ${10}^3\mathrm{W}.$

An oscillatory correlation function has been observed by the coincidence counting of multimode two-photon pairs produced with a degenerate optical parametric oscillator far below threshold. The coherent superposition of the multimode two-photon pairs provides the oscillation in the intensity correlation function. The experimental data are well fitted to a theoretical curve.

Reference is made to the paper by Remiddi [Phys. Rev. A 44, 5492 (1991)]. In this Comment we point out two misprints in the paper. We provide further verification of the corrections with a short table comparing 30 significant digit results using Remiddi’s formula (with our corrections) and the output of our recently developed triangle integral package.

We analyze a single-spin measurement using a transient process in magnetic force microscopy which could increase the maximum operating temperature by a factor of Q (the quality factor of the cantilever) in comparison with the static Stern-Gerlach effect. We obtain an exact solution of the master equation, which confirms this result. We also discuss the conditions required to create a macroscopic quantum superposition in the cantilever.

The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states, provided that measurements on probe and transformed probe states are available. Drawbacks of various approximate treatments are also considered.

We have investigated the problem of discriminating between nonorthogonal quantum states with the least probability of error. We have determined that the best strategy for some sets of states is to make no measurement at all and simply to always assign the most commonly occurring state. Conditions that describe such sets of states have been derived.