The interpretation of the experimental self-diffusion data on normal and supercooled water has been revisited in the light of both the recently reported evidence for a temperature-dependent H-bond cooperativity and the free-volume fluctuations within the water percolative patches. The proposed model, which is consistent wth the presence of a continuity of states between liquid and solid phases, was found to fit the NMR experimental data to an accuracy comparable to that obtained by a power law.

The speed of sound is the highest admissible free velocity in a medium. This property is lost in the classical transport theory that predicts the unphysical divergence of the flux with gradients. Keeping the acoustic speed provides the means to control the growth of the flux and enables us to derive a better transport theory; flux saturates as the gradients became unbounded. Initial discontinuities persist for a finite time and diffusion fronts are convected with a finite speed. Various applications are considered (heat or mass transfer, plasma diffusion, and hydrodynamics).

In electrohydrodynamic convection, the turbulence-1–turbulence-2 (T1–T2) transition is observed when the applied voltage is very high. The transient property at the T1–T2 transition is studied through the evolution of the probability distribution of the area of T2. At a voltage close to the T1–T2 threshold the distribution transiently shows double peaks, i.e., a transient bimodality.

A wedge fjord model for screened growth is used to investigate the extent to which such a topology is sufficient to account for the dendritic multifractal growth characteristic of diffusion-limited aggregation. The clusters found are dendritic fractals with growth probabilities having a left-sided multifractal measure with ${\mathit{q}}_{\mathit{c}}$=0 and ${\mathrm{\alpha }}_{\max }$=∞.

A recent experiment studied the effect of an rf solenoid magnet and a partial Siberian snake on a 120-MeV polarized proton beam. We measured the frequencies of the ‘‘rf-induced’’depolarizing resonance for different values of the snake strength; this frequency measurement determined the spin tune ${\nu }_{\mathrm{sp}}$, which is the number of spin processions in one turn around the ring. A 4% snake increased the frequency of the rf-induced depolarizing resonance by the predicted 11 kHz and thus shifted the spin tune by the predicted Δ${\nu }_{\mathrm{sp}}$=0.006 88±0.000 04; as expected the 4% snake also tilted the stable spin direction by more than 38° from the vertical.

We quantitatively formulate the nonadiabatic non-Abelian geometric phase by generalizing the Lewis invariant method to a degenerate case, which is reduced to Wilczek and Zee’s [Phys. Rev. Lett. 52, 2111 (1984)] non-Abelian geometric phase in the adiabatic limit. We also derive the effective propagator accommodating the nonadiabatic non-Abelian geometric phase and the semiclassical quantization rule in the adiabatic limit.

We study classical and quantum anholonomy for nonlinear oscillators which support linear or quadratic spectra. The validity of the semiclassical relation between Berry’s phase and Hannay’s angle is investigated.

A pure quantum state which when split in any way cannot violate Bell’s inequality is termed a Bell state. Such a state may be considered as classical a state as possible. We show that for the radiation field the Bell state is unique, and is the Glauber coherent state. The formalism allows the interpretation of a local measurement in an entangled state as a measurement with an extended apparatus on a product state.

The generalized Bohr-Sommerfeld quantization condition up to the ninth-order approximation is given explicitly, in terms of complete elliptic integrals, for two kinds of quartic oscillators V(z)=${\mathit{v}}_2$${\mathit{z}}^2$+${\mathit{v}}_4$${\mathit{z}}^4$: (i) for the quartic double barrier, where ${\mathit{v}}_2$>0 and ${\mathit{v}}_4$<0, and the energy is below the potential maximum; and (ii) for the quartic double well, where ${\mathit{v}}_2$<0 and ${\mathit{v}}_4$>0. Resonance energies for some quartic double barriers and energy levels for some quartic double wells were evaluated by solving the quantization condition numerically. In some cases the results are very good.

A simple Bell inequality for an n-particle system in a Greenberger-Horne-Zeilinger state is derived. Quantum mechanics violates this inequality by an exponentially large factor of $2^{\left(\mathit{n}\mathrm{-}2\right)/2}$ for n odd or $2^{\left(\mathit{n}\mathrm{-}1\right)/2}$ for n even.

We develop an alternative method of evaluating the coherent-state propagator by employing path-integral methods and by introducing the notion of a coherent-state-propagator action.

In order that a bivariate normal probability distribution in phase space with variances ${\mathrm{\sigma }}_{\mathit{q}}$,${\mathrm{\sigma }}_{\mathit{p}}$ and covariance ${\mathrm{\sigma }}_{\mathit{q},}$p may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg’s uncertainty relation in Schrödinger form ${\mathrm{\sigma }}_{\mathit{q}}$${\mathrm{\sigma }}_{\mathit{p}}$-${\mathrm{\sigma }}_{\mathit{q},}$${\mathit{p}}^2$≥${\mathrm{ħ}}^2$/4 should be satisfied. The diagonalization of the corresponding density matrix entails a correspondence between the statistical and the physical properties of temperature-dependent oscillator states; the expansion of the density matrix into coherent states allows a physical interpretation in phase space.

Accurate energies of helium Rydberg states have been obtained by Drachman using polarization potentials [Phys. Rev. A 26, 1228 (1982); 31, 1253 (1985); 38, 1659(E) (1988)]. The present work calculates the higher-order relativistic corrections up to order ${\mathrm{\alpha }}^2$〈(${\mathit{a}}_0$/${\mathit{r}}_2$${)}^6$〉${\mathit{e}}^2$/${\mathit{a}}_0$, where ${\mathbf{r}}_2$ is the position of the Rydberg electron. The results given simple formulas for these contributions, which can easily be evaluated for any Rydberg state. The results are compared (at lower L) to precise variational calculations, and are compared to recent precisely measured n=10 intervals.

Explicitly correlated wave functions are constructed for the ${}_{}{}^1{}_{}{}^{}\mathrm{S}$, n ${}_{}{}^3{}_{}{}^{}\mathrm{S}$, n ${}_{}{}^1{}_{}{}^{}\mathrm{P}$, n ${}_{}{}^3{}_{}{}^{}\mathrm{P}$, ${}_{}{}^1{}_{}{}^{}\mathrm{D}$, and n ${}_{}{}^3{}_{}{}^{}\mathrm{D}$ states, with n<7, of the two-electron ions from He through ${\mathrm{Ne}}^{8+}$. The variational energies are the best available for 180 of the 261 states. Electron-nuclear and electron-electron cusp checks are used to test the wave functions. For each ion, dipole oscillator strengths are calculated for 55 S-P and 40 P-D transitions. Our oscillator strengths are more accurate than previous values for 739 of the 855 transitions considered. Some coefficients for the 1/Z expansions of the energies and oscillator strengths have been estimated as an aid to extrapolating our results to higher nuclear charges.

An analysis is presented for the evaluation of integrals of the form F${\mathit{r}}_1^{\mathit{i}}$${\mathit{r}}_2^{\mathit{j}}$${\mathit{r}}_3^{\mathit{k}}$${\mathit{r}}_{23}^{\mathrm{-}2}$ ${\mathit{r}}_{31}^{\mathit{m}}$${\mathit{r}}_{12}^{\mathit{n}}$ ${\mathit{e}}_1^{\mathrm{-}\mathrm{\alpha }\mathit{r}\mathrm{-}}$${\mathrm{\beta }}_{23}^{\mathit{r}\mathrm{-}\gamma \mathit{r}}$ d${\mathbf{r}}_1$ d${\mathbf{r}}_2$ d${\mathbf{r}}_3$ which arise in the determination of certain properties for atomic three-electron systems. All convergent integrals with i≥-2, j≥-2, k≥-2, m>=-1, and n≥-1 are discussed. These integrals are solved by reduction to one-dimensional quadratures of the form ${\mathcal{F}}_0^1$f(x)w(x) dx, where w(x) is one of the four functions ln[(1+x)/(1-x)], ${\mathit{x}}^{\mathrm{-}1}$ ln[(1+x)/(1-x)], ln[(1+x)/(1-x)] ln(${\mathit{x}}^{\mathrm{-}1}$), and ${\mathit{x}}^{\mathrm{-}1}$ ln[(1+x)/(1-x)] ln(${\mathit{x}}^{\mathrm{-}1}$), and f(x) is a well-behaved function on the interval [0,1]. The polynomials, which are mutually orthogonal over the interval [0,1] for each of the preceding four weight functions w(x), are determined. These polynomials allow specialized numerical quadrature calculations to be performed, which leads to an efficient algorithm for evaluation of the above integrals.

Regional virial theorems for the Kohn-Sham one-electron orbitals are derived. The regional virial theorem of the density-functional theory is obtained.

An assessment of the usefulness of Hermite-Gaussian (HG) functions as suitable basis functions for atomic and molecular ab initio calculations is attempted by investigating the helium atom and the ${\mathrm{H}}_2^{+}$ molecule. The polynomial form of HG functions of the fourth degree gives the energy for the helium atom equal to that obtained by Slater’s triple-ζ function. A particular linear combination of HG functions of the fourth degree, Hermite off-center HG functions, and polarized functions gives the energy for ${\mathrm{H}}_2^{+}$ very close to the exact value, in spite of the fact that exponential parameters are taken from optimized off-center functions.

We examine strategies for approximating the sum of a perturbation expansion for Coulombic systems in inverse powers of the spatial dimension D using only the few lowest-order terms. Several summation methods are tested on energy expansions of the following systems: the ground state of He, the ground state of ${\mathrm{Li}}^{+}$, the first two excited S states and the lowest ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{e}}$ state of He, and the ground state of ${\mathrm{H}}_2^{+}$. The origin of the expansions, the limit D→∞, corresponds to a pseudoclassical limit, but lower-order terms are strongly affected by poles at D→1, a hyperquantum limit. Two alternative methods are recommended, weighted truncation and hybrid Pade$aa— summation, which exploit these poles to reduce the summation error. In effect, these methods modify a semiclassical 1/D expansion by incorporating quantum corrections that are often large. Weighted truncation appears to be slightly more dependable at very low orders, while hybrid Padé summation is preferable when more than the three lowest-order terms are available or when the residue of the second-order pole at D=1 is known. We demonstrate that the present methods are superior to the shifted-expansion method, which does not correctly model the singularity structure.

The soft-photon contribution to the Lamb shift of a bound state of a nonrelativistic many-particle system has been expressed by a general formula, which allows for the fully nonadiabatic treatment of the particles. This formula has been applied to estimate the radiative corrections to the binding energies of the S and P states of the dtμ molecule. The correction for the weakly bound P state has been found equal to 0.048 meV, and for the ground state the corresponding value is -1.184 meV. Simple adiabatic models for dtμ are examined and found to provide fairly accurate estimates of the Lamb shift for the two lowest states of this molecule.

Coulombic three-body systems are investigated using the hyperspherical adiabatic approach. By using a suitable variable z=tan(α/2) in the angular differential equation for the determination of the potential curves, we are able to obtain stable series-expansion solutions, valid for small and large values of the hyperspherical radius. The analysis of the mathematical singularities of the differential equations in the variable z offers an insight into the physics of the problem and into the determination of stable converging solutions as well. In order to illustrate our investigation, we apply this study to several carefully chosen systems: He, ddμ, ${\mathit{d}}_2^{+}$, and excitons bound to a Coulomb center in different semiconductors.