Detailed calorimetric measurements have been carried out on the chiral and racemic versions of one chiral liquid-crystal compound that exhibits an unusual and new smectic-$A^{\mathrm{*}}$ (Sm-$A^{\mathrm{*}}$) phase in the pure chiral compound. Both the smectic-A (Sm-A)–smectic-C (Sm-C) transition in the racemic compound and the Sm-$A^{\mathrm{*}}$–chiral–Sm-C transition in the pure chiral compound display a first-order transition with heat-capacity anomalies qualitatively similar to but quantitatively different from that observed in the ordinary Sm-A–Sm-C transition. Results from optical microscopic studies on the phase diagram of binary mixtures of the dextro and levo versions of the chiral compounds are reported.

The exponential coefficient in the first-passage-time problem for a bistable potential with highly colored noise is predicted to be (8/27 by all existing theories. On the other hand, we show herein that all existing numerical evidence seems to indicate that the coefficient is actually larger by about (4/3, i.e., that the numerical factor in the exponent is approximately (32/81. Existing data cover values of τ$V_0$/D up to ∼20, where $V_0$ is the barrier height, τ the correlation time of the noise, and D the noise intensity. We provide an explanation for the modified coefficinet, the explanation also being based on existing numerical simulations. Whether the value (8/27 predicted by all large-τ theories is achieved for even larger values of τ$V_0$/D is unknown but appears questionable (except perhaps for enormously large, experimentally inaccessible values of this factor) in view of currently available results.

We study the columnar phase in a system of parallel hard spherocylinders, using the density-functional model that we have proposed and used recently for the description of nematic and smectic liquid crystals. We obtain a first-order transition between the smectic A and the columnar phases, in good agreement with the computer-simulation results. However, the analysis of the correlation structure shows that our approximation may break down for the crystal phase.

The nonlinear dynamics of dissipative quantum systems in periodic fields is studied in the framework of a Gisin-like nonlinear Schrödinger equation with deterministic nonunitary quantum friction terms describing the system-bath couplings. The virtue of this nonunitary evolution is that it is compatible with Dirac’s superposition principle and the Hilbert-space structure of quantum kinematics. Floquet theory and the generalized Van Vleck nearly degenerate perturbation method are used to facilitate both analytical and numerical solutions. Closed-form analytic solutions can be obtained in the long-time average approximation or within the rotating-wave approximation. The methods are applied to the study of dissipative quantum dynamics of two-level systems driven by intense periodic fields. It is found that the system asymptotically approaches a limit cycle (whose orientation is subject to the quantum friction constraint), regardless of the strength of the perturbed fields and the nonlinearity constant, indicating quantum suppression of classical chaos. Further, each point of the limit cycle is found to be an attractor and ψ(t) exhibits a fractal-like evolution pattern in the course of time. The structure of the limit cycle depends strongly upon field intensity and frequency as well as the order of nonlinear multiphoton transitions. The power spectrum of the Bloch vector trajectory exhibits a dynamical symmetry inherent in the dissipative system and in the asymptotic limit cycle. A theoretical analysis is presented for the understanding of the origin and the role of the dynamical symmetry.

We discuss a class of damped relaxation methods for finding stationary (bound-state) solutions of relativistic wave equations represented by matrix equations on a discrete space lattice. Model calculations are presented for the Schrödinger and Dirac equations using a point-Coulomb potential for which analytic solutions can be obtained. A numerical application using a Gaussian potential in one dimension illustrates the general procedure for practical applications. As a realistic example, we study the Dirac equation on a three-dimensional Cartesian lattice using the Coulomb potential of a uniform charge distribution.

For a two-electron system the Kohn-Sham potential of density-functional theory is equal to the effective local potential $V_{\mathrm{eff}(x_1}$) occurring in the one-electron Schrödinger equation that is satisfied by the square root of the exact many-electron density, ${\rho }^{1/2}$($x_1$). Making use of the theory of marginal and conditional probability amplitudes, it is shown that $V_{\mathrm{eff}(x_1}$) is the sum of three potentials, each of which has a clear physical interpretation and will be studied in detail. The correlation part of the Kohn-Sham potential in a two-electron system can then be obtained by subtraction of the Coulomb and exchange potential, and it is shown how we can express this correlation potential as the sum of three physically meaningful contributions. The connection between the Kohn-Sham potential in a many-electron system and $V_{\mathrm{eff}}$ is also discussed. Calculations of the various potentials from highly accurate configuration-interaction wave functions are presented for the helium atom and for the hydrogen molecule at various distances of the two hydrogen nuclei.

Using an LSJ-coupling scheme and a configuration-interaction wave function, the relativistic energies, transition wavelengths of the 1s2s2${\mathit{p}}^2$ ${}_{}{}^5{}_{}{}^{}$P and 1s2${\mathit{p}}^3$ ${}_{}{}^5{}_{}{}^{}$S°, are studied. The relativistic correction, Breit-Pauli operator, and mass polarization correction are calculated for ions from Be i to Ne vii. Very good agreement with experiment is obtained in many cases. For example, the calculated transition wavelengths for Be i, N vi, O v, and Ne vii are 1910.15, 825.45, 694.75, and 526.57 ÅB. It is to be compared with the corresponding experimental data of 1909.5±0.6, 825.55±0.1, 694.75±0.1, and 526.65±0.1 Å. The calculated fine-structure values agree reasonably well with other theoretical results and with experiments. Some interesting comparisons between the existing theoretical data will also be discussed.

We present a formalism for treating one-dimensional problems in quaternionic quantum mechanics. As an example, we derive an explicit form for the T matrix for scattering from a square (quaternionic) barrier, and use this result to calculate the transmission and reflection coefficients. We show that the qualitative form of these coefficients is the same as in complex quantum mechanics, even when the barrier has a nonzero value for the quaternionic components of the potential.

The Schrödinger equation for the two-dimensional simple harmonic oscillator is solved using elliptic coordinates where it is separable. The separability of the problem in such coordinates is independent of the selection of the focal distance. The solutions are labeled by the total number of quanta N and by a set of characteristic values b corresponding to the eigenvalues of an observable B^, which does not commute with L^, the total angular momentum or H${^}_x$, the energy associated with the x degree of freedom. The well-known quantum energies as well as the characteristic values are obtained by imposing physical polynomial solutions.

Systematic investigations on the structure of the reduced, first-order atomic density matrices and the ‘‘exchange-only’’ correlation factors within the frameworks of the Hartree-Fock theory, local-density approximation, and nonlocal-density approximation (NLDA) are carried out. The contours of suitably averaged density matrices and correlation factors for some closed-shell atomic systems are plotted and compared, clarifying some of their significant general features. Exchange energies within the NLDA scheme for these systems have also been computed.

We calculate, by a variational procedure, the bound-state energies of the even-parity muonic molecules with total angular momentum J=1 and the energies of the (ddμ${)}^{+}$ and (dtμ${)}^{+}$ resonant states below the n=2 energy level of muonic atoms. We have found 11 resonant states with J=0 and 12 with J=1 for (ddμ${)}^{+}$ and 9 states with J=0 and 10 with J=1 for (dtμ${)}^{+}$. Some of the resonant energies, relative to the n=2 level of the muonic atoms, are less than the dissociation energy of ${\mathrm{D}}_2$, and therefore these states may play some role in muon-catalyzed fusion.

The formalism of mapping a classical canonical transformation to quantum unitary operators for a boson system is generalized to fermion systems. In terms of the ‘‘integration within an ordered product’’ technique for fermion systems, the transition of a classical transformation in Grassmann number space to a quantum image is manifestly evaluated in the fermion coherent-state representation. The normally ordered unitary operators that generate the Bogolyubov-Valatin transformation and the SU(2) rotation are derived in this way.

The exact solution to the minimally coupled Dirac equation is called the Volkov solution. An operator R^ is developed, which when applied to the free-electron state function gives us the Volkov solution. We apply the operator to the exact solution of the hydrogen atom to find that it is the approximate solution of the hydrogen atom in the presence of intense laser field. The restriction on the laser intensity is that the Kibble parameter ${\varepsilon }_K$, which is the ratio of the electron’s quiver energy $E_q$ to its rest mass energy $E_0$, is small compared to 1.

We apply a perturbative method, which takes into account the interaction between different open channels, to calculate total and partial widths of atomic resonances in the framework of the Feshbach formalism. The method requires the calculation of elastic, e.g., noncoupled open-channel wave functions, as in the case in which only one channel is open, thus avoiding the solution of complicated systems of coupled differential equations. As an illustration we have calculated energy positions, total and partial widths of ${}_{}{}^1{}_{}{}^{}$,3${\mathrm{S}}^{\mathrm{e}}$(3lnl) resonant states of He, ${\mathrm{C}}^{4+}$, ${\mathrm{N}}^{5+}$, and ${\mathrm{O}}^{6+}$. Our results show that the accuracy reached with this simple approach is comparable to other different non-Feshbach methods and that neglect of the coupling between different open channels can be considered as a reasonable approximation to obtain total and partial widths.

Earlier papers in this series have shown how the extended coupled-cluster method (ECCM) provides a widely applicable biorthogonal formulation of quantum many-body and quantum field theory. Rules for calculating matrix elements of arbitrary operators have been formulated, and an exact description of the excited states has been given in terms of a generalized random-phase approximation for the many-body, quasilocal c-number (classical), ECCM cluster amplitudes which completely and exactly parametrize the system. The present paper introduces a variational functional in order to treat the excited states differently within the ECCM framework, so as to allow extra flexibility in the choice of approximation schemes. The method is tested on the SU(2) quasispin model of Lipkin, Meshkov, and Glick [Nucl. Phys. 62, 188 (1965); 62, 199 (1965)], which contains the spontaneous breakdown of parity, and which models a shape transition in finite atomic nuclei. The method very well describes both the ground and excited states of the model Hamiltonian over a broad range of coupling parameters on both sides of the critical value corresponding to the transition.

A state of a composite quantum system is called classically correlated if it can be approximated by convex combinations of product states, and Einstein-Podolsky-Rosen correlated otherwise. Any classically correlated state can be modeled by a hidden-variable theory and hence satisfies all generalized Bell’s inequalities. It is shown by an explicit example that the converse of this statement is false.

The Ar 3s satellite spectrum has been studied by means of asymmetric (e,2e) experiments at 1-keV incident energy and in three different kinematical conditions. The intensities of the main satellite lines relative to the intensity of the 3s main line (29.3 eV) have been determined. The three chosen kinematical conditions allow for studying the dependence of the relative intensity on the momentum transfer in a region which is intermediate between the binary and dipolar regimes. The discrepancy between the relative intensity of the transition to the 3d ${}_{}{}^2{}_{}{}^{}S$ ion state measured by (e,2e) and high-energy photoionization experiments is confirmed. Sizeable contributions from transitions not belonging to the ${}_{}{}^2{}_{}{}^{}\mathrm{S}$ manifold and a kinematical dependence of the peaks centered at 36.5 and 41.3 eV have been observed.

A previous calculation for free-free transitions is generalized so as to treat one-photon (spontaneous) bremsstrahlung emitted in the course of collisions of relatively fast electrons with atomic hydrogen. While the electron-atom collision is described within the first Born approximation, the role of the atomic spectrum is taken into account exactly via the use of a compact representation of the Coulomb Green’s function. We discuss the main features of the cross sections and address some physically relevant issues such as the importance of the screening by the atomic electron, the role of the atomic structure, and limiting cases such as the soft-photon and the small-momentum transfer limits. We also discuss the differences observed between the cross sections for spontaneous bremsstrahlung and stimulated free-free transitions.

Taking as a benchmark the accurate calculations on ${}_{}{}^1{}_{}{}^{}$,3S, ${}_{}{}^1{}_{}{}^{}$,3P, and ${}_{}{}^1{}_{}{}^{}$,3D resonances under the N=2 threshold, carried out for two-electron systems, we present an appraisal of the practical aspects of, and equivalence between, existing schemes to classify doubly excited states. To relate properties of resonances for different values of the nuclear charge Z, we have also carried out calculations of their positions and widths for noninteger Z and have drawn the ensuing correlation diagrams. We show that however good the descriptions are they do not provide a completely general scheme to classify resonances. Furthermore, the proposed schemes are not equivalent, as is usually assumed.

L Auger-electron emission from Na-like configurations populated in iron projectile ions have been measured with high-energy resolution. The Auger states have been formed in collisions of 170-keV ${\mathrm{Fe}}^{17+}$ ions with He and Ne target atoms. The dominant spectral structures are due to Auger decay of states with the configurations 1$s^2$2$s^2$2$p^5$nln’l’ in ${\mathrm{Fe}}^{15+}$ and in particular from the 1$s^2$2$s^2$2$p^5$3s3p ${}_{}{}^4{}_{}{}^{}D_{7/2}^{}{}_{}{}^{}$ metastable state. The absolute energy of the 3s3p ${}_{}{}^4{}_{}{}^{}$${\mathit{D}}_{7/2}$ level is measured, and its metastable nature is demonstrated. Line assignments are obtained by using calculated transition energies and rates and by comparison to previously measured optical spectra.