Showing papers in "Physical Review A in 1984"

Electron microscopy of a cholesteric liquid crystal and its blue phase

Abstract: We report the successful application of the freeze fracture technique for obtaining transmission-electron-microscope pictures of a thermotropic cholesteric material and its blue phase. It is shown that under rapid quenching these phases supercool and conserve their structure at liquid-${\mathrm{N}}_{2}$ temperature. The micrographs obtained confirm the body-centered-cubic symmetry of the blue phase I.

Squeezing of intracavity and traveling-wave light fields produced in parametric amplification

Abstract: A general input-output theory for quantum dissipative systems is developed in which it is possible to relate output to input via the internal dynamics of a system. This is applied to the problem of computing the squeezing produced by a degenerate parametric amplifier located inside a cavity. The results for the internal modes are identical with those of Milburn and Walls [Opt. Commun. 39, 401 (1981)]. The output field is also found to have only 50% of maximal squeezing. However, by taking the output for a degenerate parametric amplifier inside a single-ended cavity and feeding this into an empty single-ended cavity, one can produce a maximally squeezed state inside this second cavity.

Exact differential equation for the density and ionization energy of a many-particle system

Abstract: The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.

Dynamical model of the liquid-glass transition

Abstract: Based on a microscopic theory developed recently, a dynamical model of density fluctuations in simple fluids and glasses is proposed and analyzed analytically and numerically. The model exhibits a liquid-glass transition, where the glassy phase is characterized by a zero-frequency pole of the longitudinal and transverse viscosities indicating the systems' stability against stress. This also implies an elastic peak in the density-fluctuation spectrum. Approaching the glass transition the slowing down of density fluctuations is controlled by the increasing longitudinal viscosity, which in turn is coupled via a nonlinear feedback mechanism to the slowly decaying density fluctuations. This causes a divergence of the structural relaxation time at a certain critical coupling constant ${\ensuremath{\lambda}}_{c}$. At the glass transition density fluctuations decay with a long-time power law $\ensuremath{\Phi}(t)\ensuremath{\sim}{t}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}=0.395$ and approaching the transition the viscosity diverges proportional to ${\ensuremath{\epsilon}}^{\ensuremath{-}\ensuremath{\mu}}$ and ${\ensuremath{\epsilon}}^{\ensuremath{-}\ensuremath{\mu}}$, where $\ensuremath{\epsilon}=|1\ensuremath{-}\frac{\ensuremath{\lambda}}{{\ensuremath{\lambda}}_{c}}|$ and $\ensuremath{\mu}=\frac{(1+\ensuremath{\alpha})}{2\ensuremath{\alpha}}$, ${\ensuremath{\mu}}^{\ensuremath{'}}=\ensuremath{\mu}\ensuremath{-}1$ below and above the transition, respectively. The long-time tail "paradox" in dense fluids is briefly discussed.

New, thermodynamically consistent, integral equation for simple fluids

Abstract: A new integral equation in which the hypernetted-chain and Percus-Yevick approximations are "mixed" as a function of interparticle separation is described. An adjustable parameter $\ensuremath{\alpha}$ in the mixing function is used to enforce thermodynamic consistency. For simple $\frac{1}{{r}^{n}}$ potential fluids, $\ensuremath{\alpha}$ is constant for all densities, and the solutions of the integral equations are in very good agreement with Monte Carlo calculations. For the one-component plasma, $\ensuremath{\alpha}$ is a slowly varying function of density, but the agreement between calculated solutions and Monte Carlo is also good. This approach has definite advantages over previous thermodynamically consistent equations.

Stability of quantum motion in chaotic and regular systems

Abstract: The evolution of a quantum state is altered when a small perturbation is added to the Hamiltonian. As time progresses, the overlap of the perturbed and unperturbed states gives an indication of the stability of quantum motion. It is shown that if a quantum system has a classically chaotic analog, this overlap tends to a very small value, with small fluctuations. On the other hand, if the classical analog is regular, the overlap remains appreciable (on a time average) and its fluctuations are much larger.

Polarization of the nuclear spins of noble-gas atoms by spin exchange with optically pumped alkali-metal atoms

Abstract: The theory of spin exchange between optically pumped alkali-Inetal atoms and noble-gas nuclei is presented. Spin exchange with heavy noble gases is dominated by interactions in long-lived van der Waals molecules. The main spin interactions are assumed to be the spin-rotation interactions yN S between the rotational angular momentum N of the alkali-metal — noble-gas pair and the electron spin S of the alkali-metal atom, and the contact hyperfine interaction aK S between the nuclear spin K of the noble-gas atom and the electron spin S. Arbitrary values for EC and for the nuclear spin I of the alkali-metal atom are assumed. Precise formal expressions for spin transfer coefficients are given along with convenient approximations based on a perturbation expansion in powers of (o.'/yX), a quantity which has been shown to be small by experiment.

Quantum network theory

Abstract: A general approach, within the framework of canonical quantization, is described for analyzing the quantum behavior of complicated electronic circuits. This approach is capable of dealing with electrical networks having nonlinear or dissipative elements. The techniques are applied to circuits capable of generating squeezed-state or two-photon coherent-state signals. Circuits capable of performing back-action-evading electrical measurements are also discussed.

Structure of three-component microemulsions in the critical region determined by small-angle neutron scattering

Abstract: The intensity distribution of the critical scattering from sodium di-2-ethylhexylsulfosuccinate $\mathrm{AOT}\ensuremath{-}{\mathrm{D}}_{2}\mathrm{O}\ensuremath{-}n$-alkane water-in-oil (W/O) microemulsions has been measured over an extensive range of droplet volume fractions (3-30 vol%) and temperatures (22 to 43\ifmmode^\circ\else\textdegree\fi{}C) in the critical region. The water/surfactant molar ratio of the microemulsion was kept at a constant value of 40.8, for which previous experiments on the temperature variation have been well documented. A structural model of W/O microemulsions based on well-defined surfactant-coated water droplets is firmly established up to a volume fraction of about 20 vol% for all temperatures studied. Data analysis assumes that the cloud points and subsequent phase separation are caused by concentration fluctuations of polydisperse droplets. The major conclusions drawn from the analysis are as follows. (1) The order parameter of the critical phenomenon can be taken to be the volume fraction of the dispersed droplets. (2) The size and polydispersity of the droplets remain essentially constant in the vicinity of the critical point (for a fixed water/surfactant ratio). (3) The critical phenomenon is driven by an increased attraction between the droplets as the critical point is approached. (4) The critical point can be approached by either raising the temperature at fixed volume fraction or by varying the carbon number of the oil solvent at fixed volume fraction and temperature. (5) The nature of the droplets does not change upon a phase separation into two coexisting microemulsions. The data also gives some evidence that the droplet picture of the microemulsion breaks down at sufficiently high concentrations of water and surfactant.

Quantum electrodynamics near an interface. II.

Abstract: A quantum-mechanical linear-response formalism is used to calculate the frequency shift and lifetime of an excited atom near an arbitrary flat interface. The results depend on the frequency-dependent atom and field susceptibilities, and in the vicinity of an interface can be expressed in terms of the appropriate Fresnel reflection coefficients; the contributions from surface excitations are easily identified. As examples, we consider an atom above a metal and a dielectric waveguide.

Quantum dynamics of a nonintegrable system

Abstract: The quantum motion of a periodically kicked rotator is shown to be related to Anderson's problem of motion of a quantum particle in a one-dimensional lattice in the presence of a static-random potential. Classically, the first problem is nonintegrable and, for certain values of the parameters, exhibits chaos and diffusion in phase space; in the second problem, diffusion takes place in configuration space. Quantum phase interference, however, is known to suppress diffusion in Anderson's problem and to produce quasiperiodic motion. By establishing a mapping between the two systems we show that a similar effect determines the dynamics of the quantum rotator. As a result its wave functions are localized in phase space and their time evolution is quasiperiodic. This result explains the quantum recurrences and boundedness of the energy found in recent numerical work.

Adiabatic following in multilevel systems

Abstract: The problem of achieving population inversion adiabatically in an $N$-level system using one or more laser fields whose detunings and/or amplitudes are continuously varied is studied analytically and numerically. The $\mathrm{SU}(N)$ coherence vector picture is shown to suggest unexpected inversion procedures and also to give a generalized interpretation of adiabatic following. It is shown that the (${N}^{2}\ensuremath{-}1$)-dimensional $\mathrm{SU}(N)$ space contains an ($N\ensuremath{-}1$)--dimensional steady-state subspace $\mathit{\ensuremath{\Gamma}}(t)$ whose orthonormal basis vectors ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{1},\dots{}, {\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{N\ensuremath{-}1}$ are given explicitly in terms of the Hamiltonian matrix elements. The motion of the system can be interpreted as a "generalized precession" of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ about $\mathit{\ensuremath{\Gamma}}$. Multilevel adiabatic following occurs when the angle $\ensuremath{\chi}(t)$ between the coherence vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ and its projection onto $\mathit{\ensuremath{\Gamma}}$ is very small. The multiple dimension of $\mathit{\ensuremath{\Gamma}}$ is shown to provide a variety of paths for adiabatic inversion. The adiabatic solution is obtained by solving $N\ensuremath{-}1$ simple equations for the directional cosines of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ on ${\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Gamma}}}_{i}$. The adiabatic solution and time scale and the state taken up by the atomic variable are discussed analytically and numerically for a three-level system.

Quantum oscillations in one-dimensional normal-metal rings

Abstract: We investigate the connection between two recent investigations on flux-periodic effects in one-dimensional normal-metal rings with inelastic diffusion length larger than the size of the ring. B\"uttiker, Imry, and Landauer have pointed out that closed rings, driven by an external flux, act like superconducting rings with a Josephson junction, except that $2e$ is replaced by $e$. Gefen, Imry, and Azbel considered such a ring connected to current leads and found a flux-periodic electric resistance. We establish a connection between these Aharonov-Bohm-like effects by demonstrating that the transmission probability of the ring, which determines the electric resistance, exhibits resonances near the energies of the electronic states of the closed ring. It is the flux dependence of the resonances which gives rise to the strong oscillatory behavior of the electric resistance.

Nonlinear-response theory for steady planar Couette flow

Abstract: We present a simplified derivation of the Yamada-Kawasaki formula for the nonlinear adiabatic response of the stress tensor to planar Couette flow. This formally exact expression is then used to prove the validity of two nonequilibrium molecular-dynamics algorithms that have been used to study fluids undergoing planar Couette flow, very far from equilibrium.

Determination of plasma-ion velocity distribution via charge-exchange recombination spectroscopy

Abstract: Spectroscopy of line radiation from plasma impurity ions excited by charge-exchange recombination reactions with energetic neutral beam atoms is rapidly becoming recognized as a powerful technique for measuring ion temperature, bulk plasma motion, impurity transport, and more exotic phenomena such as fast alpha particle distributions. In particular, this diagnostic offers the capability of obtaining space- and time-resolved ion temperature and toroidal plasma rotation profiles with relatively simple optical systems. Cascade-corrected excitation rate coefficients for use in both fully stripped impurity density studies and ion temperature measurements have been calculated to the principal ..delta..n = 1 transitions of He+, C/sup 5 +/, and O/sup 7 +/ with neutral beam energies of 5 to 100 keV/amu. A fiber optically coupled spectrometer system has been used on PDX to measure visible He/sup +/ radiation excited by charge exchange. Central ion temperatures up to 2.4 keV and toroidal rotation speeds up to 1.5 x 10/sup 7/ cm/s were observed in diverted discharges with P/sub INJ/ less than or equal to 3.0 MW.

Transition to chaos by interaction of resonances in dissipative systems. I: Circle maps

Abstract: Dissipative dynamical systems with two competing frequencies exhibit transitions to chaos. We have investigated the transition through a study of discrete maps of the circle onto itself. The transition is caused by interaction and overlap of mode-locked resonances and occurs at a critical line where the map loses invertibility. At this line the mode-locked intervals trace up a complete devil's staircase whose complementary set is a Cantor set with fractal dimension $D\ensuremath{\sim}0.87$. Numerical results indicate that the dimension is universal for maps with cubic inflection points. Below criticality the staircase is incomplete, leaving room for quasiperiodic behavior. The Lebesgue measure of the quasiperiodic orbits seems to be given by an exponent $\ensuremath{\beta}\ensuremath{\sim}0.35$ which can be related to $D$ through the scaling relation $D=1\ensuremath{-}\frac{\ensuremath{\beta}}{\ensuremath{ u}}$. The exponent $\ensuremath{ u}$ characterizes the cutoff of narrow plateaus near the transition. A variety of other exponents describing the transition to chaos is defined and estimated numerically.

Adiabatic-connection approach to Kohn-Sham theory

Abstract: The Kohn-Sham method for energy calculation in inhomogeneous electron systems relies on a comparison of functionals describing interacting and noninteracting electrons. An alternate approach draws the link between interacting and noninteracting systems explicitly, via an adiabatic connection of eigenstates. This adiabatic-connection scheme eliminates the "Fermi-statistics" problem and provides partial answers to some other conceptual difficulties that arise when the Kohn-Sham method is applied in practice. In addition, dimensional arguments can be given that justify the use of local-density approximations for exchange and correlation within the adiabatic connection framework. These arguments do not involve a "slowly varying" assumption and are valid for any system, however inhomogeneous.

Parameter-free model of the correlation-polarization potential for electron-molecule collisions

Abstract: A model potential that includes both correlation and polarization effects is proposed for electron-molecule collisions. It is based, as suggested by O'Connell and Lane, on a hybridization of local electron-gas theory for short distances and the asymptotic form of the polarization potential. It is energy independent and very simple to apply, depending only on the molecular charge density and polarizabilities. The potential has been calculated for several molecules (H/sub 2/, N/sub 2/, CO/sub 2/, HF, HCl, and CO); the crossing point between the correlation and polarization potentials is remarkably constant, averaging 0.96 eV. Application in scattering calculations for H/sub 2/ and N/sub 2/ yields very encouraging results.

Lifetimes of alkali-metal—atom Rydberg states

Abstract: We report a comprehensive set of calculations of the lifetimes of Rydberg states in alkali-metal atoms, using realistic potentials to represent the atomic core. The effects due to core polarizability, spin-orbit interaction, and blackbody radiation are explicitly included. A complete cross reference listing of all available experimental lifetimes is also attempted. The results compare well with experiment for all principal quantum numbers $n$ examined and should provide guidance for future experimental investigations. The relation of the present approach to other works is discussed.

Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light

Abstract: A new method of picosecond and femtosecond transient spectroscopy yielding information about ultrafast relaxation processes without requiring ultrashort light pulses is presented. It is based on the present theoretical analysis of the resonant degenerate four-wave-mixing process excited by two temporally incoherent light beams with wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}$ which are originated from a single beam at frequency $\ensuremath{\omega}$ but have mutual time delay $\ensuremath{\tau}$. Under the assumption that the incoherent light field has Gaussian random complex amplitude and that the resonant material consists of the usual two-level atoms, the statistically averaged intensity of the output light field with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{3}=2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ at $\ensuremath{\omega}$ is calculated as a function of $\ensuremath{\tau}$. Even with the light having a much longer duration than both ${T}_{1}$ (the longitudinal relaxation time) and ${T}_{2}$ (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\ensuremath{\tau}$, represents a decay profile determined mainly by ${T}_{2}$ for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\ensuremath{\tau}}_{c}$ is much shorter than the relaxation times. The correlation trace does not always represent a single-exponential decay but is sometimes slightly deformed by the ${T}_{1}$ effect. However, it does not cause a significant error in the determination of ${T}_{2}$. Moreover, as $\frac{{T}_{2}}{{T}_{1}}\ensuremath{\rightarrow}0$, the trace becomes a single-exponential decay curve determined only by ${T}_{2}$. The feature of the results obtained by the present method is similar to that obtained by the conventional coherent transient spectroscopy with short pulses, such as the photon echo. The time resolution in the present method, however, is limited only by ${\ensuremath{\tau}}_{c}$ much shorter than the light duration. By regarding the incoherent light as a series of random ultrashort pulses, the present four-wave-mixing process is also interpreted as the ensemble of numerous transient four-wave-mixing processes caused by various combinations of these pulses.

Percolation model of immiscible displacement in the presence of buoyancy forces

Abstract: We consider the quasistatic displacement of a nonwetting fluid by a wetting one in a porous medium in the presence of buoyancy forces. A simple percolation model of this process is presented and analyzed both theoretically and by Monte Carlo simulation. It is shown that the fact that percolation is a critical phenomenon, with diverging correlation length at the critical point, has a significant effect on the physics of the system, in particular on the dependence of nonwetting phase residual saturation on the density contrast between the phases. An extension of these ideas to the case where the pressure field is generated by viscous rather than buoyancy forces is suggested.

Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms

Abstract: Using accurate correlated wave functions calculated earlier by Bunge and by Larsson, we have constructed the Hohenberg-Kohn-Sham density functionals and exchange-correlation (ground-state) potentials and have obtained orbital energy eigenvalues for a number of light atoms by in principle exact numerical algorithms. While the uppermost occupied density-functional eigenvalue always gives an exact excitation energy as has been shown earlier, we find that eigenvalues for deeper shells lie above the corresponding excitation energy. We have compared our essentially exact density-functional (DF) results with those obtained in the local-density (LD) approximation. We find that the LD theory approximates the exchange-correlation energy rather well, but that it gives larger errors in the exchange-correlation potential and in the DF orbital eigenvalues. In all cases we have found that the LD error in the orbital eigenvalue is larger than the difference between the true DF eigenvalue and the corresponding exact excitation energy. Possible implications of these results for solid-state work are briefly discussed.

Bound on the maximum negative ionization of atoms and molecules

Abstract: It is proved that N c the number of negative particles that can be bound to an atom of nuclear charge z, satisfies N c <2 Z + K. For a molecule of K atoms, N, <2Z + K where Z is the total nuclear charge. As an example, for hydrogen N c = 2, and thus HH-- is not stable, which is a result not proved before. The bound particles can be a mixture of different species, e.g., electrons and π mesons; statistics plays no role. The theorem is proved in the static-nucleus approximation, but if the nuclei are dynamical, a related, weaker result is obtained. The kinetic energy operator for the particles can be either [p — eA (x)/c]2 − 2m (nonrelativistic with magnetic field) or {[pc —eA(x)] 2 + m 2 c 4 } 1/2 − mc 2 (relativistic with magnetic field). This result is not only stronger than that obtained before, but the proof (at least in the atomic case) is simple enough to be given in an elementary quantum-mechanics course.

Theory of electronically inelastic scattering of electrons by molecules

Abstract: We discuss a multichannel formulation of the Schwinger and a related variational principle (of one order higher than the Schwinger principle) in a form suitable for application to the scattering of low-energy electrons by both linear and nonlinear molecules. The theory includes the effects of polarization straightforwardly and should be particularly useful for obtaining electronically inelastic cross sections. An expansion of the trial scattering wave function in a discrete basis is possible. With certain choices for these basis functions this feature can be particularly advantageous.

Variational calculations on the helium isoelectronic sequence

Abstract: We have performed variational calculations on the helium isoelectronic sequence for values of the nuclear charge $Z$ ranging from 1 to 10. The basis used is a modification of that employed by Frankowski and Pekeris in 1966, whose calculation has not been superseded before now. Using 230-term wave functions, we obtain for $Z=2$ through 10 variational energies accurate to better than a few parts in ${10}^{13}$. Our results illustrate the importance of using basis functions which have the same analytic structure as the exact wave function being approximated.

Geometrical models of interface evolution

Abstract: We introduce a class of models for the motion of a boundary between time-dependent phase domains in which the interface itself satisfies an equation of motion. The intended application is to systems for which competing stabilizing and destabilizing forces act on the phase boundary to produce irregular or patterned structures, such as those which occur in solidification. We discuss the kinematics of moving interfaces in two or more dimensions in terms of their intrinsic geometric properties. We formulate local equations of motion as tractable simplifications of the complex nonlocal dynamics that govern moving-interface problems. Special solutions for dendritic crystal growth and their stability are analyzed in some detail.

Characterization of experimental (noisy) strange attractors

Abstract: In experiments involving deterministic chaotic signals, contamination by random noise is unavoidable. We discuss a practical method that disentangles the deterministic chaos from the random part. The method yields a characterization of the strange attractors together with an estimate of the size of random noise.

Relative diffusion in turbulent media: The fractal dimension of clouds

Abstract: A recent experiment indicates that clouds in the atmosphere have fractal surfaces which are characterized by a fractal dimension $D\ensuremath{\sim}2.35$. Here we present a theory of the fractal dimension of clouds. We show that the fractal dimension of clouds is calculable from the theory of relative turbulent diffusion. We claim that previous approaches to the theory of relative diffusion are in contradiction with this experiment and that a newly developed theory gives $D\ensuremath{\sim}2.35$ as a natural consequence. The new theory of relative diffusion is simultaneously in agreement with the intermittency-modified "$\frac{4}{3}$ (power) law" [i.e., the $\frac{(4+2\ensuremath{\mu})}{3}$ (power) law, where $\ensuremath{\mu}$ is the intermittency exponent].