Two physical models to explain the unusual behavior of biological systems put forward by Fröhlich and Davydov are reviewed. The Davydov Hamiltonian is transformed into normal coordinates and the Fröhlich Hamiltonian is canonically transformed into an equivalent from within the Hartree-Fock approximation. A model Hamiltonian capable of relating both theories is proposed. The resulting analysis employs only one type of second-quantized operators which describe the effect on the active dipolar modes of vibration in biological cells. An equation of motion is derived for the creation and annihilation operators that are used. When the phenomenon of Bose condensation is taken into account, the field translation variable is shown to obey a nonlinear Schrödinger equation. Its solutions are provided and their significance is discussed. Some of the solutions are shown to correspond to properties already examined by Fröhlich and Davydov. New solutions are found and interpreted as interfaces between either an ordered and a disordered phase or two ordered phases existing in the biosystem. The relationship between the two theories of biological order is demonstrated and discussed.

In this paper we follow the Fröhlich model of long-range coherence in biological systems and use the field-theoretic Hamiltonian of Wu and Austin. We calculate the complex dielectric constant of the metabolically active dipolar parts in the cell. The actual computation proceeds in two stages. In the first stage the imaginary part of the dielectric constant is obtained by the method of continued fractions. In the second stage the real part of the dielectric constant is calculated by an application of the Kramers-Kronig theorem. The main objective of the work presented in this paper is the real part of the dielectric constant. We also discuss the contributions from water which constitutes the majority of the cell content. Our results confirm the predictions of Fröhlich, and we give analytical expressions which can be utilized in the Fröhlich potential.

We have considered for binary fluids the universal dynamic amplitude ratio $R$ which connects the typical frequency $\Gamma$ of the order-parameter fluctuations to the viscosity $\overline{\eta }$ and to the correlation length $\xi$. We have analyzed the mode-coupling (MC) approach and the renormalization-group (RG) theory. The mode-coupling approach accounts for background terms in both $\overline{\eta }$ and $\Gamma$, whereas RG includes corrections to scaling in the transport coefficients with an effective exponent $\overline{\Delta }\simeq 0.7$. We emphasize that the two approaches are similar in formulation, the correction terms from MC showing a leading exponent $\nu =0.63\mathrm{}$, close to $\overline{\Delta }$. The correction amplitudes $a_{\Gamma }$ (linewidth) and $a_{\overline{\eta }}$ (viscosity) are essentially positive in the MC approach. Moreover, we claim that their ratio should be universal if we assume the Bhattacharjee-Ferrell crossover viscosity function: $\frac{a_{\overline{\eta }}}{a_{\Gamma }}=2\mathrm{}{x}_{\overline{\eta }}$, with $x_{\overline{\eta }}\simeq 0.06$, the critical viscosity exponent. We also define an amplitude factor $\tilde{R}\mathrm{}(q,t)\mathrm{}$, the asymptotic value of which is $R$. It allows the corrections to scaling, in the framework of the RG theory, to be taken into account. New viscosity measurements have been made with the isobutyric acid-water (I-W) and triethylamine-water (T-W) systems. New Rayleigh linewidth measurements have been performed in the T-W mixture. Analyses of the viscosity data in I-W, T-W, nitrobenzene-$n$-hexane (N-H), nitroethane-3-methylpentane (N-M), and chlorex-$n$-dodecane (C-D) systems have led us to introduce correction terms for the I-W and T-W systems, with an experimental exponent ≃0.7. I-W corrections have been found negative. The linewidth data, analyzed in the N-H, I-W, C-D, N-M, and T-W systems, show that corrections are present in $\tilde{R}$ for the N-M and T-W mixtures, with exponent ~ 0.7. T-W corrections have been found to be negative, when using negative statics corrections. Finally, the asymptotic values of $R$ were found in the range 1.00-1.14, with a mean uncertainty of 7%. They are in agreement with both the recent MC (1.027) and RG (1.038) expectations.

The inertial-range behavior of measured temperature structure functions, up to order 12, is compared with predictions by the log-normal and the $\beta$ model. Both models are unsatisfactory from a quantitative viewpoint. The comparison between measurements and models indicates that the intermittency of the temperature field is different from that of the velocity field.

A simple method of elimination of fast variables in nonlinear systems is proposed. The method can be carried out to any desired order in the parameter which determines the separation of time scales. Two models are discussed: a deterministic set of equations with appropriate initial ensembles of the fast-varying variables, and a stochastic set of equations. In the first model the reduced equation of motion for the relevant variable is still deterministic. The second model is discussed in light of observed nonlinear effects near nonequilibrium instabilities.

Monte Carlo calculations which rely on the statistical iteration of some operator can sometimes lead to results in which the variance grows as the iterations proceed. Alternatively the variance can be stable but the result incorrect. The effects are demonstrated by the Monte Carlo iteration of a 2× 2 matrix and analyzed in detail for this simple case. In addition an algebraic formulation of a full Monte Carlo calculation with many simultaneous configurations including a method for keeping the number of configurations constant is given. With this formulation it is shown that the naive sampling of the wave function and naive estimate of the eigenvalue based on the growth in the number of configurations will be stable but biased. It is made plausible that for a sufficiently large number ($M$) of simultaneous configurations the naive method leads to a result which approaches the correct one as $M\to \infty$. It is shown that the correct average eigenvalue and eigenvector is a certain weighted average defined so that it avoids the problem of the growing variance and thus becomes more accurate as the chain is extended.

This paper is concerned with the liquid-expanded (LE) -liquid-condensed (LC) transition in monolayers of amphiphilic molecules at the air-water interface. A model, which can be mapped into the Blume-Emery-Griffiths Hamiltonian, has been considered before within the (mean-field) Bragg-Williams approximation and it gave results which could be successfully compared with experiment. The LE-LC transition has been associated with a chiral-symmetry breaking of the hydrocarbon-chain defects. This model is treated here with a Migdal-Kadanoff approximate position-space renormalization group. Renormalization-group flows are consistent with those obtained by previous authors. The connection between experimental and Hamiltonian parameters is easiest for a particular choice of ensemble, which turns out to be rather subtle for this problem. As in the work of Lavis, Southern, and Bell, isotherms in the surface-pressure—molecular-area plane do not show a signature of the LE-LC transition. The better agreement between experiments (showing a compressibility jump at the LE-LC transition) and mean-field theory suggests that in these cases long-range forces depending on the nature of the polar head and on the water substrate $p\mathrm{H}$ are responsible for the jump.

Activation rates are calculated for stochastic bistable flows driven by asymmetric dichotomic Markov noise (a two-state Markov process). This noise contains as limits both a particular type of non-Gaussian white shot noise and white Gaussian noise. Apart from investigating the role of colored noise on the escape rates, one can thus also study the influence of the non-Gaussian nature of the noise on these rates. The rate for white shot noise differs in leading order (Arrhenius factor) from the corresponding rate for white Gaussian noise of equal strength. In evaluating the rates we demonstrate the advantage of using transport theory over a mean first-passage time approach for cases with generally non-white and non-Gaussian noise sources. For white shot noise with exponentially distributed weights we succeed in evaluating the mean first-passage time of the corresponding integro-differential master-equation dynamics. The rate is shown to coincide in the weak noise limit with the inverse mean first-passage time.

In the light of a couple of new and important experiments in threshold ionization, several aspects of the Coulomb-dipole threshold law, $\mathcal{Q}\propto E{\left(\ln E\right)}^{-2\mathrm{}}M\left(E\right)\mathrm{}$ are reexamined. The principal results are as follows. (a) The logarithmic factor has a natural cutoff ${\left\{\ln \right[E \frac{\left(\mathrm{Ry}\right)}{5}\left]\right\}}^{-2\mathrm{}}$ when, as indicated, $E$ is expressed in Rydberg units. (b) The modulation factor for electron-impact ionization has the form $M\cong 1+\left(\frac{D}{\alpha }\right)sin(\alpha \ln E+\phi )$ in which the effect of a superposition of partial waves gives a factor $D$ which is expected to be less than one. This alters the relation between frequency and amplitude that is predicted to arise in the spin-asymmetry ratio as a function of $E$. Finally, (c) the range of validity of the threshold law ($E<\mathrm{}{E}_r$) is estimated in terms of a formula between $E_r$ and the dipole parameter $\alpha$ of $M\left(E\right)\mathrm{}$. Some implications of this, particularly for the recent two-electron photodetachment experiment of Donahue and co-workers [Phys. Rev. Lett 48 1538 (1982); 52 164(E) (1984)] are drawn.

The composition of the three lowest ${}_{}{}^1{}_{}{}^{}D$ states of BeI has been investigated using the multiconfiguration Hartree-Fock method. Though the $2p^2$ configuration lies above the $2s4d$ configuration in the Hartree-Fock approximation, correlation in the localized $2p^2$ configuration and its interaction with the higher-lying Rydberg series, including the continuum, are such that the $2p^2$ state is depressed to the extent that the lowest ${}_{}{}^1{}_{}{}^{}D$ state is predominately $2p^2$, the second largely $2s3d$, and the third almost entirely $2s4d$.

The ground-state density $n$ of a many-electron system obeys a Schrödinger-like differential equation for $n^{\frac{1}{2}}\left(\overrightarrow{\mathrm{r}}\right)$, which may be solved by standard Kohn-Sham programs. The exact local effective (nonexternal) potential, $v_{\mathrm{eff}}\left(\overrightarrow{\mathrm{r}}\right)$, is displayed explicitly in terms of wave-function expectation values, from which $v_{\mathrm{eff}}\left(\overrightarrow{\mathrm{r}}\right)>~0$ for all $\overrightarrow{\mathrm{r}}$. A derivation for $n$ as $\left|\overrightarrow{\mathrm{r}}\right|\to \infty$ implies that this new effective potential tends asymptotically to zero, as does the exact Kohn-Sham potential, with the highest occupied eigenvalue as the exact ionization energy. A new exact expression is also presented for the exchange-correlation hole density ${\rho }_{\mathrm{xc}}(\overrightarrow{\mathrm{r}}, {\overrightarrow{\mathrm{r}}}^{\prime })$ about an electron at $\overrightarrow{\mathrm{r}}$, as $\left|\overrightarrow{\mathrm{r}}\right|\to \infty$.

A second-order linear differential equation with continuous periodic coefficients is solved exactly in terms of elementary functions. Equations of this type arise commonly in several areas of physics, and the solutions may find practical applications. As an illustration, the results are applied to the problem of an electron in a one-dimensional periodic potential.

We consider proton scattering from hydrogen atoms in the presence of a laser beam that resonantly (or nearly resonantly) excites the hydrogen atoms from the $1s$ to the $2p$ state. The laser beam propagates in a direction perpendicular to the proton beam, and it is linearly polarized, with polarization either parallel (longitudinal) or perpendicular (transverse) to the direction of incidence of the proton. We allow the collision to couple the $1s$, $2s$, and $2p$ states and we treat the interaction of the laser with the atom in the two-state rotating-wave approximation. We have calculated the integrated cross section, $\sigma \mathrm{}\left(2s\right)\mathrm{}$, for excitation of the $2s$ state. We find that the laser enhancement of $\sigma \mathrm{}\left(2s\right)\mathrm{}$ is small for longitudinal polarization, but for transverse polarization $\sigma \mathrm{}\left(2s\right)\mathrm{}$ varies rapidly with laser intensity, and in the intensity range ${10}^9$-${10}^{10}$ W/${\mathrm{cm}}^2$ $\sigma \mathrm{}\left(2s\right)\mathrm{}$ is of the order of 100 times larger than its value in the field-free case.

This paper reports a study of collisions between Rb atoms in $\mathrm{ns}$, $\mathrm{np}$, and $\mathrm{nd}$ states ($27<~n<~70$) and Xe. The experimental data show that collisions result in transitions from the initial level to states in adjacent high-$l$ manifolds and that, at the lower values of $n$, there are significant differences in the cross sections for such state-changing processes for $\mathrm{ns}$, $\mathrm{np}$, and $\mathrm{nd}$ states. These differences are discussed with reference to the amount of energy transfer in the collisions, and the data are compared with recent Born-approximation calculations.

The triply differential cross section for the ionization of atomic hydrogen by electron impact in the presence of a laser field has been calculated by employing the Coulomb Born approximation. The presence of a laser field reduces the triply differential cross section appreciably from the corresponding field-free cases.

Single-beam attenuation measurements of velocity-dependent total scattering cross sections for the interactions of metastable helium (${\mathrm{He}}^{*}$) on Kr and Xe targets have been measured in the 1-5-km/s relative-velocity range. The results are compared with cross sections obtained by full quantum calculations for a Lennard-Jones (12-6) potential with the parameters $\epsilon$ and $\sigma$ adjusted for a best fit. The results (in atomic units) are $\epsilon =3.38\mathrm{}\times {10}^{-4\mathrm{}}$ a.u., $\sigma =7.80\mathrm{}$ a.u., for the ${\mathrm{He}}^{*}$+Kr system and $\epsilon =5.34\mathrm{}\times {10}^{-4\mathrm{}}$ a.u. and $\sigma =7.79\mathrm{}$ a.u. for the ${\mathrm{He}}^{*}$+Xe system.

The coupling of two bistable systems is considered. The coupling is shown to modify the behavior of the output such that it exhibits multistability. Moreover, the resulting system is shown to exhibit bistability for parameters for which the uncoupled systems have monostable behavior.

The sensitivity to variations in screening in the photoionization of nonexcited electrons from excited atoms is studied by calculating the photoelectric cross sections for various excitation modes. The photoionization of a $3p$ electron of potassium ($Z=19\mathrm{}$) and the photoionization of $6s$ and $5s$ electrons of barium ($Z=56\mathrm{}$) are considered. In potassium we have compared cases for which the hole produced by the excitation is outer ($4s\to 4p$, $4s\to 3d$, $4s\to \epsilon p$), inner ($1s\to 4s$, $2s\to 4s$, $2p\to 4s$), or in the same shell ($3p\to 4s$) as the ionized electron. Holes in shells external to the subshell photoionized do not significantly alter the photoionization cross sections, while inner-shell holes reduce the screening and consequently increase the cross sections. Similar results are obtained for barium. The influence of the excitation on the Cooper minima and the asymmetry parameter is also discussed.

The relationship between static and dynamic contributions to line shifts in hydrogen plasmas is investigated with use of a set of approximations common to line-shape theories. It is shown that when the coupling between states of different principal quantum number is neglected, the asymmetry of the second-order width operator (due to detailed balance with the plasma) introduces a shift whose impact limit cancels approximately one-half of the second-order static shift. While the details of the calculation depend upon the approximations made, the primary conclusion that the second-order shift due to fluctuations can be as important as that due to static correlations does not. The possible implications of this result for plasmas with charged radiators are briefly discussed.

The resonance lines of the hydrogenlike ions C VI, N VII, and O VIII were observed in laser-produced plasmas with electron densities in the range ${10}^{21}$-${10}^{22}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and electron temperatures between about 70 and 100 eV. The lines of the hydrogenlike ions were recorded photographically with a 3-m grazing-incidence spectrograph. No signigicant plasma line shift was observed.