# Showing papers in "Physical Review A in 1982"

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Bell Labs

^{1}TL;DR: In this article, the canonical partition function for classical many-body systems is transformed so that the temperature-independent packing statistics and the thermal excitations are uniquely separated, and the results suggest that melting hinges upon defect softening in the quenched packings, and a crude "theory" of melting for the Gaussian core model is developed.

Abstract: The canonical partition function for classical many-body systems is transformed so that the temperature-independent packing statistics and the thermal excitations are uniquely separated. This requires classification of particle configurations according to multidimensional potential-energy minima that can be reached by steepest-descent paths ("quenches"). Such classifications have been constructed for several starting configurations in the solid, fluid, and coexistence phases of the two-dimensional Gaussian core model. These quenches reveal a remarkable degree of polycrystalline order hidden within the fluid phase by "vibrational" distortion, and that order appears to have a large correlation length. The results suggest that melting hinges upon defect softening in the quenched packings, and a crude "theory" of melting for the Gaussian core model is developed in the Appendix.

1,060 citations

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TL;DR: In this article, a new approach to the polarization propagator for finite Fermi systems is presented, which makes explicit use of the diagrammatic perturbation expansion for the polarization, and reformulates the exact summation in terms of a simple algebraic scheme referred to as the algebraic diagrammatic construction (ADC).

Abstract: Within the framework of the many-body Green's-function method we present a new approach to the polarization propagator for finite Fermi systems. This approach makes explicit use of the diagrammatic perturbation expansion for the polarization propagator, and reformulates the exact summation in terms of a simple algebraic scheme, referred to as the algebraic diagrammatic construction (ADC). The ADC defines in a natural way a set of approximation schemes ($n$th-order ADC schemes) which represent infinite partial summations exact up to $n$th order of perturbation theory. In contrast to the random-phase-approximation (RPA)-like schemes, the corresponding mathematical procedures are essentially Hermitian eigenvalue problems in limited configuration spaces of unperturbed excited configurations. Explicit equations for the first- and second-order ADC schemes are derived. These schemes are thoroughly discussed and compared with the Tamm-Dancoff approximation and RPA schemes.

753 citations

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[...]

TL;DR: In this article, the Kohn-Sham effective potential is defined such that its sum of lowest orbital energies equals the true interacting ground-state energy, which is the most invariant with respect to changes in the one-body potential of the true Hamiltonian.

Abstract: By utilizing the knowledge that a Hamiltonian is a unique functional of its ground-state density, the following fundamental connections between densities and Hamiltonians are revealed: Given that ${\ensuremath{\rho}}_{\ensuremath{\alpha}}, {\ensuremath{\rho}}_{\ensuremath{\beta}},\dots{},{\ensuremath{\rho}}_{\ensuremath{\omega}}$ are ground-level densities for interacting or noninteracting Hamiltonians ${H}_{1}, {H}_{2},\dots{},{H}_{M}$ ($M$ arbitrarily large) with local potentials ${v}_{1}$,${v}_{2}$,$\dots{}$,${v}_{M}$, but given that we do not know which $\ensuremath{\rho}$ belongs with which $H$, the correct mapping is possible and is obtained by minimizing $\ensuremath{\int}d\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}} [{v}_{1}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}){\ensuremath{\rho}}_{\ensuremath{\alpha}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})+{v}_{2}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}){\ensuremath{\rho}}_{\ensuremath{\beta}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})+\ensuremath{\cdots}{v}_{M}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}){\ensuremath{\rho}}_{\ensuremath{\omega}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})]$ with respect to optimum permutations of the $\ensuremath{\rho}$'s among the $v$'s. A tight rigorous bound connects a density to its interacting ground-state energy via the one-body potential of the interacting system and the Kohn-Sham effective one-body potential of the auxiliary noninteracting system. A modified Kohn-Sham effective potential is defined such that its sum of lowest orbital energies equals the true interacting ground-state energy. Moreover, of all those effective potentials which differ by additive constants and which yield the true interacting ground-state density, this modified effective potential is the most invariant with respect to changes in the one-body potential of the true Hamiltonian. With the exception of the occurrence of certain linear dependencies, $a$ density will not generally be associated with any ground-state wave function (is not wave function $v$ representable) if that density can be generated by a special linear combination of three or more densities that arise from a common set of degenerate ground-state wave functions. Applicability of the "constrained search" approach to density-functional theory is emphasized for non-$v$-representable as well as for $v$-representable densities. In fact, a particular constrained ensemble search is revealed which provides a general sufficient condition for non-$v$ representability by a wave function. The possible appearance of noninteger occupation numbers is discussed in connection with the existence of non-$v$ representability for some Kohn-Sham noninteracting systems.

552 citations

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TL;DR: In this article, an analysis of macroscopic optical nonlinearity coefficients of molecular units is presented, in the absence of significant intermolecular effects, as the tensorial sum of molecular hyperpolarizabilities.

Abstract: Efficiency of three-wave interactions in molecular crystals depends on the conjugation of the molecular unit, which in turn is a one- or two-dimensional property. This strong anisotropy reduces the number of non-negligible molecular lowest-order hyperpolarizability coefficients to four. The lowest-order macroscopic optical nonlinearity can be expressed, in the absence of significant intermolecular effects, as the tensorial sum of molecular hyperpolarizabilities. This analysis is applied to the 17 relevant noncentrosymmetric crystal point groups, generalizing a previous analysis of nonlinear-optical properties of methyl-(2,4-dinitrophenyl)-aminopropanoate crystals. In several cases, the molecular unit anisotropy is shown to impose structural relations between coefficients of macroscopic nonlinearities, in addition to the usual relations resulting from the crystal point symmetry only. In such cases, nonlinear-optics experiments can be used for testing molecular anisotropy and molecular orientations within the unit cell in the absence of significant nonlinearity arising from intermolecular coupling. Similar relations can be derived between electro-optic coefficients, but limited to the case of weak contributions of intermolecular vibration to the electro-optic effect. We investigate for each point group the possibility of inferring hyperpolarizability coefficients from macroscopic nonlinear measurements, a complementary approach to that based on theoretical molecular calculations or electric-field-induced second-harmonic generation in solution. In the case of highly anisotropic one-dimensional charge-transfer systems (exemplified by $p$-nitroaniline), for each point group and a given molecular hyperpolarizability, the optimal orientation of the charge transfer axis, leading to the highest phase-matchable coefficient, is given. It is shown that crystal point groups 1,2,$m$, and $\mathrm{mm}2$ correspond to the highest possible value of this coefficient, while other crystal symmetry is less favorable. These considerations are applied to four available efficient molecular crystals and used either as a check of molecular orientations in a case of low crystalline symmetry or to estimate otherwise unavailable molecular nonlinear coefficients.

547 citations

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[...]

TL;DR: In this paper, the authors propose and analyze an experiment designed to probe the extent to which information accessible to an observer and the "eraser" of this information affects measured results.

Abstract: We propose and analyze an experiment designed to probe the extent to which information accessible to an observer and the "eraser" of this information affects measured results. The proposed experiment could also be operated in a "delayed-choice" mode.

528 citations

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419 citations

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TL;DR: In this paper, it is shown that the interface free energy between bulk phases with a macroscopically flat interface can be estimated from the variation of certain probability distribution functions of finite blocks with block size.

Abstract: It is suggested that the interface free energy between bulk phases with a macroscopically flat interface can be estimated from the variation of certain probability distribution functions of finite blocks with block size. For a liquid-gas system the probability distribution of the density would have to be used. The method is particularly suitable for the critical region where other methods are hard to apply. As a test case, the two-dimensional lattice-gas model is treated and it is shown that already, from rather small blocks, one obtains results consistent with the exact soluion of Onsager for the surface tension, by performing appropriate extrapolations. The surface tension of the three-dimensional lattice-gas model is also estimated and found to be reasonably consistent with the expected critical behavior. The universal amplitude of the surface tension of fluids near their critical point is estimated and shown to be in significantly better agreement with experimental data than the results of Fisk and Widom and the first-order 4-d renormalization-group expansion. Also the universal amplitude ratio used in nucleation theory near the critical point is estimated.

369 citations

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[...]

TL;DR: In this paper, the effects of initial-state correlation were studied by comparing cross sections obtained using a configuration-interaction-type initial state wave function with those obtained by a Hartree-Fock initial-State wave function, and they found that earlier single-center cross sections were not well converged with respect to their expansion parameters.

Abstract: The photoionization of molecular nitrogen has been studied using a frozen-core Hartree-Fock final-state wave function with a correlated intitial-state wave function. The final-state wave function was obtained using the iterative Schwinger variational method. The effects of initial-state correlation were studied by comparing cross sections obtained using a configuration-interaction-type initial-state wave function with those obtained using a Hartree-Fock initial-state wave function. In this paper we compare our accurate single-center expansion results with other theoretical results. We find that earlier single-center cross sections were not well converged with respect to their expansion parameters. The results of the continuum multiple-scattering method and the Stieltjes-Tchebycheff moment-theory approach are found to be in qualitative but not quantitative agreement with the present results. We also compare our computed total cross sections as well as integrated target angular distributions with experimental results for photoionization leading to the $X^{2}\ensuremath{\Sigma}_{g}^{+}$, $A^{2}\ensuremath{\Pi}_{u}$, and $B^{2}\ensuremath{\Sigma}_{u}^{+}$ states of ${\mathrm{N}}_{2}^{+}$. We find generally good agreement, which is improved by the inclusion of initial-state correlation effects, especially in the resonant photoionization channel leading to the $X^{2}\ensuremath{\Sigma}_{g}^{+}$ state of ${\mathrm{N}}_{2}^{+}$. We also report integrated detector angular distributions for these three channels.

341 citations

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TL;DR: In this paper, a numerical model for the helix soliton was proposed to predict that such solitons should appear under normal physiological conditions, supported by the assignment of a recently measured laser-Raman spectrum of a metabolically active cell to internal vibrations of the soliton.

Abstract: After modifying Davydov's original equations for the $\ensuremath{\alpha}$-helix soliton to include ten additional dipole-dipole coupling terms and to represent helical symmetry, a numerical study predicts that such solitons should appear under normal physiological conditions. This conclusion is supported by the assignment of a recently measured laser-Raman spectrum of a metabolically active cell to internal vibrations of the soliton. Analytical studies of continuum approximations to the numerical model provide additional insight into the soliton dynamics.

277 citations

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TL;DR: In this paper, an experimental study of the chaotic states and the routes to chaos in the driven pendulum as simulated by a phase-locked-loop electronic circuit is presented, for a particular value of the quality factor, for which the chaotic behavior is found to be rich in structure.

Abstract: An experimental study of the chaotic states and the routes to chaos in the driven pendulum as simulated by a phase-locked-loop electronic circuit is presented. For a particular value of the quality factor ($Q=4$), for which the chaotic behavior is found to be rich in structure, the state diagram (phase locked or unlocked) is established as a function of driving frequency and amplitude, and the nature of the chaos in these states is investigated and discussed in light of recent models of chaos in dynamical systems. The driven pendulum is found to exhibit symmetry breaking as a precursor to the period-doubling route for chaos. Although period doubling is found to be fairly common in the phase-locked states of the pendulum, it does not always manifest itself in complete bifurcation cascades. Intermittent behavior between two unstable phase-locked states is also commonly observed.

277 citations

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[...]

TL;DR: In this paper, the structural relationship between microscopic and macroscopic tensors is analyzed to characterize the linear and nonlinear-optical properties of molecular crystals exhibiting a strong donor-acceptor intramolecular interaction.

Abstract: We analyze the structural relationship between microscopic and macroscopic tensors which characterize the linear- and nonlinear-optical properties of molecular crystals exhibiting a strong donor-acceptor intramolecular interaction, with particular reference to methyl-(2,4-dinitrophenyl)-aminopropanoate (MAP). The quasiplanar structure of the active part of these molecules results in a strong and characteristic anisotropy of the optical hyperpolarizabilities, which can be traced up to the macroscopic level when taking into account the crystal symmetry as well as the orientation of the molecules in the unit cell. The experimental data on MAP are thoroughly analyzed on this basis, and it is found that a two-dimensional model of the lowest-order hyperpolarizability tensor results in a structural relation between the macroscopic tensor components, which is in agreement with experimental data. In addition, the principal dielectric axes of this monoclinic crystal are determined by the orientation of the aromatic plane in the unit cell. The overall analysis also enables the determination of four independent components of the molecular hyperpolarizability tensor from experimental data only, and the results have been compared to those of a semiempirical intermediate neglect of differential overlap calculation. The anisotropy of this tensor reveals that the intramolecular charge transfer responsible for the large optical nonlinearity is predominantly from the amino group to the nitro group in para position, rather than towards the nitro group in ortho position. Finally the overall analysis provides a basis for discussing what should be the best orientation of the molecules in the unit cell for maximizing the crystal nonlinearity. The result is that phase-matchable nonlinear coefficients up to six times larger than in MAP could be observed in compounds with similar molecular hyperpolarizabilities but an optimum crystal structure.

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TL;DR: In this article, aperiodic or chaotic behavior for one-dimensional maps just before a tangent bifurcation occurs appears as intermittency in which long laminar-like regions irregularly separated by bursts occur.

Abstract: The aperiodic or chaotic behavior for one-dimensional maps just before a tangent bifurcation occurs appears as intermittency in which long laminarlike regions irregularly separated by bursts occur. Proceeding from the picture proposed by Pomeau and Manneville, numerical experiments and analytic calculations are carried out on various models exhibiting this behavior. The behavior in the presence of external noise is analyzed, and the case of a general power dependence of the curve near the tangent bifurcation is studied. Scaling relations for the average length of the laminar regions and deviations from scaling are determined. In addition, the probability distribution of path lengths, the stationary distribution of the maps, the correlation function and power spectrum of the map in the intermittent region, and the Lyapunov exponent are obtained.

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ExxonMobil

^{1}TL;DR: In this article, the authors examined the phase transition properties of nematic liquid crystals aligned by a short-range, arbitrary-strength substrate potential in the framework of Landau-de Gennes theory and showed that the substrate potential not only induces a boundary layer in which the order-parameter values can be significantly different from that of the bulk, but also introduces a new "boundary-layer phase transition" which occurs at temperatures higher than the bulk-transition temperature.

Abstract: Phase-transition properties of nematic liquid crystals aligned by a short-range, arbitrary-strength-substrate potential are examined in the framework of Landau---de Gennes theory. It is shown that the substrate potential, which can arise from surface treatment of liquid-crystal display cells, not only induces a boundary layer in which the order-parameter values can be significantly different from that of the bulk, but also introduces a new "boundary-layer phase transition" which occurs at temperatures higher than the bulk-transition temperature. This novel transition is found to take place only in a limited range of substrate potential strength. For 4-pentyl-4'-cyanobiphenyl (PCB), the limiting values of this range are computed to be \ensuremath{\sim}0.075 and \ensuremath{\sim}0.15 erg/${\mathrm{cm}}^{2}$. Calculations are performed for both the semi-infinite-sample case and the finite-thickness-sample case. Various phase diagrams are presented to show the effects of sample thickness and substrate potential on the bulk as well as the boundary-layer phase-transition temperatures. The paper concludes with a discussion of experimental possibilities.

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TL;DR: In this article, total scattering cross sections have been measured in the same apparatus for positrons and electrons colliding with each of the molecules at the respective positronium-formation thresholds using a beam transmission technique.

Abstract: Total scattering cross sections have been measured in the same apparatus for positrons and electrons colliding with ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and C${\mathrm{O}}_{2}$ using a beam transmission technique. The projectile impact energies range from 1 - 500 eV for ${e}^{+}\ensuremath{-}{\mathrm{H}}_{2},2\ensuremath{-}500$ eV for ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{H}}_{2},0.5\ensuremath{-}750$ eV for ${e}^{+}\ensuremath{-}{\mathrm{N}}_{2},2.2\ensuremath{-}700$ eV for ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{N}}_{2},0.5\ensuremath{-}60$ eV for ${e}^{+}\ensuremath{-}{\mathrm{CO}}_{2}$, and $2\ensuremath{-}50$ eV for ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{CO}}_{2}$. The onset of positronium formation is clearly seen by an abrupt rise in the total cross sections for positrons colliding with each of the molecules at the respective positronium-formation thresholds. The positron measurements are compared with the electron measurements at intermediate energies for ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$. This comparison reveals a merging of the cross sections for ${\mathrm{H}}_{2}$ at energies above 200 eV, while for ${\mathrm{N}}_{2}$ the electron results remain higher than the positron results at all energies. Estimates are made of potential experimental errors, as well as the experimental resolution for discrimination against projectiles scattered at small forward angles.

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TL;DR: In this article, a direct method for obtaining conditions under which certain degree-of-freedom Hamiltonian systems are integrable, i.e., possess $N$ integrals in involution, is described.

Abstract: A direct method is described for obtaining conditions under which certain $N$-degree-of-freedom Hamiltonian systems are integrable, i.e., possess $N$ integrals in involution. This method consists of requiring that the general solutions have the Painlev\'e property, i.e., no movable singularities other than poles. We apply this method to several Hamiltonian systems of physical significance such as the generalized H\'enon-Heiles problem and the Toda lattice with $N=2 \mathrm{and} 3$, and recover all known integrable cases together with a few new ones. For some of these cases the second integral is written down explicitly while for others integrability is confirmed by numerical experiments.

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TL;DR: In this article, a variational least squares-fitting method was proposed for self-consistent field density functional calculations with the Coulomb potential, and the results showed the superiority of variational over conventional least square-fitting methods.

Abstract: A previously developed method for self-consistent-field density-functional calculations involving a variational fit to the charge density is generalized to the case in which the total (electronic plus nuclear) Coulomb potential is fit. Previously the total energy $E(\ensuremath{\rho},\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\rho}})$ was viewed as a functional of the exact $\ensuremath{\rho}$ and fitted $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\rho}}$ charge density. The energy expression was modified to be correct when $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\rho}}=\ensuremath{\rho}$ while at the same time allowing $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\rho}}$ to be obtained variationally through $\frac{\ensuremath{\partial}E(\ensuremath{\rho},\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\rho}})}{\ensuremath{\partial}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\rho}}}=0$. Herein an expression for $E(\ensuremath{\rho},\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V})$, where $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}$ is the fit to the Coulomb potential, is derived with similar properties. In particular, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}$ can be determined variationally through $\frac{\ensuremath{\partial}E(\ensuremath{\rho},\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V})}{\ensuremath{\partial}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}}=0$. In various linear-combination-of-atomic-orbitals calculations on atomic neon, the superiority of variational over conventional least-squares-fitting methods is demonstrated.

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TL;DR: In this paper, a technique for modifying the laser power spectrum by use of an acousto-optic modulator is described, and the theory of the power spectrum resulting from frequency modulation by Gaussian noise is reviewed.

Abstract: A technique for modifying the laser power spectrum by use of an acousto-optic modulator is described. The theory of the power spectrum resulting from frequency modulation by Gaussian noise is reviewed, and several examples of broadened laser power spectra are presented.

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TL;DR: The internal energy of the classical one-component plasma is calculated using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for 1.

Abstract: We calculate the internal energy of the classical one-component plasma using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for $1l\ensuremath{\Gamma}l300$ in order to determine the effect of a differing number of particles on the thermodynamics. By fitting the internal energy to a function of $\ensuremath{\Gamma}$ and $N$ (the particle number), we find the free energy for both the liquid and solid for an infinite number of particles.

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TL;DR: In this paper, a comparison of results with those obtained using the conventional two-term spherical harmonic technique and using the Monte Carlo technique is made of electron energy distributions, transport coefficients, and excitation coefficients for electrons in a model atom valid in the case of low and high electron energies.

Abstract: The recently developed density gradient and multiterm spherical harmonic expansion technique for the numerical solution of the electron Boltzmann equation is evaluated by comparison of results with those obtained using the conventional two-term spherical harmonic technique and using the Monte Carlo technique. Comparisons are made of electron energy distributions, transport coefficients, and excitation coefficients for electrons in ${\mathrm{N}}_{2}$ at moderate electric-field to gas-density ratios $\frac{E}{N}$ where the large cross section for vibrational excitation leads to significant errors when conventional solutions of the Boltzmann equation are used. The $\frac{E}{N}$ values were varied from (1 - 200)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$ V ${\mathrm{m}}^{2}$, corresponding to mean electron energies from 0.3 to 5 eV. The first two terms of the density-gradient expansion are used. As the number of terms $n$ in the spherical harmonic expansion is increased from the conventional two terms to $n\ensuremath{\ge}4$, the spherically symmetric component of the electron energy distribution and the transport and excitation coefficients become independent of $n$ and close to results obtained from the Monte Carlo calculation. The errors resulting from the use of two spherical harmonics at $\frac{E}{N}=7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ V ${\mathrm{m}}^{2}$, for example, are approximately 1, 5, and 30% for the drift velocity, the transverse diffusion coefficient, and the electronic excitation coefficients, respectively. For the lower $\frac{E}{N}$ values the errors in the transport coefficients are approximately proportional to an energy-loss-per-collision parameter. The variation of the coefficients of the lower-degree terms in the spherical-harmonic expansion with $n$ is examined through a comparison with an analytical solution of the Boltzmann equation for a model atom valid in the case of low $\frac{E}{N}$ and high electron energies. Monte Carlo techniques are used to show that the effects of electrodes are negligible for the conditions of recent measurements of electron excitation coefficients in ${\mathrm{N}}_{2}$.

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TL;DR: In this article, the frequency shifts of hyperfine splittings of the ground states of hydrogen and the alkali atoms were estimated from the dc hyperfine Stark shifts, which have previously been measured in the ground state of hydrogen, and were shown to be significant in primary Cs atomic beam frequency standards.

Abstract: Frequency shifts of hyperfine splittings of $^{2}S_{\frac{1}{2}}$ states due to the blackbody radiation field are calculated It is shown that they can be estimated from the dc hyperfine Stark shifts, which have previously been measured in the ground states of hydrogen and the alkali atoms The shift at 300 K is large enough to be significant in primary Cs atomic beam frequency standards, and should be measurable A simple method of calculating the hyperfine Stark shifts is described, which is based on the Bates-Damgaard method for determining radial matrix elements and the Fermi-Segr\`e formula for determining the contact hyperfine matrix elements It is applied to ${\mathrm{Ba}}^{+}$ and ${\mathrm{Hg}}^{+}$, for which no experimental data are yet available, and which are currently of interest for frequency standards

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TL;DR: In this article, a new prescription for the cyclotron frequency in terms of the observable eigenfrequencies of the imperfect trap was proposed, which is completely insensitive to a misalignment of the magnetic field direction with the axis of the Penning electrodes, and also insensitive to the most significant imperfections in the electrostatic potential.

Abstract: The phenomenal accuracies achieved for the spectroscopy of single charged particles suspended in Penning traps has prompted this study of the imperfect Penning trap. The principal result is a new prescription for the cyclotron frequency in terms of the observable eigenfrequencies of the imperfect trap. The new prescription is completely insensitive to a misalignment of the magnetic field direction with the axis of the Penning electrodes, and it is also insensitive to the most significant imperfections in the electrostatic potential. These systematic effects can therefore be completely circumvented in measurements of the anomalous magnetic moments of the electron and positron, and also in experiments on protons and heavier ions where the effects are much larger.

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TL;DR: In this paper, the authors derived expressions for stopping power and energy-loss straggling in a medium with internal motion for penetrating charged particles to the corresponding quantities applying to the equivalent medium at rest.

Abstract: Expression have been derived that relate the stopping power and energy-loss straggling in a medium with internal motion for penetrating charged particles to the corresponding quantities applying to the equivalent medium at rest These expressions have been based on a general binary-encounter picture and apply to nonrelativistic velocities and arbitrary mass ratios Convenient expansions have been found in the limits of very high and very low projectile velocity The results are applied to both nuclear and electronic stopping of charged particles The capability of the scheme is tested upon the degenerate free-electron gas, for which accurate expansions at high and low projectile speed are known, with regard to both stopping and straggling The scheme allows evaluation of shell corrections to stopping power and straggling of atomic and molecular gases beyond the range of validity of the leading terms in an expansion in inverse powers of electron velocity A seeming disparity between high-speed straggling parameters calculated for the Fermi gas on the one hand, and an atomic target on the other hand, is attributed to different ground-state properties of the two systems in zero order An essential difference is pointed out between the predictions of the dielectric theory and the present scheme with regard to the velocity dependence of energy-loss straggling in the low-speed limit

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[...]

Yale University

^{1}TL;DR: In this article, the self-energy radiative correction to the energy level of an electron in the Coulomb field, with nuclear charge in the range 10-110, is described.

Abstract: A calculation of the self-energy radiative correction to the energy level of an electron in the $2{S}_{\frac{1}{2}}$, $2{P}_{\frac{1}{2}}$, or $2{P}_{\frac{3}{2}}$ state in a Coulomb field, with nuclear charge $Z$ in the range 10-110, is described.

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TL;DR: In this paper, an adiabatic scanning calorimeter has been used to study the thermal behavior of the liquid-crystal octylcyanobiphenyl (8CB) in the temperature range between 10 and 50°C.

Abstract: An adiabatic scanning calorimeter has been used to study the thermal behavior of the liquid-crystal octylcyanobiphenyl (8CB) in the temperature range between 10 and 50\ifmmode^\circ\else\textdegree\fi{}C. The solid---to---smectic-$A$ ($\mathrm{KA}$), the smectic-$A$---to---nematic ($\mathrm{AN}$), as well as the nematic-to-isotropic (NI) phase transitions, which fall in this temperature range, have been investigated in great detail. From our measuring procedure the enthalpy behavior (including latent heats) as well as the heat capacity have been obtained. For the KA transition the latent heat was 25.7\ifmmode\pm\else\textpm\fi{}1.0 kJ/mol and for the NI transition it was 612\ifmmode\pm\else\textpm\fi{}5 J/mol. Within the resolution of our experiment we find that the $\mathrm{AN}$ transition is a continuous one. For the latent heat, if any, we arrive at an upper limit of 0.4 J/mol (or 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ J/g). The observed anomaly in the heat capacity for the $\mathrm{AN}$ transition is not consistent with a nearly logarithmic singularity as predicted by the $\mathrm{XY}$ model, instead we obtain a critical exponent $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=0.31\ifmmode\pm\else\textpm\fi{}0.03$. This result is consistent with the anisotropic scaling relation ${\ensuremath{
u}}_{\ensuremath{\parallel}}+2{\ensuremath{
u}}_{\ensuremath{\perp}}=2\ensuremath{-}\ensuremath{\alpha}$. The pretransitional effects near the NI transition are in qualitative agreement with the hypothesis of quasitricritical behavior.

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TL;DR: In this article, the photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion.

Abstract: Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.

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TL;DR: In this paper, Kramers's original model of the thermally activated escape rate over a barrier was generalized for Brownian-motion theory with long-time memory, and the model was extended to Brownian motion with long time memory.

Abstract: Kramers's original modeling of the thermally activated escape rate over a barrier is generalized for Brownian-motion theory with long-time memory

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TL;DR: In this paper, an algorithm proposed by Takens, which can determine the capacity (generalized dimensionality) of a dynamical system from the time series of a single observable, is tested numerically for several intrinsically stochastic models.

Abstract: An algorithm proposed by Takens, which can determine the capacity (generalized dimensionality) of a dynamical system from the time series of a single observable, is tested numerically for several intrinsically stochastic models. The algorithm is found to converge too slowly (if at all) to be useful for the analysis of experimental data.

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TL;DR: In this paper, a technique to produce stationary nonequilibrium states in a molecular-dynamics system was developed based on the introduction of stochastic boundary conditions to simulate the contact with a thermal wall.

Abstract: We have developed a technique to produce stationary nonequilibrium states in a molecular-dynamics system; this method is based on the introduction of stochastic boundary conditions to simulate the contact with a thermal wall. The relaxation times involved in such contact are short enough (\ensuremath{\sim}${10}^{\ensuremath{-}11}$ sec) to make the technique suitable for computer experiments. The method allows the simulation of bulk properties in a system coupled with a heat reservoir and the study of the local thermodynamical equilibrium. Furthermore, it gives a physical description of the heat transfer near a thermal wall. The method has been applied to simulate high thermal gradients in a region of dense fluids ranging from the gas-liquid coexistence line to the freezing line, to check the validity of the linear thermal response (Fourier's law). We have found that the linear region extends at least up to gradients of the order of 1.8\ifmmode\times\else\texttimes\fi{}${10}^{9}$ K/cm for argon. In the bulk region where boundary effects are negligible we have verified the validity of the local equilibrium hypothesis for all simulated gradients.

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[...]

TL;DR: In this article, the relativistic effects of the ground-state monatomic negative ions with $Zl86$ were calculated using the selfinteraction correction (SIC) to the local spin-density approximation (LSD) for exchange and correlation.

Abstract: The extra-electron binding energies of the ground-state monatomic negative ions with $Zl86$ are calculated using the self-interaction correction (SIC) to the local spin-density approximation (LSD) for exchange and correlation. The results agree reasonably with experiment, and the errors reflect the familiar "interconfigurational energy error" common to LSD and SIC. Some of the rare earths, e.g., Ce and possibly Gd, are predicted to form stable negative ions. In addition we have the following: (1) Relativistic (other than spin-orbit) contributions to the electron affinities are included and discussed. In Au the relativistic effects boost the calculated affinity from 1.5 to 2.5 eV. (2) The doubly negative ions ${\mathrm{O}}^{2\ensuremath{-}}$ and ${\mathrm{Te}}^{2\ensuremath{-}}$ are predicted to have no stable ground state. (3) Electron affinities are calculated for a few excited atomic states. (4) The calculated ground-state densities $n(r)$ of all the neutral atoms and negative ions are monotonically decreasing functions of $r$. (5) Corrections to the random-phase-approximation electron-gas correlation energy are shown to cancel out of SIC calculations for atoms.