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Simultaneous laser oscillation of four nondegenerate polarization and propagation direction eigenstates of a single TEM-00 mode was observed in a ring laser cavity. The observed polarization and frequency properties of the ring laser were analyzed in terms of the Jones matrix calculus.
A model applicable to normal metal tunnel junctions is presented. This model, referred to herein as the stationary state model, is an extension of the extended basis function theory of Kleinman and Duke (1972). Under the assumption that elastic tunneling is the dominant transport mechanism under static bias, the theory has been extended to include the case where there is an ac component of bias potential, and the fluctuation spectrum has been derived. In this approach structure eigenstates are used as the basis, allowing observables to be evaluated without recourse to the perturbation theory inherent in the transfer Hamiltonian model. Comparison is made to the appropriate results of the first order transfer Hamiltonian model, and it is found that there is close but not always exact agreement to lowest order in the tunneling exponential. The stationary state model should be accurate with large barrier transmission, as it includes all orders of the tunneling exponential. The model as presented here should be applicable to normal metal tunnel junctions, where elastic tunneling is the dominant transport mechanism (under static bias), up to infrared excitation frequencies.
The concepts and computational tools of theortical chemistry are used to investigate molecular properties needed in direct solar-pumped lasers. Compounds of the type RR'CXY, with R and R' organic groups, and X and Y halide atoms were identified as likely candidates because of their highly enhanced absorption coefficients over compounds with a single halide atom. The use of a combination of vibrational excitation followed by electronic excitation to enhance quantum yields at certain wavelengths is indicated. A self-consistent eikonal approximation to state-to-state transitions was tested for CH3I and is useful for other problems involving electronic energy and charge transfer. An approach to calculate potential energy surfaces and transition dipoles was developed which is based on the generation of eigenstates of the nonrelativisitc Hamiltonian followed by incorporation of the spin-orbit coupling by configuration interaction.
Experiments in which a long vertical, heated wire is surrounded by concentric annuli of a melt and its crystalline solid show that the convection state changes from a stable unicell surrounded by a stationary cylindrical solid-liquid interface, to a complex time-dependent flow surrounded by a rotating, helical solid-liquid interface. This transition occurs at a Grashof number of approximately 150, which is an order of magnitude less than the critical Grashof number calculated for a liquid annulus surrounded by rigid walls. A linear stability analysis has been carried out for an infinitely tall vertical annulus. When the deformable nature of the crystal-melt interface is taken into account in the boundary conditions, two new modes of instability arise. The most dangerous mode is asymmetrical and corresponds to helical waves travelling vertically upwards. The critical Grashof number and the scaling properties of the eigenstate agree with experiments. The results clearly demonstrate the coupling of convection with crystal-melt interfacial instabilities.
The aerothermodynamic studies of proposed space missions require atmospheric charge-transfer data. N2(+) eigenstate energies are calculated with use of the complete-active-space self-consistent-field method with an extended Gaussian basis set. The N(+)-N charge-exchange cross section, determined from these energies, agrees with merged-beam measurements. This contradicts the previous theoretical conclusion. A simple physical description of the long-range interaction is presented and should expedite future charge-transfer studies.
Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.
Solidification and crystal growth processes involve thermal and solutal gradients within a molten phase. In the presence of gravity, such gradients result in convective flows which interact with diffusion fields at the solid-liquid interface. Dendritic growth kinetics was studied in transparent model systems which freeze similarily to most metals. Succinonitrile shows a strong influence of convection at supercoolings below about 1K. Fluid flows adjacent to solid-liquid interfaces and the behavior of shear flows in vertical annular geometries are studied. Novel low-frequency eigenstates were discovered and classified as coupled modes, for their involvement with interfacial deformation coupled to the fluid flow, and are unknown in systems without deformable interfaces. The dependence of coupled convection modes on interfacial geometry, gravity, fluid properties, and transformation characteristics studied for several annual flow arrangements with nominally pure solid-liquid systems.
Variational calculations of subband eigenstates in an infinite quantum well with an applied electric field using Gram-Schmidt orthogonalized trial wave functions are presented. The results agree very well with the exact numerical solutions even up to 1200 kV/cm. It is also shown that, for increasing electric fields, the energy of the ground state decreases, while that of higher subband states increases slightly up to 1000 kV/cm and then decreases for a well size of 100 A.
The semirelativistic approach, as applied to sum-rule calculations, can yield very inaccurate results for high-Z systems; the apparently good agreement previously reported is fortuitous, due to the application of an approximate eigenstate of the semirelativistic Hamiltonian. Attention is given to one-electron atomic systems, and the results obtained are discussed with a view to their implications for many-electron systems. The many-electron problem is complicated by a lack of clarity as to the relative importance of contributions due to correlation effects among the electrons, their effect on the E2 oscillator strength, and the retardation correction to the E1 transition.
Previous work has shown that the cooling of SN 1987A excludes a Dirac-neutrino mass greater than theta(20 keV) for nu(sub e), nu(sub mu), or nu(sub tau). The emission of wrong-helicity, Dirac neutrinos from SN 1987A, is re-examined. It is concluded that the effect of a Dirac neutrino on the cooling of SN 1987A has been underestimated due to neutrino degeneracy and additional emission processes. The limit that follows from the cooling of SN 1987A is believed to be greater (probably much greater) than 10 keV. This result is significant in light of the recent evidence for a 17 keV mass eigenstate that mixes with the electron neutrino.
Mathematical model enables design of filter assembly of birefringent plates as integral part of resonator cavity of tunable solid-state laser. Proper design treats polarization eigenstate of entire resonator as function of wavelength. Program includes software modules for variety of optical elements including Pockels cell, laser rod, quarter- and half-wave plates, Faraday rotator, and polarizers.
Operator angle-action variables are studied in the frame of the SU(2) algebra, and their eigenstates and coherent states are discussed. The quantum mechanical addition of action-angle variables is shown to lead to a noncommutative Hopf algebra. The group contraction is used to make the connection with the harmonic oscillator.
State of the art ab initio electronic structure methods have been used to investigate the (FHCl)- molecular anion. It is proposed that the geometric structure and binding energies of the complex are r(e)(H-F) = 0.963 +/- 0.003 A, R(e)(H-Cl) = 1.925 +/- 0.015 A, and D0(HF + Cl(-)) = 21.8 +/- 0.4 kcal/mol. A Morokuma decomposition of the ion-molecular bonding give the following electrostatic, polarization, exchange repulsion, dispersion, and charge-transfer plus higher-order mixing components of the vibrationless complexation energy: -27.3, -5.2, +18.3, -4.5, and -5.0 kcal/mol, respectively. A couples cluster single and doubles global surface is constructed from 208 and 228 energy points for linear and bent configurations, respectively, these being fit to rms errors of only 3.9 and 9.3/cm, respectively, below 8000/cm. Converged J = 0 and J = 1 variational eigenstates of the (FHCl)- surface to near the HF + Cl(-) dissociation threshold are determined. The fundamental vibrational frequencies are found to be nu1 = 247/cm, nu2 = 876/cm, and nu3 = 2884/cm. The complete vibrational eigenspectrum is analyzed.
Although the problem of electromagnetic radiation by a quantum harmonic oscillator is considered in textbooks on quantum mechanics, some of its aspects have remained unclear until now. By this, we mean that usually the initial quantum states of both the oscillator and the field are assumed to be characterized by a definite energy level of the oscillator and definite occupation numbers of the field modes. In connection with growing interest in squeezed states, it would be interesting to analyze the general case when the initial states of both subsystems are arbitrary superpositions of energy eigenstates. This problem was considered in other work, where the power of the spontaneous emission was calculated in the case of an arbitrary oscillator's initial state, but the field was initially in a vacuum state. In the present article, we calculate the rate of the oscillator average energy, squeezing, and correlation parameter change under the influence of an arbitrary external radiation field. Some other problems relating to the interaction between quantum particles (atoms) or oscillators where the electromagnetic radiation is an arbitrary (in particular squeezed) state were investigated.
We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.
The origin of Dicke cooperative states was studied by considering two harmonic oscillators driven by a common field of radiation. The origin is assumed for superradiance in a system of molecules where no mutual interactions exist, but all of the molecules encounter the same field of radiation. A phasing operator as Phi(sub Nu) equals D(alpha) + P(sub Nu)D(alpha), where D(alpha) is the displacing operator and P(sub Nu) the projection operator for constant energy Nu for two oscillators, was derived. The eigenstates of the phasing operator Phi are found to show a finite correlation as in the Dicke cooperative states.
Coherent states on the m-sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied. They are eigenstates of the operators a(sub m)(+), a(sub m) which create and annihilate clusters of m-particles. Applications of this formalism in the study of Hamiltonians that describe m-particle clustering are also considered.
The model describing three coupled quantum oscillators with decay of Rayleigh mode into the Stokes and vibration (phonon) modes is examined. Due to the Manley-Rowe relations the problem of exact eigenvalues and eigenstates is reduced to the calculation of new orthogonal polynomials defined both by the difference and differential equations. The quantum statistical properties are examined in the case when initially: the Stokes mode is in the vacuum state; the Rayleigh mode is in the number state; and the vibration mode is in the number of or squeezed states. The collapses and revivals are obtained for different initial conditions as well as the change in time the sub-Poisson distribution by the super-Poisson distribution and vice versa.