Time-independent Theory Research Articles

Time-independent theory of multiphoton ionization of an atom by an intense field.

We formulate a computationally feasible method for calculating multiphoton ionization rates for atoms exposed to intense fields in the intensity regime where perturbation theory ceases to apply. The method is based on the time-independent picture of ionization, which starts with the Floquet ansatz. The question of the gauge of the radiation field is discussed in some detail. Various expressions for the ionization amplitude are derived from a variational principle, with the radiation field expressed in the velocity gauge. We consider in particular an approximation in which the wave vector developing from the initial state is replaced by a trial vector that is the Floquet expansion truncated just below the threshold for ionization, and in which the wave vector developing into the final state is replaced by a trial vector that is just the wave vector appearing in the Kroll-Watson low-frequency approximation in scattering theory. We have applied this approximation to hydrogen and we present some results for both nonresonant and resonant multiphoton ionization. We argue that the experimentally observed resonance structure in the above-threshold peaks of the ionization signal occurs through the electron jumping from one dressed-state energy-eigenvalue curve to another.

A 29-root soluble model for the nonlinear calculation of a four-body propagator

The time-independent mean-field theory of collisions is applied to the collision of four one-dimensional particles. Their two-body interactions are taken as separable, with Lorentzian form factors. This allows completely analytical solutions. A unique and satisfactory physical branch emerges out of 29 candidate solutions. It is very stable when the strength of the interaction is modified.

Time-dependent response theory

In this paper we extend the nonlinear response theory developed by Evans, Morriss and Holian to describe the response of many-body classical systems to time-dependent external fields. The resulting formalism is applicable to both adiabatic and thermostatted systems. The results are then related to a number of known special cases: time-dependent linear response theory, and time independent nonlinear response theory as described by the transient time correlation approach and the Kawasaki response formula.

Theory of Metal-Solid Electrolyte Interface

AbstractA comprehensive time independent theory of the solid electrolyte(SE)–metal electrode interface is presented, using the assumption that cations are the only mobile charge carrier in the electrolyte. The temperature and the dc current across the SE are the only free parameters for the solutions along with three intrinsic parameters which depend on the properties of the particular system. The phenomenological model of the interface double layer is based on the Gouy–Chapman–Stern model.The numerical solutions of the theory for porous tungstenzeolite system enables us to predict most of the properties in the SE system such as;the current–overpotential characteristics, the capacitances of the double layer, concentration profile in the diffusion layer, the potential profile across the interface, electrochemical exchange current, and the potential of zero charge(PZC) etc. An experimental technique to measure the PZC of SE systems has been also proposed.

Theory of electron diffraction from planar ideal crystals

A theory of electron diffraction from a planar ideal crystal of arbitrary thickness is presented. It is based on Schrödinger's equation. Both the relativistic corrections in energy and wavelength and the electron 'absorption' due to the presence of inelastic scattering may be incorporated as usual. This theory is constructed in an exact differential-equation approach known as rigorous coupled-wave analysis. This is an exact method of diffraction analysis that has been extensively tested for its numerical calculation scheme. The exact solution for electron wave amplitudes of all diffraction orders is formally presented in terms of a standard eigenvalue problem and explicitly expressed in matrix form. Numerical calculation can be implemented on digital computers in a straightforward manner. An approximate conservation law is given for the transmittance and reflectance, which are then the relevant dynamical quantities to be measured in a realistic time-dependent diffraction process and to be calculated in this time-independent diffraction theory for comparison. Two derivations of the well known Bragg law are sketched.

On- and off-shell convergence of the time-independent mean-field theory of collisions.

The mean-field approximation to the many-body Green's function (E-H${)}^{\mathrm{\ensuremath{-}}1}$ is derived by the use of products of single particle orbitals for trial functions in a variational formalism. It is shown that the matrix elements of the Green's function behave smoothly as ImE is varied towards the on-shell limit ImE=0.

Time-independent constitutive theories for cyclic plasticity

The article is mainly concerned with time-independent plasticity in the range of cyclic loadings. Three different approaches are considered for the description of kinematic behaviour: (i) the use of independent multiyield surfaces, (ii) models with two surfaces only, (iii) the so-called “nonlinear-kinematic hardening rule” defined by a differential equation. The thermodynamic framework from which the third approach is derived and the conditions of varying temperature are considered. Connections between the three kinds of models are pointed out. Also, some specific rules to describe cyclic hardening or cyclic softening of the material are proposed. Finally, the limits of the models considered, and the difficulties associated with their practical use and their implementation in computer codes are discussed in detail.

Whither existence theory?

Abstract It is sugested that in certain cases the Fredholm alernativ theorem can be-used to simplify existence proofs in time-independent linear transport theory. Existing results in abstract kinetic equations theory are generalized as to encompass polarized light transfer as well as certain inhomogeneous finite slab media.

The albedo problem in the case of multiple synthetic scattering taking place in a plane-symmetric slab—I: Exact theory and numerical results

The albedo problem for a slab in the presence of synthetic scattering as a substitute for anisotropic scattering is treated within the framework of time-independent one-velocity transport theory. The transport equation is transformed into a Boltzmann-type equation, from which expressions for the coefficients of reflection and transmission are deduced. Some interesting limiting cases are discussed. Extensive tables of R-and T-values are established for various slab thicknesses, various angles of incidence and various types of synthetic scattering both in the conservative case and in an example which is representative of the non-conservative case.

Time-independent wave-packet theory of collisions

Time-independent wave-packet theory of collisions

Molecular abundances and nucleation in protostellar envelopes

This work is basically concerned with grain nucleation occurring in protostellar envelopes. On the basis of the dissociation equilibrium theory, molecular and atomic abundances are obtained for massive protostar envelopes. Application of time-independent homogeneous nucleation theory results in the possibility of atomic Fe condensation.

Variational estimate of a breakup amplitude

Estimates of the correction to the Born amplitude are obtained from a variational principle. A wave packet representation is used to provide an off-shell amplitude in a time-independent theory of collisions. The theory is applied numerically to a breakup reaction p + $^{3}\mathrm{H}$ \ensuremath{\rightarrow} p + n + d.NUCLEAR REACTIONS Time independent, off-shell amplitude, obtained from variational principle. Wave packet representation generates fragmentation exclusive cross sections.

Energy of a test charge in time-independent Yang-Mills theories

It is shown that $\ensuremath{\Delta}({q}_{a}{{A}_{a}}^{0})$ is the work done if a test charge ${q}_{a}$ is moved adiabatically from one point to another in Yang-Mills theories where the ${A}_{a}^{u}$ are time independent.

A time-independent quantum mechanical theory for multiphoton dissociation of diatomic molecules

A nonperturbative expression for the rate of dissociation from the ground vibrational state of a diatomic molecule in the presence of an infrared laser field is derived using R-matrix techniques. No rotating wave approximation and no metastable levels are introduced. The result is applied to a model system and to HF to obtain the dependence of multiphoton dissociation rate upon laser frequency and intensity. Dissociation is predicted at fields of order 1013 W/cm2.

Contributions to the time independent theory of Rayleigh scattering in liquids

Based upon the molecular light scattering theory of Kielich [8], the second order light scattering caused by the optical dipole interaction in the liquid state is derived. In the general case of molecules with anisotropic polarizability the isotropic and anisotropic Rayleigh factors of the second order scattering are written explicitly in terms of the two parts representing the DID interaction (A) and the self reaction (B). By considering a simple model of shell structure of the liquid state, an extinction factor is introduced which reduces the class A of scattering and which depends on structural parameters of the liquid state (i.e. the mean values of the coordination number, of the number of holes in the first shell and the radial pair distribution function). Applied to liquids with spherical molecules, and with reasonable assumptions about the structural parameters, the anisotropic Rayleigh factor can be predicted in close agreement with the experimental value, as has been demonstrated for carbon tetra...

Multiphoton ionization rate with a non-Lorentzian-band-shape laser

A time-independent single-rate theory for multiphoton ionization processes is developed to cover cases with a partially coherent (finite-bandwidth) driving laser. We use the Ornstein-Uhlenbeck fluctuating-phase model to describe the driving field, which has therefore a non-Lorentzian spectrum, and the effective two-level model to represent the atomic system. We present analytic and numerical methods that permit discussion of the effects of non-Lorentzian band-shape laser light, and we give analytically the bandwidth dependence of the rate in the wings of the ionization curve. Our model contains a simple scaling relationship that permits the rate for $N$-photon-resonant ($N+1$)-photon ionization to be obtained directly from the one-photon-resonant two-photon ionization rate. We treat explicitly the cases $N=1$ and $N=2$.

Contributions to the time-independent theory of Rayleigh scattering in liquids

Molecular formulae for the isotropic and anisotropic scattering are derived by considering the internal field acting upon a molecule within a dense medium and its fluctuation caused by density fluctuations. The anisotropic scattering formula of classical theory is retained but modified by the factors of the internal field. The new formula for the isotropic scattering depends sensitively on the principal values of the optical polarizability tensor and on the parameters describing the anisotropic internal field. Assuming the internal field to be given by the semimacroscopic approach of the Onsager-Scholte model with an ellipsoidal cavity, comparison of the calculated isotropic Rayleigh factor with the experimental value allows a prediction of the degree of the cavity anisotropy for different liquid densities.

Feshbach-Villars formalism and pion-nucleon scattering

The Feshbach-Villars Hamiltonian formulation of the Klein-Gordon equation is used as the basis for a scattering theory for relativistic, spin-zero, particles. Time dependent and time independent scattering theories are developed. The time independent theory is used as the framework for a separable potential model for ..pi..N elastic scattering in P waves. This potential leads to a ..pi..N T matrix which has the right and left hand cuts associated with two-particle unitarity and crossing, respectively, as well as the direct and crossed nucleon poles with the proper residues. The effects of nucleon recoil are included. With a particular choice of the form factors in the potential, the Chew-Low T matrix is reproduced.

Time independent quantum theory of electron transfer collisions using a nonorthogonal basis and R-matrix propagation

We briefly review the difficulties associated with the traditional adiabatic quantum treatment of low energy charge transfer collisions between atoms and suggest that the charge transfer problem can be most conveniently treated by using atomic-centered basis functions and expressing the Hamiltonian simultaneously with respect to two separate atomic origins. As a result, we must solve the quantum nuclear equations of motion in a nonorthogonal basis. We demonstrate that this may be efficiently done by building the R-matrix propagator in this basis. Flux is automatically conserved even though the R matrix is built up from a series of nonunitary transformations. A simple model problem designed to represent the radial coupling in the reaction Li++Na→Li+Na+ is solved to illustrate the technique.

Time Dependent Probabilistic Failure Model for the Strength of Fiber Reinforced Plastics

The fracture strength of GRP (Glassfiber Reinforced Plastics), which depends on the applied time of stress and the stress rate, was analyzed by using a time dependent probabilistic failure model. The fracture process was assumed to be a 1-step stochastic process and the transition probability of failure to be γSδf(t) where S and t represent stress and time, respectively and γ and δare constants. The evaluation of the damage in the case when the stress varied was done by "the reduced time method" proposed in this paper. When f(t)=tγ and S=at (γ, a; constants), the fracture stress Sc was calculated as follows. [numerical formula] where Dc is a constant. The constant a is stress rate and so the effect of stress rate on the fracture stress could be clearly presented. Static fatigue strength was also analyzed. The analytical results showed a good agreement with experimental results For glass plates and glassfiber composites, the constants γ and δ were found to be about -0.7 and 6.26, respectively. therefore, the traditional time independent probabilistic theory overestimates the effect of strain rate on the strength of materials.