Oppenheimer Model Research Articles

Decoding the electron dynamics in high-order harmonic generation from asymmetric molecular ions in elliptically polarized laser fields

The high-order harmonic generation from an asymmetric molecular ion is theoretically investigated based on the Born–Oppenheimer model with two-dimensional electron dynamics. It is shown that the harmonic intensity changes periodically in elliptically polarized laser fields. The periodical character is ellipticity-dependent. By establishing the physical image, the periodicity of the harmonic intensity can be ascribed to the contributions of the ground state and the excited state. Furthermore, the electron dynamics from different electronic states can be selected via combining the elliptically polarized laser field with a static electric field. The harmonics dominated either by ground state or excited state are emitted once in an optical cycle in the combined laser field.

A quantum-mechanical non-Born–Oppenheimer model of a molecule in a strong magnetic field

Interactions of a stationary external magnetic field with the spin and orbital magnetic momenta of a molecule are included in the quantum mechanical model where the Born–Oppenheimer approximation is not assumed. The model is used to calculate some of the lowest-lying internal bound states of the molecule for various strengths of the magnetic field. All-particle explicitly correlated Gaussian functions are used in the calculations.

Erratum to “Determination of Non–Adiabatic Scattering Wave Functions in a Born–Oppenheimer Model"

instead of ψ(x, t, ,±) = σ=± ψ(x, t, ,±). With this definition, Proposition 4.1 should be replaced by Proposition 4.1′ Assume H1, H2, H3 and C0. Then, for any 0 < β < 1/2, we have the following L(IR)–norm estimate as t → ±∞, ‖ψ(x, t, ) − (ψ−(x, t, ,±) + ψ(x, t, ,∓)) ‖ = O (1/|t|β). In eqn. (4.4), “ψ(x, t, ,−) =” should be replaced by “ψ−(x, t, ,−) ,” and the qualification “for negative x’s” should be added. Similarly, in the next sentence, the stipulation “for positive x’s” should be added. The proof of Proposition 4.1 should be amended as follows: Equation (7.14) should begin with

On the Singular Limit of the Quantum-Classical Molecular Dynamics Model

In molecular dynamics applications there is a growing interest in so-called mixed quantum-classical models. These models describe most atoms of the molecular system by means of classical mechanics but describe an important, small portion of the system by means of quantum mechanics. A particularly extensively used model, the quantum-classical molecular dynamics (QCMD) model, consists of a singularly perturbed/ Schrödinger equation nonlinearly coupled to a classical Newtonian equation of motion. This paper studies the singular limit of the QCMD model for finite dimensional Hilbert spaces. The main result states that this limit is given by the time-dependent Born--Oppenheimer model of quantum theory---provided the Hamiltonian under consideration has a smooth spectral decomposition. This result is strongly related to the quantum adiabatic theorem. The proof uses the method of weak convergence by directly discussing the density matrix instead of the wave functions. This technique avoids the discussion of highly oscillatory phases. On the other hand, the limit of the QCMD model is of a different nature if the spectral decomposition of the Hamiltonian happens not to be smooth. We will present a generic example for which the limit set is not a unique trajectory of a limit dynamical system but rather a funnel consisting of infinitely many trajectories.

Insurgency, counterinsurgency, and the rational peasant

Many rational choice treatments of guerrilla insurgency have focused on the strategic calculus by which government and insurgent elites use the tactical weapons of coercion and benefits to win the support of nonelites. This paper uses Frohlich and Oppenheimer's model of the rational tax payer/tax evader to develop a model of the decision calculus by which nonelites respond to the tactical behavior of elites and thereby choose between supporting the incumbent regime, its insurgent opposition or neither. This model is then used to assess the likely impact of various insurgent and counterinsurgent tactics on nonelite support and loyalty.

Status Maintenance or Status Competition? Wife's Relative Wages as a Determinant of Labor Supply and Marital Instability

This paper tests two contending theories about the effect of the interaction between husband's and wife's earnings capabilities on the wife's laborforce participation and on the probability of marital dissolution. The first of these is Parsons' status competition model which suggests that, other things equal, the higher a woman's wage potential relative to her husband's the more peripheral should be her labor force attachment. Violation of this constraint by her employment in a status competitive position is presumed to lead to increased risk of marital disruption. By contrast, Oppenheimer's status maintenance model proposes that the family's efforts to enhance its position in the socioeconomic hierarchy is an inducement to the wife's employment the more congruent her potential laborforce achievement is with her husband's. Our results generally support the Oppenheimer model, although some support for Parsons' model was found. We conclude by emphasizing the need for study of the interactive linkages between husbands' and wives' careers. Models explaining male and female labor market experiences are increasingly developing largely in isolation from each other, with little in the way of systematic analyses exploring the interplay of husbands' and wives' work-related decisions and achievements. This paper is a departure from this trend. In particular, it draws on a persistent thread of speculation over the last several decades regarding the implications of a wife's employment for disruptive competition between marital partners.' Two major streams of thought are represented in the literature, each reaching strikingly different conclusions about the likely effect such status competition will have on a woman's proclivity to enter the labor force. This paper tries to examine

Wave propagation in a binary gas mixture as described by kinetic models of the Boltzmann equations

The initial‐value problem defined by the linear one‐dimensional Oppenheim model, which qualitatively describes wave propagation in a binary gas mixture and which is representative of other kinetic models, is examined. An asymptotic study of the dispersion relation and its analytic continuation is carried out to determine the structure of the solution.

Mathematical aspects of kinetic model equations for binary gas mixtures

A system of integrodifferential equations, which has a structure similar to the Boltzmann equations for a binary gas mixture and which qualitatively describes wave propagation, is investigated. The Oppenheim model is used and a linear initial−value problem is considered. The initial−value problem is shown to be well set mathematically with certain specifications on the initial distribution functions. Justification is made for the use of Fourier−Laplace transforms. A discussion is made of the dispersion relation and its analytic continuation. The roots σ (k) of the dispersion relation are shown to lie in three distinct regions of the σ plane: the hydrodynamic region, the semihydrodynamic region, and the rarefied region. It is established that the roots σ (k) are bounded by −1 + δ &amp;lt; Reσ ⩽ 0 under the assumption of plane−wave solutions which implies that the system is stable and that plane waves cease to exist if Reσ ⩽ −1 + δ.

Some Remarks on the Logic of Explanation in the Social Sciences

If one were to write a history of the philosophy of science in the spirit of T. S. Kuhn, one would have to consider the model of scientific explanation which Popper proposed and Hempel and Oppenheim developed to be one of the great paradigms of contemporary analytical philosophy of science. This analogue to the historically important paradigms of the individual sciences seems to me to be justifiable for the following reasons: first, the Hempel—Oppenheim model (or HO-model, as I shall call it) claims universal methodological validity; second, discussions on the problem of explanation have centred on this model for some time; third, the recent cognitive progress in this field has been largely the result of the interrelation between criticism of this model on the one hand and its improvement and explication on the other hand; and lastly, this model stands for a particular comprehension of the problems and possibilities of science, a concept of quite important practical consequence.

Some Remarks on the Logic of Explanation in the Social Sciences

If one were to write a history of the philosophy of science in the spirit of T. S. Kuhn, one would have to consider the model of scientific explanation which Popper proposed and Hempel and Oppenheim developed to be one of the great paradigms of contemporary analytical philosophy of science. This analogue to the historically important paradigms of the individual sciences seems to me to be justifiable for the following reasons: first, the Hempel—Oppenheim model (or HO-model, as I shall call it) claims universal methodological validity; second, discussions on the problem of explanation have centred on this model for some time; third, the recent cognitive progress in this field has been largely the result of the interrelation between criticism of this model on the one hand and its improvement and explication on the other hand; and lastly, this model stands for a particular comprehension of the problems and possibilities of science, a concept of quite important practical consequence.