Search results for "Hamiltonian"
showing 10 items of 662 documents
Electric field controllable magnetic coupling of localized spins mediated by itinerant electrons: a toy model
2017
In this paper, we propose a toy model to describe the magnetic coupling between the localized spins mediated by the itinerant electron in partially delocalized mixed-valence (MV) systems. This minimal model takes into account the key interactions that are common for all such systems, namely, electron transfer in the valence-delocalized moiety and magnetic exchange between the localized spins and the delocalized electrons. The proposed descriptive model is exactly solvable which allows us to qualitatively and quantitatively discuss the main features of the whole class of partially delocalized MV systems. In the case of relatively strong exchange coupling, the combined action of these two int…
Simultaneous Determination of Force Constants and Dipole Moment Derivatives of Methane.
1998
The expressions of the effective Hamiltonian and dipole moment spectroscopic parameters in the tetrahedral formalism are used simultaneously to fit the force field and dipole moment derivatives of the methane molecule. Data, the so-called "observed parameters," are the values of the spectroscopic parameters determined from the frequencies and line strengths analyses. The ambiguities of most parameters (in the polyad scheme) are treated consistently with the Hamiltonian reduction chosen in the frequency analyses. As an illustration, the method is applied to the tetrahedral XY4 isotopic species only. The quadratic and cubic force field constants have been determined in addition to the linear …
Development of the Hamiltonian and transition moment operators of symmetric top molecules using the O(3)⊃C∞v⊃C3v group chain
2005
Abstract We present a development of the Hamiltonian, dipole moment, and polarizability operators for XY3Z molecules. These rovibrational operators are written with the aid of a tensorial formalism derived from the one already used in Dijon and adapted to the XY3Z symmetric tops in a recent paper [A. El Hilali, V. Boudon, M. Loete, J. Mol. Spectrosc. 234 (2005) 166–174]. We use the O (3) ⊃ C∞v ⊃ C3v group chain. Expressions for the matrix elements are derived for these operators.
Spectroscopy of XY5Z (C4v) Molecules: Development of the Hamiltonian and the Transition Moment Operators Using a Tensorial Formalism
2000
We present a development of the Hamiltonian, dipole moment, and polarizability operators of XY(5)Z (C(4v)) molecules using a tensorial formalism derived from the one developed previously in Dijon for XY(6) molecules. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum simulations. Expressions for the matrix elements are derived for all these operators. Copyright 2000 Academic Press.
The Ramsey method in high-precision mass spectrometry with Penning traps: Theoretical foundations
2007
Abstract This paper presents in a quantum mechanical framework a theoretical description of the interconversion of the magnetron and modified cyclotron motional modes of ions in a Penning trap due to excitation by external rf-quadrupole fields with a frequency near the true cyclotron frequency. The work aims at a correct description of the resonance line shapes that are observed in connection with more complicated excitation schemes using several excitation pulses, such as Ramsey’s method of separated oscillating fields. Quantum mechanical arguments together with the “rotating wave approximation” suggest a model Hamiltonian that permits a rigorous solution of the corresponding Heisenberg eq…
A Symmetry Adapted Approach to the Dynamic Jahn-Teller Problem
2011
In this article we present a symmetry-adapted approach aimed to the accurate solution of the dynamic Jahn-Teller (JT) problem. The algorithm for the solution of the eigen-problem takes full advantage of the point symmetry arguments. The system under consideration is supposed to consist of a set of electronic levels \({\Gamma }_{1},{\Gamma }_{2}\ldots {\Gamma }_{n}\) labeled by the irreducible representations (irreps) of the actual point group, mixed by the active JT and pseudo JT vibrational modes \({\Gamma }_{1},{\Gamma }_{2}\ldots {\Gamma }_{f}\) (vibrational irreps). The bosonic creation operators b +(Γγ) are transformed as components γ of the vibrational irrep Γ. The first excited vibra…
Remarks on quadratic Hamiltonians in spaceflight mechanics
2006
A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.
A local picture associated with a triply degenerate vibrational mode: vibrational and rovibrational local states
1998
International audience; Abstract: A symmetrized basis adapted to the study of some vibrational excited states of spherical top molecules is proposed. This basis, consistent with the Cartesian picture associated with a three-dimensional mode, is then tested numerically through various XY6 and XY4 molecules. In addition, some simulations, made with 238UF6 and a simplified version of an effective Hamiltonian, clearly show that the method can be further extended through the construction of a symmetrized local rovibrational basis.
Study of the stretching modes of the arsine molecule
2003
Abstract To study local mode XY 3 molecules, we use properties of the group chain U ( 4 ) ⊃ U ( 3 ) ⊃ K ( 3 ) ⊃ S ( 3 ) ≈ C 3 v . For the Hamiltonian, we deduce diagonal terms and coupling terms between bonds. We analyze the stretching modes of the arsine molecule. An algebraic transition operator is built and applied to the same molecular system.
Collisional models in a nonperturbative approach
1992
Abstract A nonperturbative method set forth recently for handling quantum dynamics in the intermediate regime (far from either the sudden or the adiabatic limit) is applied to soluble two-state collisional models.