The classical and quantal dynamics of non-hydrogenic Rydberg atoms in magnetic fields are investigated. Previous attempts to infer classical behaviour from quantum properties produced conflicting results: at low scaled energies (epsilon = -0.5) the nearest-neighbour statistics (NNS) were found to be at the chaotic (Wigner) limit while quantum phase-space distributions suggested a high degree of regularity.Here the classical limit is investigated directly by solving the equations of motion of the Diamagnetic Kepler problem (DKP) with an additional non-Coulombic model potential. It is found that typically trajectories are, over a long time-scale, ergodic. However over a shorter time-scale-in between collisions with the core-classical trajectories remain confined on the tori of the DKP. The origin of a well-known resonance in the NNS of hydrogen at epsilon = -0.316 is clarified by the comparison with the non-hydrogenic behaviour. However, the classical model only partially explains the quantum behaviour. The difficulties of quantizing such a system are discussed.

Mesoscopic systems occupy a special place in the physical sciences: They lie somewhere between the microscopic and macroscopic worlds. Here we study persistent currents of normal-metal rings in a magnetic field and with a magnetic flux through the center of the ring. We discuss the effects of finite temperature and ensemble averaging. By these computations we are able to simulate experimental results for both single rings and arrays of rings.

The states of an atom in external electric fields become quasi-bound since the electron can ionize by tunneling through the potential barrier into the continuum. Due to the external electric field the ionization threshold of the atom is lowered from the field-free value. This process becomes important for states close to the classical ionization energy or above. These resonance states can be studied using the complex coordinate method. In this method the Hamiltonian of the system is continued into the complex plane by a complex dilatation, therefore the Hamiltonian is no longer Hermitian and can support complex eigenenergies associated with decaying states. Resonances are uncovered by the rotated continuum spectra with complex eigenvalue and square-integrable (complex rotated) eigenfunctions. The basic idea is to combine this complex coordinate rotation method with the finite element method, and the discrete variable technique. These two methods have been successfully used to compute atomic data for the hydrogen atom in external magnetic and electric fields. We obtain a complex symmetric Hamiltonian matrix, which we solve using the implicitly restarted Arnoldi method (ARPACK). These methods have been extended to alkali atoms in external strong magnetic and electric fields by including model potentials and have also been successfully used in studying various effective one-particle problems.

In this article we present model potential parameters for alkali metal atoms Li to Cs and the Li isoelectronic sequence. Model potentials combined with discrete variable and finite element techniques allow an accurate and quick numerical method to compute atomic data in external fields even on small computers. Results obtained for binding energies, effective principal quantum numbers, and oscillator strengths for various transitions ape compared with experimental values and other theoretical computations, (C) 1999 Academic Press.

: The photoionization cross-sections of the hydrogen atom in strong magnetic fields of magnetic White Dwarf stars were calculated with a direct numerical integration method using the Landau basis as a high field approach. The validity regime of these solutions overlap with those of the spherical symmetry and complement other recently developed methods. An important result is the relation between the density of states and the normalization for the more than one open channel regime leading to additional coupling terms not taken into account by multi channel quantum defect methods.

Empiric models have been introduced to describe frequency dependence of dielectric permittivity. Simple exponential models are often not satisfactory, while advanced non-exponential models (usually referred as “anomalous relaxation”) are commonly required to better explain experimental observations of complex systems. For viscoelastic materials, the so-called fractional derivatives models are powerful for both dynamic and loss moduli prediction. In this paper, the analysis of the main models used in the characterization of dielectric and viscoelastic materials such as five-parameter fractional Zener model and empiric Havriliak–Negami model are analysed. The fractional shape parameters describing the symmetric and asymmetric broadening of the complex modulus don't have the same influence in low and high frequencies. In contrast to the five-parameter Zener model, the empiric model asymmetry parameter has an influence on complex modulus at low frequencies comparing to the loss modulus peak frequency. A no resonance technique based on a forced vibrations procedure is used to investigate the frequency dependent complex shear modulus of a polyurethane foam, not influenced by its fluid phase, in the range 0.1–500 Hz. It is shown that the Havriliak–Negami model can predict the frequency dependence for a wide frequency range.

We present effective numerical algorithms based on discrete variable techniques and finite elements for solving the non-separable three-dimensional Schrödinger equation and a method for the solution of the two electron problem in a strong magnetic field, that combines the hyperspherical close coupling and the Finite Element method. As an example we will present some atomic data for the hydrogen and the helium atom in external fields relevant for magnetic white dwarf stars.

We present an accurate and flexible method for the numerical simulation of the evolution of electronic wave packets in alkali atoms. At a testing ground for our approach, we calculate the dynamics of Stark wave packets in cesium for different electric-field strengths. An agreement with recent experimental results is demonstrated, and especially the influence of the electric-field strength and the core scattering on the recurrence spectra is reproduced accurately. [S1050-2947(97)08711-8].

In a quantum mechanical treatment, an atom in external parallel electric and magnetic fields ionizes at energies above the classical ionization threshold and, at energies below tunnels through a potential barrier, in each case forming quasi-bound states (resonances). Such resonances can be calculated for hydrogen using the complex-coordinate method. The combination of this method with the R-matrix method allows the corresponding resonances to be calculated for non-hydrogenic Rydberg atoms. We employ such a combination of methods in an investigation of these resonances in sodium for various relative strengths of parallel, laboratory strength, external fields. Results are also presented for hydrogen in strong fields.

We present here a study of the quantum phase space localization (Wigner functions) in dependence of semiclassical quantization rules for the hydrogen atom in magnetic fields. We consider primarily two energy regions. In the first the corresponding classical system is near-integrable and in the second near fully chaotic. We study phase space localization (scars) close to stable and unstable trajectories, tori and the invariant manifold associated with the almost circular, unstable periodic trajectory. We find that these classical structures are an important element for the structure of the wavefunctions and the semiclassical quantization predictions are in good agreement with the quantal results.

It has turned out that quantum wave functions of chaotic model systems show an enhanced probability of presence along classical periodic orbits. Inspired by this quantum chaological connection, we analyse Wigner distributions for the diamagnetic hydrogen atom. We report on classical and quantal Poincaré surfaces-of-section and discuss the strength of localization in dependence of semiclassical quantization conditions.

The finite-element method provides a convenient and accurate procedure for the calculation of the expectation values of quantum observable. We calculated energies, wave functions, and expectation values of r1n for n = -1, 1, and 2, and of pidelta(r1) for the singlet n 1S and triplet n 3S states (n = 1,2,3,4) of helium. In contrast to the standard methods with globally defined basis functions, the accuracy of the expectation values of physical observable is comparable to the accuracy of the eigenvalues. The results are-reported here and compared with those of Baker et al. [Relativistic, Quantum Electrodynamic, and Weak Interaction Effects in Atoms, edited by Walter Johnson, Peter Mohr, and Joseph Sucher, AIP Conf. Proc. No. 189 (AIP, New York, 1989); Phys. Rev. A 41, 1247 (1990)], Drake [Nucl. Instrum. Methods Phys. Res. B 31, 7 (1988)], Pekeris [Phys. Rev. 115, 1216 (1959)], Accad et al. [Phys. Rev. A 4, 516 (1971)], and Haftel and Mandelzweig [Phys. Rev. A 38, 5995 (1988)].

The authors present the first study of the quantum phase-space behaviour (Wigner functions) for non-hydrogenic atoms in magnetic fields as well as a comprehensive study of spectral properties. They consider primarily an energy regime (scaled energy -0.5) where hydrogen is near-integrable and hydrogenic wavefunctions would be localized on tori. They find that the quantum energy level statistics for non-hydrogenic atoms are at the 'chaotic' (Wigner) limit. However, the quantum phase space distributions, contrary to what one would expect if the underlying classical motion were chaotic, remain dominated by torus-like structures. But the wavefunctions do explore a larger fraction of phase-space than in the hydrogenic case where, in the integrable regime, Wigner wavefunctions are generally localized on a single torus. Due to the non-semiclassical nature of the core they are localized on more than one torus; additional structures other than the tori are also present. Possible interpretations of the results in terms of models of the underlying classical dynamics are discussed.

It has turned out that the analysis ofclassical periodic orbits is the key to understanding the modulations in thequantal spectra of hydrogen Rydberg atoms in magnetic fields. Inspired by this quantum chaological connection, we analyse some fundamental periodic orbits of the diamagnetic Kepler problem, abandoning the condition of vanishing azimuthal angular momentuml z used in the literature so far. We report the bifurcation and confluence schemes of the orbits in their dependence onl z and discuss the structural changes in terms of catastrophe theory.

Lyapunov characteristic exponents are calculated for classical trajectories of the Hamiltonian describing a hydrogen atom in a uniform magnetic field, and particular attention is given to periodic orbits. As the magnetic field is turned on, instability grows around the almost circular orbit which is a precise circle in the integrable limit \ensuremath{\varepsilon}=-\ensuremath{\infty}, \ensuremath{\varepsilon} being the scaled energy of the system. The Lyapunov exponent of the almost circular orbit is proportional to \ensuremath{\Vert}\ensuremath{\varepsilon}${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}3/2}$ near the integrable limit, and this is consistent with a square-root law found by G. Benettin [Physica D 13, 211 (1984)] for the onset of instability in certain billiards.