Browsing by Author "Zech, Ingrid"

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Open Access
Analysis of hydrogen Rydberg spectra in a uniform magnetic field: uncovering the transition from regularity to irregularity in a real quantum system
(1986) Wunner, Günter; Woelk, Ulrich; Zech, Ingrid; Zeller, Gudrun; Ertl, Thomas; Geyer, Florian; Steitz, Arno; Schweizer, Wolfgang; Ruder, Hanns
Studies of the behaviour of quantum systems in a range of energy where their classical counterparts undergo transitions from regularity to irregularity, as manifested in phase space by the gradual destruction of invariant tori, to date have largely been confined to model Hamiltonian systems such as harmonic oscillators with cubic, quartic, or higher-degree polynomial corrections, or the stadium problem. We show that phenomena which have turned out characteristic of the onset of "quantum stochasticity" in these model systems can in fact be recovered in the quantal energy spectra of a "real" physical system, viz. spectra of hydrogen Rydberg atoms in strong magnetic fields. This implies that one has a simple prototype system at hand in which to study - not only in theory but also in experiment, quantitatively and in detail, and as a function of a continuously tunable external parameter - phenomena that are expected to be typical of the quantum properties of nonintegrable systems in general.
Open Access
Numerical modeling of the non-isothermal positive column of an Ar+-laser
(1992) Zech, Ingrid; Ertl, Thomas; Herold, Heinz; Ruder, Hanns; Köhler, Walter E.; Tiemann, Wilhelm
A hydrodynamic description of the positive column is used to study the radial variation of particle densities, drift velocities, temperatures and heat fluxes of electrons, singly-charged ions and neutral atoms and the radial electric field. Elastic collisions between the plasma particles and neutrals as well as Coulomb collisions between ions and electrons are taken into account. The relevant equations to solve are the balance equations of particle densities, momentum, energy and the equations for the heat fluxes for each of the three studied particle types; the Poisson equation has to be added for closure. They form a system of 13 nonlinear differential equations with critical points. One singularity occurs when the ions reach the ion sound velocity which is the case inside the positive column. Therefore, a numerical method for multipoint boundary value problems was used which can also successfully handle removable singular points. The applied relaxation method is an iterative method which demands some preliminary knowledge of the solution looked for. The necessary knowledge can be retrieved from the quasineutral model and from a simplified two-fluid model.
Open Access
Rydberg atoms in uniform magnetic fields: uncovering the transition from regularity to irregularity in a quantum system
(1986) Wunner, Günter; Woelk, Ulrich; Zech, Ingrid; Zeller, Gudrun; Ertl, Thomas; Geyer, Florian; Schweizer, Wolfgang; Ruder, Hanns
We investigate the eigenvalue spectra of hydrogen Rydberg atoms in strong magnetic fields for manifestations of quantum stochasticity and find (i) a smooth transition from a Poisson-type to a Wigner-type distribution of level spacings in the range of energy where classical motion becomes increasingly chaotic, (ii) the occurrence of multiple avoided crossings, and (iii) connected with this, an extreme sensitivity of oscillator strengths, and thus of observable spectra, with respect to small variations of an external parameter, viz., the magnetic field strength.