We investigate the eigenvalue spectra of hydrogen Rydberg atoms in strong magnetic fields for manifestations of quantum stochasticity and find (j) a smooth transition from a Poisson.type to a Wignertype distribution of level spacings in the range of energy where classical motion becomes increasingly chaotic, (ij) the occurrence of mulliple avoided crossings, and (jji) connected with this. an extreme sensitivity of oscillator strengths, and thus of observ able spectra, with respect to small va riations of an external parameter, viz., the magnetic field strength. PACS numbers: 31.60.+b, 05.45.+b, 32.70.Cs Studies of the behavior 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 restricted to model Hamiltonian systems. W ell known exam ples are the st adium problem,1 the quantum Sinai's billiard,2 or harmonic oscillators with cubic,l quartic,4 or still higher-degree polynomial corrections. S In this Letter we show that phenomena which have turned out characteristic of the onset of "quantum stochasticity" in these model systems ca n in fact be recovered in the quanta I energy spectra of a real physical system, viz., of Rybderg atoms in uniform magnetic fields . This means 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 or the quantum properties of nonintegrable systems in general. The methods of characterization of "chaotic" quantum spectra which we adopt in this Letter are (j) the statisti· cal analysis of flu ctua tions of energy eigenvalue sequences in the transition region between regularity and irregularity, (ij) the search for multiple avoided c rossings of levels in this region . and (iii) the sensitivity of eigenvalues and transition rates to small changes in the perturbation, viz., the magnetic field.Rydberg atoms in strong microwave fields have been proposed6 for investigations of " quantum stochasticity," and experimental results for the field ionization of electrically polarized hydrogen R ydberg atoms have recently been compared with classical calculations in the chaotic regime. 7 We believe that Rydberg atoms in magnetic fields lend themselves even more read ily to complete st udies of the transition from reg ularity to irregularity, since quantal calculations are still feasible in the corresponding range or energy. By contrast, quantal calculations of the microwave ionization of Rydberg atoms are prohibitive because huge numbers of bound levels and the continuum must be included.After separating the trivial azimuthal dependence, the Hamiltonian of an electron under the combined influence of a fixed Coulomb potential and a uniform magnet ic field , OJ Gn atom ic units, P-B/Bo with Bo-2(am~c)2/(eh)C!i 4.70x IDS n, red uces to that o...
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.
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