Biomedical subjects

Gregor Tanner

Publications and source records attributed to Gregor Tanner.

5 recordsLinked to original sources

PubMed2005

Classical dynamics of two-electron atoms at zero energy.

We give a complete description of the classical dynamics of two electrons in the Coulomb potential of a positively charged nucleus for total energy E=0 and angular momentum L=0. The effectively four-dimensional phase space can be divided into partitions spanned by the stable and unstable manifold of the Wannier ridge space. We identify a further approximate symmetry by choosing an appropriate Poincaré surface of section in this dynamical system. In addition, a dividing surface between the dynamics influenced by the two collinear spaces, the stable Zee space and the strongly chaotic eZe space can be identified. We discuss potential extensions of the binary symbolic dynamics found in collinear two-electron atoms to the noncollinear parts of the phase space for E< or =0.

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PubMed2005

Classical dynamics of two-electron atoms near the triple collision.

The classical dynamics of two electrons in the Coulomb potential of an attractive nucleus is chaotic in large parts of the high-dimensional phase space. Quantum spectra of two-electron atoms, however, exhibit structures which clearly hint at the existence of approximate symmetries in this system. In a recent paper [Phys. Rev. Lett. 93, 054302 (2004)], we presented a study of the dynamics near the triple collision as a first step towards uncovering the hidden regularity in the classical dynamics of two electron atoms. The nonregularizable triple collision singularity is a main source of chaos in three body Coulomb problems. Here, we will give a more detailed account of our findings based on a study of the global structure of the stable and unstable manifolds of the triple collision.

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PubMed2004

Classical dynamics near the triple collision in a three-body Coulomb problem.

We investigate the classical motion of three charged particles with both attractive and repulsive interactions. The triple collision is a main source of chaos in such three-body Coulomb problems. By employing the McGehee scaling technique, we analyze here for the first time in detail the three-body dynamics near the triple collision in 3 degrees of freedom. We reveal surprisingly simple dynamical patterns in large parts of the chaotic phase space. The underlying degree of order in the form of approximate Markov partitions may help in understanding the global structures observed in quantum spectra of two-electron atoms.

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PubMed2002

Wave chaos in the elastic disk.

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

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PubMed1992

Quantization of chaotic systems.

Starting from the semiclassical dynamical zeta function for chaotic Hamiltonian systems we use a combination of the cycle expansion method and a functional equation to obtain highly excited semiclassical eigenvalues. The power of this method is demonstrated for the anisotropic Kepler problem, a strongly chaotic system with good symbolic dynamics. An application of the transfer matrix approach of Bogomolny is presented leading to a significant reduction of the classical input and to comparable accuracy for the calculated eigenvalues.

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