Doppler Institute for Mathematical Physics

will organize on November 28-29, 2003

a miniconference on mathematics, physics, and history under the name


commemorating the 200th birthday of Christian Doppler
and ten years of the institute existence

  • Speakers and talk titles
  • Venue
  • Schedule
  • Abstracts
  • Moments of the meeting

  • Speakers and talk titles:


    The conference takes place in the main building of Faculty of Nuclear Sciences and Physical Engineering of the Czech Technical University

    Brehová 7, 11519 Praha 1

    We will be meeting in the lecture hall No. 111


    Friday, November 28
    Saturday, November 29


    J.E. Avron: Euler disc
    Euler disc is a mechanical toy with intriguing behavior that is not full understood. The talk will consist of demonstrations and an outline of the theory. Some open problems shall also be discussed.

    J.-M. Combes: Edge conductivity in quantum Hall systems
    We discuss quantization of edge conductivity in a one electron model confined to a semi-infinite planar domain containing impurities. A sum rule allows to derive exact quantization in various situations. In particular it is shown that deviation of edge conductivity in the Nth Landau band from its ideal value N is linked to existence of "edge currents without edges". Exact quantization is also shown to hold in some models of high disorder.

    H.-D. Doebner: Extensions of quantum mechanics - nonlinear Schroedinger equations
    A family of nonlinear extensions of nonrelativistic quantum mechanical evolution equations is presented. The family is based on on a quantisation method for the kinematics (Quantum Borel Kinematic). A corresponding time dependence yields a family of nonlinear Schrödinger equations. Difficulties of nonlinear operators and nonlinear evolutions in the usual quamtum mechanical framework are discussed. Examples to measure such nonlineraties through quantum mechanical precision experiments are explained.

    P. Exner: Resonance effects in leakyquantum wires
    We consider a model of a "leaky" the Hamiltonian of which is a two-dimensional Schroedinger operator, and ask about resonance effects for negative-energy states guided along such a structure. Using an approximation by point interactions we present a numerical evidence that these systems may exhibit two types of resonances, due to propagating-mode reflections and due to quantum tunelling. We also analyse a solvable model of a straight wire and a quantum dot modeled by a point.

    A. Joye: Adiabatic approximations and exponential asymptotics
    We discuss the quantum adiabatic approximation and describe recent work with G. Hagedorn that determines the time development of exponentially small non-adiabatic transitions for some special models.

    S.T. Kuroda: Some topics in eigenvalue computations
    We review our works (works done in our group) on this topics. We will talk about, possibly not standard, methods of computing eigenvalues of, say, Schroedinger operators. The emphasis will be on functional-analytic investigations, not on acutual computations.

    E.H. Lieb: The dilute, cold Bose gas: a truly quantum-mechanical many-body problem
    The peculiar quantum-mechanical properties of the ground state of Bose gases that have been proved rigorously in the last few years (with R. Seiringer, J-P. Solovej and J. Yngvason) will be reviewed. For the low density gas with finite range interactions these properties include the leading order term in the ground state energy, the validity of the Gross-Pitaevskii description in traps, Bose-Einstein condensationand superfluidity in traps, and the transition from 3-dimensional behaviorto 1-dimensional behavior as the cross-section of the trap decreases. The latter is a highly quantum-mechanical phenomenon.
    For the charged Bose gas at high density, the leading term in the energy found by Foldy in 1961 for the one-component gas and Dyson's conjecture of the N^{7/5} law for the two-component gas has also been verified. These results help justify Bogolubov's 1947 theory of pairing in Bose gases.

    P. Seba: Random matrix theory and statistical properties of exotic systems
    We will demonstrate that statistical distributions originally coming from the random matrix theory can be used to describe properties of such exotic systems like bus transport in Mexico, distribution of cars on German highways, cross channel correlations of human brain potentials (EEG) and distribution of phonems in various languages.

    I. Stoll: The life and work of Christian Doppler
    Short synopsis: Christian Doppler's youth and ambitions. Doppler's teaching activities in Prague. Membership of Royal Bohemian Society of Sciences. The highlight of Dopples's scientific achievements. The retreat in Banska Stiavnica and variations of earth magnetism. Last years in Vienna; at the beginnings of Austrian physics. The journey of Doppler's vision into physics (Fizeau, Huggins, Mach, Einstein).

    J. Tolar: Ten years of the Doppler Institute
    The Faculty of Nuclear Sciences and Physical Engineering of Czech Technical University in Prague concentrates on engineering branches requiring solid knowledge of mathematics and physics. Our Seminar of Mathematical Physics, since its start in 1988, has become center of our cooperation on which the Doppler Institute of mathematical physics (DI) was founded in 1993 as a research and pedagogical division of the Faculty. The objective of the scientific research of the DI collaborators is to develop core disciplines of modern mathematical quantum physics. In its pedagogical activities DI provides help to students at the beginning of their active scientific career. This contribution will be devoted to the survey of our scientific and pedagogical activities during the past 10 years as well as to our plans for the future.

    M. Znojil: Magyari equations as a non-square eigenvalue problem
    The standard formulation of the linear N by N problem Hx = Ex will be extended to certain non-square Hamiltonians H in a "feasible" non-linear manner. A few possible applications will be mentioned though, mainly, our attention will be paid to the Magyari's project of the determination of a "quasi-harmonic" degeneracy of a general polynomial oscillator. On mathematical side we will outline a generalized Rayleigh-Schroedinger perturbation construction of solutions. In particular, its (so called 1/D - expansion) application to polynomial oscillators will be described in detail, with emphasis on the enigmatic exact solvability of this problem in zero order (where two alternative constructions are known up to now).

    Moments of the meeting

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