Mathematical Physics Seminar
    Rutgers University
    Hill Center, Room 705

    September Schedule

    Organized by: Joel L. Lebowitz

    Please join us every Thursday at 11:45am in the
    kitchen of room 705 for coffee and cookies

    Speaker: H. Brezis, Rutgers University
    Date: 9/7/06
    Time & Place: 12-1pm ; Hill 705
    Title: "Can You Hear the Degree?"
    Abstract: A few years ago -- following a suggestion by -- -- I. M. Gelfand--
    I discovered an intriguing connection between the topological degree of a map
    from the circle into itself and its Fourier coefficients. The relation is fully justified
    when the map is smooth. However, the situation turns out to be much
    more complex if one assumes only continuity, or even Holder continuity.
    I will present recent developments and open problems.

    Speaker: O. Costin, Ohio State Uniiversity
    Date: 9/14/06
    Time & Place: 12-1pm ; Hill 705
    Title: "Borel summability in PDEs and applications"
    Abstract: The talk focuses on recent developments in Borel summability
    of formal solutions of PDEs, with special emphasis on the Schr\"odinger equation in
    time periodic forcings and nonlinear equations such as Navier-Stokes.

    We study the time-periodically forced nonrelativistic Hydrogen atom with potential
    $-b/r+\Omega(r)\cos\omega t$. $\Omega$ is real-valued, compactly supported in $r$,
    and with no zeros on its support. As $t\to\infty$ the particle undergoes, with probability
    1, transition to the continuum from an arbitrarily localized state (ionizes).

    In nonlinear equations, the methods are used to show existence and uniqueness of
    solutions in relatively general settings, and will be illustrated on a constructive proof
    of short term existence of solutions of Navier-Stokes.

    Work in collaboration with J. Lebowitz and S. Tanveer.



    *THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM*


    Speaker: R. Costin, Ohio State University
    Date: 9/14/06
    Time & Place: 2-3pm ; Hill 705
    Title: "Results on the classification of ODEs in regions containing several regular
    singular points"
    Abstract: In a region with one regular singularity (of the linear part) generic
    differential equations are analytically equivalent to their linear part; if the
    region contains several such singularities, this no longer happens. The talk
    will present the obstructions to linearization and the classification of equations
    in such regions.



    Speaker: L. Chayes, UCLA
    Date: 9/21/06
    Time & Place: 12-1pm ; Hill 705
    Title: "The 1D Exclusion Process with Inhomogeneous and Random Environments"
    Abstract: The standard one dimensional exclusion process is examined in systems
    where the local bias is inhomogeneous with particular emphasis on systems that have
    independent disorder. The physical emphasis of the talk will concern the
    effects of the exclusion interaction: Despite the fact that for low (or high)
    particle density, the homogeneous exclusion models behave like their non interacting
    counterparts, here it will be demonstrated that the interaction is "strongly relevant"
    and can drastically alter the transport properties of the system. On the more
    mathematical side, the existence of nonreversible stationary distributions will
    be demonstrated and, for the case of independent disorder, the necessary and
    sufficient conditions for the existence of such distributions will be provided.

    Speaker: S. Fishman, Technion
    Date: 9/28/06
    Time & Place: 12-1pm ; Hill 705
    Title: "Tunneling Out of Phase Space Islands of Maps"
    Abstract: Experimentally observable Quantum Accelerator Modes are used
    as a test case for the study of some general aspects of quantum decay from classical
    stable islands immersed in a chaotic sea. The modes are shown to correspond to
    metastable states, analogous to the Wannier-Stark resonances. Different regimes
    of tunneling, marked by different quantitative dependence of the lifetimes on
    the effective Planck's constant, are identified, depending on the resolution of KAM
    substructures that is achieved on its scale. The theory of Resonance Assisted
    Tunneling is revisited, and found to well describe decay whenever applicable.
    Relevance for various physical systems will be discussed.

    **THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM**

    Speaker: N. Andrei, Rutgers University
    Date: 9/28/06
    Time & Place: 2-3pm; Hill 705
    Title:Non-equilibrium Transport in Quantum Impurity Systems (Bethe-Ansatz
    for open systems)
    Abstract: We develop an exact non-perturbative framework to compute steady-state
    properties of quantum-impurities subject to a finite bias. We show that the steady-
    state physics of these systems is captured by nonequilibrium scattering eigenstates
    which satisfy an appropriate Lippman-Schwinger equation. Introducing a
    generalization of the equilibrium Bethe-Ansatz - the Scattering Bethe-Ansatz (SBA),
    we explicitly construct the scattering eigenstates. This allows us to derive
    exact, nonperturbative results for the steady-state properties of the system such
    as the non-equilibrium currents, non-equilibrium density of states and
    the rate of entropy production.