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Funded by The Danish National Research Foundation
An introduction to the Mathematical Physics seminar will be avaliable shortly.
If nothing else is mentioned, the seminar will be held at the Department of Mathematical Sciences, University of Aarhus.
Abstract: Various results concerning the smoothness of gap boundaries for Harper type operators are extended to a large class of "twisted integral operatos" in $L^2(Z^2)$. The results hold true also for analogous classes of operators in $L^2(R^n)$ and imply the fact that the gap boundaries for magnetic Schrodinger and Dirac operators are, up to a logarithmic factor, Lipschitz continuous in the magnetic field strenght. The proofs are based on gauge covariance and magnetic perturbation theory
Abstract: I will analyse self-adjoint operators on the bosonic Fock space defined as quadratic polynomials in creation/annihilation operators. I will show that there exists 9 distinct classes of such operators exhibiting various behavior in the infra-red and ultra-violet regime. I will describe their scattering theory, which is quite unusual (from the point of view of people accustomed to Schrodinger operators). The analysis of these operators is helpful in understanding various phenomena in quantum field theory
Abstract: Recently, Avron and his co-workers reopened the question of quantum transport in mesoscopic samples coupled to particle reservoirs by semi-infinite leads. They give a rigorous analysis of the case when the sample undergoes an adiabatic evolution, which generates a current through the leads (the so called BPT formula). Using a tight-binding framework, we complement their work by giving a rigorous proof of the Landauer-Büttiker formula, which deals with the current generated by an adiabatic evolution on the leads. As it is well known in physics, these formulae link the conductance coefficients for such systems to the $S$-matrix of the associated scattering problem. As an application, we discuss the resonant transport through a quantum dot. The single charge tunneling processes are mediated by extended edge states simultaneously localized near several leads. This work is joint with A. Jensen and V. Moldoveanu
Abstract: I will present a Hamiltonian model of a particle coupled to a suitable wave field, describing the particle's environment, in which a simple version of Ohm's law is valid. When an external force is applied, the particle reaches asymptotically a constant speed proportional to the applied field. I will review the related literature, compare this phenomenon to the one of radiative dissipation, and indicate some of the many open problems
Abstract: The talk consists of 3 parts. 1. Mathematical formulation of the Fermi Golden Rule---2nd order perturbation computation of eigenvalues and resonances in a general setting, using the so-called Level Shift Operator 2. Return to Equilibrium--mathematical formulation of the fact that a generic quantum system in equilibrium admits only one stationary state. Elements of the proof (involving von Neumann algebras and Fermi Golden Rule) 3. Markovian limit of the reduced dynamics---another application of the Fermi Golden Rule--will be described. The relationship between 2. and 3. will be given.
Abstract: The abstract can be found at: http://www.maphysto.dk/events2/Abstracts/dy.pdf
Abstract: Consider the example of a classical system with electric or magnetic field homogeneous of degree -1. Generically there will be a finite number of directions in space in which a particle can move freely to infinity. These orbits can be stable or unstable depending on the behavior of the linearized equations. In a framework which generalizes these examples, we show that there are no quantum states corresponding to unstable classical channels. This is joint work with Erik Skibsted.