Discrete time adiabatic theorems for quantum mechanical systems

The theory of adiabatic asymptotics is adapted to systems with discrete time evolution. The corresponding theorems about the approximation of physical time evolution by the adiabatic time evolution are shown to hold true in a discrete setting. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(259) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Discrete time adiabatic theorems for quantum mechanical systems

The theory of adiabatic asymptotics is adapted to systems with discrete time evolution. The corresponding theorems about the approximation of physical time evolution by the adiabatic time evolution are shown to hold true in a discrete setting. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(259) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Geometric properties of transport in quantum hall systems

In this first section, we present a short review of theoretical approaches to the quantum Hall effect. For an in depth coverage, we refer to the recent book D. J. Thouless (1998), as well as to M. Stone (1992). Let us recall how a quantum Hall system in a laboratory looks like: a strong magnetic field runs perpendicular through a probe of a conductor or semiconductor, forming a two-dimensional system; this setup is typically realized as inversion layers in field effect transistors, formed at the interface between an insolator and a semiconductor under the influence of an electric field perpendicular to the interface. If the temperature of the system is near zero, the electrons are bound by a deep potential well, forming a two-dimensional system. We identify this inversion layer with the x-y plane, hence B is parallel to the z-axis. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(390) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Models of the Hofstadter type

Spectra and eigenfunctions of discrete hamiltonians are computed using algebraic, analytic and numerical tools. In particular we consider the Hofstadter and the Second Neighbor Square Lattice model, the Triangular Lattice model in an inhomogenous magnetic field, the Doubly-discrete Quantum Pendulum and the Honeycomb model. Qualitative properties of the spectra are related to symmetries. Semiclassical analysis in the algebraic setting for the Doubly-discrete Quantum Pendulum is shown to match numerical results well. The connection to integrable models is mentioned. (orig.)Available from TIB Hannover: RR 1596(209) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

The shape resonance

SIGLETIB: RN 4586 (143) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Loop group factorization of biorthogonal wavelet bases

We present a factorization theorem for certain polynomial loops in the matrix group GL(2, C). The theorem leads to the construction of an algorithm for the factorization of pairs of biorthogonal filters with finite impulse response in simple terms, resulting in a reduction of the complexity of the corresponding wavelet transform. (orig.)Available from TIB Hannover: RR 1596(281) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Adiabatic quantum transport: quantization and fluctuations

Quillen's local index theorem is used to study the charge transport coefficients (adiabatic curvature) associated to the ground state of the Schroedinger operator for charged (spin less) particles on a closed, multiply connected surface. The formula splits the adiabatic curvature into an explicit integral part and a fluctuating part depending on the regularized determinant of the Hamiltonian. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(125) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Adiabatic theorems and applications to the quantum Hall effect

SIGLETIB Hannover: RN 4586(158) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman