94 research outputs found
Stability of the electron cyclotron resonance
We consider the magnetic AC Stark effect for the quantum dynamics of a single
particle in the plane under the influence of an oscillating homogeneous
electric and a constant perpendicular magnetic field. We prove that the
electron cyclotron resonance is insensitive to impurity potentials.Comment: version to appear in Comm. Math. Phy
Spectral Stability of Unitary Network Models
We review various unitary network models used in quantum computing, spectral
analysis or condensed matter physics and establish relationships between them.
We show that symmetric one dimensional quantum walks are universal, as are CMV
matrices. We prove spectral stability and propagation properties for general
asymptotically uniform models by means of unitary Mourre theory
Energy-time uncertainty principle and lower bounds on sojourn time
One manifestation of quantum resonances is a large sojourn time, or
autocorrelation, for states which are initially localized. We elaborate on
Lavine's time-energy uncertainty principle and give an estimate on the sojourn
time. For the case of perturbed embedded eigenstates the bound is explicit and
involves Fermi's Golden Rule. It is valid for a very general class of systems.
We illustrate the theory by applications to resonances for time dependent
systems including the AC Stark effect as well as multistate systems.Comment: Version to appear in Annales Henri Poincar\'
Engineering stable quantum currents at bulk boundaries
We study transport properties of discrete quantum dynamical systems on the lattice, in particular Coined Quantum Walks and the Chalker-Coddington model. We prove existence of a non trivial charge transport and that the absolutely continuous spectrum covers the whole unit circle under mild assumptions. For Quantum Walks we exhibit explicit constructions of coins which imply existence of stable directed quantum currents along classical curves. The results are of topological nature and independent of the details of the model
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