628 research outputs found
Large coupling behaviour of the Lyapunov exponent for tight binding one-dimensional random systems
Studies the Lyapunov exponent gamma lambda (E) of (hu)(n)=u(n+1)+u(n-1)+ lambda V(n)u(n) in the limit as lambda to infinity where V is a suitable random potential. The authors prove that gamma lambda (E) approximately ln lambda as lambda to infinity uniformly as E/ lambda runs through compact sets. They also describe a formal expansion (to order lambda -2) for random and almost periodic potentials
On the spectrum and Lyapunov exponent of limit periodic Schrodinger operators
We exhibit a dense set of limit periodic potentials for which the
corresponding one-dimensional Schr\"odinger operator has a positive Lyapunov
exponent for all energies and a spectrum of zero Lebesgue measure. No example
with those properties was previously known, even in the larger class of ergodic
potentials. We also conclude that the generic limit periodic potential has a
spectrum of zero Lebesgue measure.Comment: 12 pages. To appear in Communications in Mathematical Physic
Scattering Theory of Dynamic Electrical Transport
We have developed a scattering matrix approach to coherent transport through
an adiabatically driven conductor based on photon-assisted processes. To
describe the energy exchange with the pumping fields we expand the Floquet
scattering matrix up to linear order in driving frequency.Comment: Proceedings QMath9, September 12th-16th, 2004, Giens, Franc
Hofstadter butterfly as Quantum phase diagram
The Hofstadter butterfly is viewed as a quantum phase diagram with infinitely
many phases, labelled by their (integer) Hall conductance, and a fractal
structure. We describe various properties of this phase diagram: We establish
Gibbs phase rules; count the number of components of each phase, and
characterize the set of multiple phase coexistence.Comment: 4 prl pages 1 colored figure typos corrected, reference [26] added,
"Ten Martini" assumption adde
Charge Deficiency, Charge Transport and Comparison of Dimensions
We study the relative index of two orthogonal infinite dimensional
projections which, in the finite dimensional case, is the difference in their
dimensions. We relate the relative index to the Fredholm index of appropriate
operators, discuss its basic properties, and obtain various formulas for it. We
apply the relative index to counting the change in the number of electrons
below the Fermi energy of certain quantum systems and interpret it as the
charge deficiency. We study the relation of the charge deficiency with the
notion of adiabatic charge transport that arises from the consideration of the
adiabatic curvature. It is shown that, under a certain covariance,
(homogeneity), condition the two are related. The relative index is related to
Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the
relative index is computed explicitly for all Landau levels.Comment: 23 pages, no figure
On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schroedinger operators
We show for a large class of discrete Harper-like and continuous magnetic
Schrodinger operators that their band edges are Lipschitz continuous with
respect to the intensity of the external constant magnetic field. We generalize
a result obtained by J. Bellissard in 1994, and give examples in favor of a
recent conjecture of G. Nenciu.Comment: 15 pages, accepted for publication in Annales Henri Poincar
On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians
We study the regularity properties of the Hausdorff distance between spectra
of continuous Harper-like operators. As a special case we obtain H\"{o}lder
continuity of this Hausdorff distance with respect to the intensity of the
magnetic field for a large class of magnetic elliptic (pseudo)differential
operators with long range magnetic fields.Comment: to appear in the Proceedings of the 'Spectral Days' conference,
Santiago de Chile 201
Quantum Transport in Molecular Rings and Chains
We study charge transport driven by deformations in molecular rings and
chains. Level crossings and the associated Longuet-Higgins phase play a central
role in this theory. In molecular rings a vanishing cycle of shears pinching a
gap closure leads, generically, to diverging charge transport around the ring.
We call such behavior homeopathic. In an infinite chain such a cycle leads to
integral charge transport which is independent of the strength of deformation.
In the Jahn-Teller model of a planar molecular ring there is a distinguished
cycle in the space of uniform shears which keeps the molecule in its manifold
of ground states and pinches level crossing. The charge transport in this cycle
gives information on the derivative of the hopping amplitudes.Comment: Final version. 26 pages, 8 fig
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