2,274 research outputs found
Bloch electron in a magnetic field and the Ising model
The spectral determinant det(H-\epsilon I) of the Azbel-Hofstadter
Hamiltonian H is related to Onsager's partition function of the 2D Ising model
for any value of magnetic flux \Phi=2\pi P/Q through an elementary cell, where
P and Q are coprime integers. The band edges of H correspond to the critical
temperature of the Ising model; the spectral determinant at these (and other
points defined in a certain similar way) is independent of P. A connection of
the mean of Lyapunov exponents to the asymptotic (large Q) bandwidth is
indicated.Comment: 4 pages, 1 figure, REVTE
Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical Coupling
We show that the integrated density of states of the almost Mathieu operator
is absolutely continuous if and only if the coupling is non-critical. We deduce
for subcritical coupling that the spectrum is purely absolutely continuous for
almost every phase, settling the measure-theoretical case of Problem 6 of Barry
Simon's list of Schr\"odinger operator problems for the twenty-first century.Comment: 13 pages, to appear in Inv. Mat
Double butterfly spectrum for two interacting particles in the Harper model
We study the effect of interparticle interaction on the spectrum of the
Harper model and show that it leads to a pure-point component arising from the
multifractal spectrum of non interacting problem. Our numerical studies allow
to understand the global structure of the spectrum. Analytical approach
developed permits to understand the origin of localized states in the limit of
strong interaction and fine spectral structure for small .Comment: revtex, 4 pages, 5 figure
Continuity of the measure of the spectrum for quasiperiodic Schrodinger operators with rough potentials
We study discrete quasiperiodic Schr\"odinger operators on \ell^2(\zee)
with potentials defined by -H\"older functions. We prove a general
statement that for and under the condition of positive Lyapunov
exponents, measure of the spectrum at irrational frequencies is the limit of
measures of spectra of periodic approximants. An important ingredient in our
analysis is a general result on uniformity of the upper Lyapunov exponent of
strictly ergodic cocycles.Comment: 15 page
Suppressed spin dephasing for 2D and bulk electrons in GaAs wires due to engineered cancellation of spin-orbit interaction terms
We report a study of suppressed spin dephasing for quasi-one-dimensional
electron ensembles in wires etched into a GaAs/AlGaAs heterojunction system.
Time-resolved Kerr-rotation measurements show a suppression that is most
pronounced for wires along the [110] crystal direction. This is the fingerprint
of a suppression that is enhanced due to a strong anisotropy in spin-orbit
fields that can occur when the Rashba and Dresselhaus contributions are
engineered to cancel each other. A surprising observation is that this
mechanisms for suppressing spin dephasing is not only effective for electrons
in the heterojunction quantum well, but also for electrons in a deeper bulk
layer.Comment: 5 pages, 3 figure
The Ten Martini Problem
We prove the conjecture (known as the ``Ten Martini Problem'' after Kac and
Simon) that the spectrum of the almost Mathieu operator is a Cantor set for all
non-zero values of the coupling and all irrational frequencies.Comment: 31 pages, no figure
Heterogeneous oxidation reaction of gas-phase ozone with anthracene in thin films and on aerosols by infrared spectroscopic methods
Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians
We consider the spectrum of discrete Schr\"odinger operators with Sturmian
potentials and show that for sufficiently large coupling, its Hausdorff
dimension and its upper box counting dimension are the same for Lebesgue almost
every value of the frequency.Comment: 12 pages, to appear in Commun. Math. Phy
Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators
In this paper, we consider one dimensional adiabatic quasi-periodic
Schr\"{o}dinger operators in the regime of strong resonant tunneling. We show
the emergence of a level repulsion phenomenon which is seen to be very
naturally related to the local spectral type of the operator: the more singular
the spectrum, the weaker the repulsion
On semiclassical dispersion relations of Harper-like operators
We describe some semiclassical spectral properties of Harper-like operators,
i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and
position. The spectral region corresponding to the separatrices of the
classical Hamiltonian is studied for the case of integer flux. We derive
asymptotic formula for the dispersion relations, the width of bands and gaps,
and show how geometric characteristics and the absence of symmetries of the
Hamiltonian influence the form of the energy bands.Comment: 13 pages, 8 figures; final version, to appear in J. Phys. A (2004
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