2,506 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
Band spectra of rectangular graph superlattices
We consider rectangular graph superlattices of sides l1, l2 with the
wavefunction coupling at the junctions either of the delta type, when they are
continuous and the sum of their derivatives is proportional to the common value
at the junction with a coupling constant alpha, or the "delta-prime-S" type
with the roles of functions and derivatives reversed; the latter corresponds to
the situations where the junctions are realized by complicated geometric
scatterers. We show that the band spectra have a hidden fractal structure with
respect to the ratio theta := l1/l2. If the latter is an irrational badly
approximable by rationals, delta lattices have no gaps in the weak-coupling
case. We show that there is a quantization for the asymptotic critical values
of alpha at which new gap series open, and explain it in terms of
number-theoretic properties of theta. We also show how the irregularity is
manifested in terms of Fermi-surface dependence on energy, and possible
localization properties under influence of an external electric field.
KEYWORDS: Schroedinger operators, graphs, band spectra, fractals,
quasiperiodic systems, number-theoretic properties, contact interactions, delta
coupling, delta-prime coupling.Comment: 16 pages, LaTe
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
Enhanced ionization in small rare gas clusters
A detailed theoretical investigation of rare gas atom clusters under intense
short laser pulses reveals that the mechanism of energy absorption is akin to
{\it enhanced ionization} first discovered for diatomic molecules. The
phenomenon is robust under changes of the atomic element (neon, argon, krypton,
xenon), the number of atoms in the cluster (16 to 30 atoms have been studied)
and the fluency of the laser pulse. In contrast to molecules it does not
dissappear for circular polarization. We develop an analytical model relating
the pulse length for maximum ionization to characteristic parameters of the
cluster
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
Bethe ansatz for the Harper equation: Solution for a small commensurability parameter
The Harper equation describes an electron on a 2D lattice in magnetic field
and a particle on a 1D lattice in a periodic potential, in general,
incommensurate with the lattice potential. We find the distribution of the
roots of Bethe ansatz equations associated with the Harper equation in the
limit as alpha=1/Q tends to 0, where alpha is the commensurability parameter (Q
is integer). Using the knowledge of this distribution we calculate the higher
and lower boundaries of the spectrum of the Harper equation for small alpha.
The result is in agreement with the semiclassical argument, which can be used
for small alpha.Comment: 17 pages including 5 postscript figures, Latex, minor changes, to
appear in Phys.Rev.
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
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
Quantum Return Probability for Substitution Potentials
We propose an effective exponent ruling the algebraic decay of the average
quantum return probability for discrete Schrodinger operators. We compute it
for some non-periodic substitution potentials with different degrees of
randomness, and do not find a complete qualitative agreement with the spectral
type of the substitution sequences themselves, i.e., more random the sequence
smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics
Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?
An analytical realization is suggested for the finite-size scaling algorithm
based on the consideration of auxiliary quasi-1D systems. Comparison of the
obtained analytical results with the results of numerical calculations
indicates that the Anderson transition point is splitted into the band of
critical states. This conclusion is supported by direct numerical evidence
(Edwards and Thouless, 1972; Last and Thouless, 1974; Schreiber, 1985; 1990).
The possibility of restoring the conventional picture still exists but requires
a radical reinterpretetion of the raw numerical data.Comment: PDF, 11 page
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