2,050 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
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
Some effects of ultraviolet radiation on the pathogenicity of Botrytis fabae, Uromyces fabae and Erysiphe graminis
RESP-378
Generic Continuous Spectrum for Ergodic Schr"odinger Operators
We consider discrete Schr"odinger operators on the line with potentials
generated by a minimal homeomorphism on a compact metric space and a continuous
sampling function. We introduce the concepts of topological and metric
repetition property. Assuming that the underlying dynamical system satisfies
one of these repetition properties, we show using Gordon's Lemma that for a
generic continuous sampling function, the associated Schr"odinger operators
have no eigenvalues in a topological or metric sense, respectively. We present
a number of applications, particularly to shifts and skew-shifts on the torus.Comment: 14 page
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
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
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.
Dynamical ionization ignition of clusters in intense and short laser pulses
The electron dynamics of rare gas clusters in laser fields is investigated
quantum mechanically by means of time-dependent density functional theory. The
mechanism of early inner and outer ionization is revealed. The formation of an
electron wave packet inside the cluster shortly after the first removal of a
small amount of electron density is observed. By collisions with the cluster
boundary the wave packet oscillation is driven into resonance with the laser
field, hence leading to higher absorption of laser energy. Inner ionization is
increased because the electric field of the bouncing electron wave packet adds
up constructively to the laser field. The fastest electrons in the wave packet
escape from the cluster as a whole so that outer ionization is increased as
well.Comment: 8 pages, revtex4, PDF-file with high resolution figures is available
from http://mitarbeiter.mbi-berlin.de/bauer/publist.html, publication no. 24.
Accepted for publication in Phys. Rev.
Statistics of resonances and of delay times in quasiperiodic Schr"odinger equations
We study the statistical distributions of the resonance widths , and of delay times in one dimensional
quasi-periodic tight-binding systems with one open channel. Both quantities are
found to decay algebraically as , and on
small and large scales respectively. The exponents , and are
related to the fractal dimension of the spectrum of the closed system
as and . Our results are verified for the
Harper model at the metal-insulator transition and for Fibonacci lattices.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
The physics of dynamical atomic charges: the case of ABO3 compounds
Based on recent first-principles computations in perovskite compounds,
especially BaTiO3, we examine the significance of the Born effective charge
concept and contrast it with other atomic charge definitions, either static
(Mulliken, Bader...) or dynamical (Callen, Szigeti...). It is shown that static
and dynamical charges are not driven by the same underlying parameters. A
unified treatment of dynamical charges in periodic solids and large clusters is
proposed. The origin of the difference between static and dynamical charges is
discussed in terms of local polarizability and delocalized transfers of charge:
local models succeed in reproducing anomalous effective charges thanks to large
atomic polarizabilities but, in ABO3 compounds, ab initio calculations favor
the physical picture based upon transfer of charges. Various results concerning
barium and strontium titanates are presented. The origin of anomalous Born
effective charges is discussed thanks to a band-by-band decomposition which
allows to identify the displacement of the Wannier center of separated bands
induced by an atomic displacement. The sensitivity of the Born effective
charges to microscopic and macroscopic strains is examined. Finally, we
estimate the spontaneous polarization in the four phases of barium titanate.Comment: 25 pages, 6 Figures, 10 Tables, LaTe
- …