1,057 research outputs found
Multidimensional continued fractions, dynamical renormalization and KAM theory
The disadvantage of `traditional' multidimensional continued fraction
algorithms is that it is not known whether they provide simultaneous rational
approximations for generic vectors. Following ideas of Dani, Lagarias and
Kleinbock-Margulis we describe a simple algorithm based on the dynamics of
flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of
covolume one) that indeed yields best possible approximations to any irrational
vector. The algorithm is ideally suited for a number of dynamical applications
that involve small divisor problems. We explicitely construct renormalization
schemes for (a) the linearization of vector fields on tori of arbitrary
dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page
Considerations on rescattering effects for threshold photo- and electro-production of on deuteron
We show that for the S-state -production in processes and the rescattering effects due to the
transition: (or are cancelled
out due to the Pauli principle. The large values for these effects predicted in
the past may result from the fact that the spin structure of the corresponding
matrix element and the necessary antisymmetrization induced by the presence of
identical protons (or neutrons) in the intermediate state was not taken into
account accurately. One of the important consequences of these considerations
is that photo- and electro-production on deuteron near threshold can
bring direct information about elementary neutron amplitudes.Comment: Add a new sectio
Meissner effect, Spin Meissner effect and charge expulsion in superconductors
The Meissner effect and the Spin Meissner effect are the spontaneous
generation of charge and spin current respectively near the surface of a metal
making a transition to the superconducting state. The Meissner effect is well
known but, I argue, not explained by the conventional theory, the Spin Meissner
effect has yet to be detected. I propose that both effects take place in all
superconductors, the first one in the presence of an applied magnetostatic
field, the second one even in the absence of applied external fields. Both
effects can be understood under the assumption that electrons expand their
orbits and thereby lower their quantum kinetic energy in the transition to
superconductivity. Associated with this process, the metal expels negative
charge from the interior to the surface and an electric field is generated in
the interior. The resulting charge current can be understood as arising from
the magnetic Lorentz force on radially outgoing electrons, and the resulting
spin current can be understood as arising from a spin Hall effect originating
in the Rashba-like coupling of the electron magnetic moment to the internal
electric field. The associated electrodynamics is qualitatively different from
London electrodynamics, yet can be described by a small modification of the
conventional London equations. The stability of the superconducting state and
its macroscopic phase coherence hinge on the fact that the orbital angular
momentum of the carriers of the spin current is found to be exactly ,
indicating a topological origin. The simplicity and universality of our theory
argue for its validity, and the occurrence of superconductivity in many classes
of materials can be understood within our theory.Comment: Submitted to SLAFES XX Proceeding
Global well-posedness for the KP-I equation on the background of a non localized solution
We prove that the Cauchy problem for the KP-I equation is globally well-posed
for initial data which are localized perturbations (of arbitrary size) of a
non-localized (i.e. not decaying in all directions) traveling wave solution
(e.g. the KdV line solitary wave or the Zaitsev solitary waves which are
localized in and periodic or conversely)
Structural and optical studies of FeSb2 under high pressure
Nanostructured orthorhombic FeSb2 and an amorphous phase were formed by
mechanical alloying starting from a mixture of high purity elemental Fe and Sb
powders. The effects of high pressures on structural and optical properties
were studied using X-ray diffraction (XRD) and Raman spectroscopy (RS). XRD
patterns showed the presence of the orthorhombic FeSb2 phase up to the maximum
pressure applied (28.2 GPa). The XRD patterns showed also an increase in the
amount of the amorphous phase with increasing pressure up to 23.3 GPa. At 14.3
GPa, together with the former phases, a new phase was observed and indexed to a
tetragonal FeSb2 phase, but its volume fraction is small at least up to 23.3
GPa. For the orthorhombic FeSb2 phase, the pressure dependence of the volume
fitted to a Birch-Murnaghan equation of state gave a bulk modulus = 74.2 +- 3.0
GPa and its pressure derivative = 7.5 +- 0.6. RS measurements were performed
from atmospheric pressure up to 45.2 GPa. For the orthorhombic FeSb2 phase, the
Raman active mode was observed up to the maximum pressure applied, while the
mode disappeared at 16.6 GPa. For pressures higher than 21 GPa, the Raman
active mode of a tetragonal FeSb2 phase was observed, confirming ab initio
calculations reported in the literature.Comment: 31 pages, 11 figures and 2 tables. Already submitted for publicatio
Laboratory Development
This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440
Recent progress on the chiral unitary approach to meson meson and meson baryon interactions
We report on recent progress on the chiral unitary approach, analogous to the
effective range expansion in Quantum Mechanics, which is shown to have a much
larger convergence radius than ordinary chiral perturbation theory, allowing
one to reproduce data for meson meson interaction up to 1.2 GeV. Applications
to physical processes so far unsuited for a standard chiral perturbative
approach are presented. Results for the extension of these ideas to the meson
baryon sector are discussed, together with applications to kaons in a nuclear
medium and atoms.Comment: Contribution to the KEK Tanashi Symposium on Physics of Hadrons and
Nuclei, Tokyo, December 1998, 10 pages, 3 postscript figures. To be published
as a special issue of Nuclear Physics
Multiple Andreev Reflection and Giant Excess Noise in Diffusive Superconductor/Normal-Metal/Superconductor Junctions
We have studied superconductor/normal metal/superconductor (SNS) junctions
consisting of short Au or Cu wires between Nb or Al banks. The Nb based
junctions display inherent electron heating effects induced by the high thermal
resistance of the NS boundaries. The Al based junctions show in addition
subharmonic gap structures in the differential conductance dI/dV and a
pronounced peak in the excess noise at very low voltages V. We suggest that the
noise peak is caused by fluctuations of the supercurrent at the onset of
Josephson coupling between the superconducting banks. At intermediate
temperatures where the supercurrent is suppressed a noise contribution ~1/V
remains, which may be interpreted as shot noise originating from large multiple
charges.Comment: 7 pages, 7 figures, extended versio
Maximally-localized Wannier functions for entangled energy bands
We present a method for obtaining well-localized Wannier-like functions (WFs)
for energy bands that are attached to or mixed with other bands. The present
scheme removes the limitation of the usual maximally-localized WFs method (N.
Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)) that the bands of
interest should form an isolated group, separated by gaps from higher and lower
bands everywhere in the Brillouin zone. An energy window encompassing N bands
of interest is specified by the user, and the algorithm then proceeds to
disentangle these from the remaining bands inside the window by filtering out
an optimally connected N-dimensional subspace. This is achieved by minimizing a
functional that measures the subspace dispersion across the Brillouin zone. The
maximally-localized WFs for the optimal subspace are then obtained via the
algorithm of Marzari and Vanderbilt. The method, which functions as a
postprocessing step using the output of conventional electronic-structure
codes, is applied to the s and d bands of copper, and to the valence and
low-lying conduction bands of silicon. For the low-lying nearly-free-electron
bands of copper we find WFs which are centered at the tetrahedral interstitial
sites, suggesting an alternative tight-binding parametrization.Comment: 13 pages, with 9 postscript figures embedded. Uses REVTEX and epsf
macro
Photoproduction of the Lambda(1405) on the proton and nuclei
We study the gamma p ---> K^+ Lambda(1405) reaction at energies close to
threshold using a chiral unitary model where the resonance is generated
dynamically from K^-p interaction with other channels constructed from the
octets of baryons and mesons. Predictions are made for cross sections into
several channels and it is shown that the detection of the K^+ is sufficient to
determine the shape and strength of the Lambda(1405) resonance. The
determination of the resonance properties in nuclei requires instead the
detection of the resonance decay channels. Pauli blocking effects on the
resonance, which have been shown to be very important for the resonance at rest
in the nucleus, are irrelevant here where the resonance is produced with a
large momentum. The nuclear modifications here would thus offer information on
the resonance and K^- nucleus dynamics complementary to the one offered so far
by K^- atoms.Comment: 9 pages, 4 postscripts figure
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