333 research outputs found
Deterministic Weak Localization in Periodic Structures
The weak localization is found for perfect periodic structures exhibiting
deterministic classical diffusion. In particular, the velocity autocorrelation
function develops a universal quantum power law decay at 4 times Ehrenfest
time, following the classical stretched-exponential type decay. Such
deterministic weak localization is robust against weak enough randomness (e.g.,
quantum impurities). In the 1D and 2D cases, we argue that at the quantum limit
states localized in the Bravis cell are turned into Bloch states by quantum
tunnelling.Comment: 5 pages, 2 figure
Strong valence fluctuation in the quantum critical heavy fermion superconductor beta-YbAlB4: A hard x-ray photoemission study
Electronic structures of the quantum critical superconductor beta-YbAlB4 and
its polymorph alpha-YbAlB4 are investigated by using bulk-sensitive hard x-ray
photoemission spectroscopy. From the Yb 3d core level spectra, the values of
the Yb valence are estimated to be ~2.73 and ~2.75 for alpha- and beta-YbAlB4,
respectively, thus providing clear evidence for valence fluctuations. The
valence band spectra of these compounds also show Yb2+ peaks at the Fermi
level. These observations establish an unambiguous case of a strong mixed
valence at quantum criticality for the first time among heavy fermion systems,
calling for a novel scheme for a quantum critical model beyond the conventional
Doniach picture in beta-YbAlB4.Comment: 4 pages, 3 figures, revised version accepted for publication in PR
Quantum Criticality without Tuning in the Mixed Valence Compound beta-YbAlB4
Fermi liquid theory, the standard theory of metals, has been challenged by a
number of observations of anomalous metallic behavior found in the vicinity of
a quantum phase transition. The breakdown of the Fermi liquid is accomplished
by fine-tuning the material to a quantum critical point using a control
parameter such as the magnetic field, pressure, or chemical composition. Our
high precision magnetization measurements of the ultrapure f-electron based
superconductor {\beta}-YbAlB4 demonstrate a scaling of its free energy
indicative of zero-field quantum criticality without tuning in a metal. The
breakdown of Fermi-liquid behavior takes place in a mixed-valence state, in
sharp contrast with other known examples of quantum critical f-electron systems
that are magnetic Kondo lattice systems with integral valence.Comment: 26 pages, 7 figures including supporting online matelial
The Geometry and Moduli of K3 Surfaces
These notes will give an introduction to the theory of K3 surfaces. We begin
with some general results on K3 surfaces, including the construction of their
moduli space and some of its properties. We then move on to focus on the theory
of polarized K3 surfaces, studying their moduli, degenerations and the
compactification problem. This theory is then further enhanced to a discussion
of lattice polarized K3 surfaces, which provide a rich source of explicit
examples, including a large class of lattice polarizations coming from elliptic
fibrations. Finally, we conclude by discussing the ample and Kahler cones of K3
surfaces, and give some of their applications.Comment: 34 pages, 2 figures. (R. Laza, M. Schutt and N. Yui, eds.
Anomalous Coherent Backscattering of Light from Opal Photonic Crystals
We studied coherent backscattering (CBS) of light from opal photonic crystals
in air at different incident inclination angles, wavelengths and along various
[hkl] directions inside the opals. Similar to previously obtained CBS cones
from various random media, we found that when Bragg condition with the incident
light beam is not met then the CBS cones from opals show a triangular line
shape in excellent agreement with light diffusion theory. At Bragg condition,
however, we observed a dramatic broadening of the opal CBS cones that depends
on the incident angle and [hkl] direction. This broadening is explained as due
to the light intensity decay in course of propagation along the Bragg direction
{\em before the first} and {\em after the last} scattering events. We modified
the CBS theory to incorporate the attenuation that results from the photonic
band structure of the medium. Using the modified theory we extract from our CBS
data the light mean free path and Bragg attenuation length at different [hkl].
Our study shows that CBS measurements are a unique experimental technique to
explore photonic crystals with disorder, when other spectroscopical methods
become ambiguous due to disorder-induced broadening.Comment: 10 pages, 5 figure
Localization in a random phase-conjugating medium
We theoretically study reflection and transmission of light in a
one-dimensional disordered phase-conjugating medium. Using an invariant
imbedding approach a Fokker-Planck equation for the distribution of the probe
light reflectance and expressions for the average probabilities of reflection
and transmission are derived. A new crossover length scale for localization of
light is found, which depends on the competition between phase conjugation and
disorder. For weak disorder, our analytical results are in good agreement with
numerical simulations.Comment: RevTex, 4 pages, 4 figure
Vortex-antivortex wavefunction of a degenerate quantum gas
A mechanism of a pinning of the quantized matter wave vortices by optical
vortices in a specially arranged optical dipole traps is discussed. The
vortex-antivortex optical arrays of rectangular symmetry are shown to transfer
angular orbital momentum and form the "antiferromagnet"-like matter waves. The
separable Hamiltonian for matter waves in pancake trapping geometry is proposed
and 3D-wavefunction is factorized in a product of wavefunctions of the 1D
harmonic oscillator and 2D vortex-antivortex quantum state. The 2D
wavefunction's phase gradient field associated via Madelung transform with the
field of classical velocities forms labyrinth-like structure. The macroscopic
quantum state composed of periodically spaced counter-rotating BEC superfluid
vortices has zero angular momentum and nonzero rotational energy.Comment: 11 pages, 5 figure
Anisotropic multiple scattering in diffuse media
The multiple scattering of scalar waves in diffusive media is investigated by
means of the radiative transfer equation. This approach amounts to a
resummation of the ladder diagrams of the Born series; it does not rely on the
diffusion approximation. Quantitative predictions are obtained, concerning
various observables pertaining to optically thick slabs, such as the mean
angle-resolved reflected and transmitted intensities, and the shape of the
enhanced backscattering cone. Special emphasis is put on the dependence of
these quantities on the anisotropy of the cross-section of the individual
scatterers, and on the internal reflections due to the optical index mismatch
at the boundaries of the sample. The regime of very anisotropic scattering,
where the transport mean free path is much larger than the scattering
mean free path , is studied in full detail. For the first time the
relevant Schwarzschild-Milne equation is solved exactly in the absence of
internal reflections, and asymptotically in the regime of a large index
mismatch. An unexpected outcome concerns the angular width of the enhanced
backscattering cone, which is predicted to scale as
, in contrast with the generally
accepted law, derived within the diffusion approximation.Comment: 53 pages TEX, including 2 tables. The 4 figures are sent at reques
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