7,650 research outputs found
Kodaira-Spencer formality of products of complex manifolds
We shall say that a complex manifold is emph{Kodaira-Spencer formal} if its Kodaira-Spencer differential graded Lie algebra
is formal; if this happen, then the deformation theory of
is completely determined by the graded Lie algebra and the base space of the semiuniversal deformation is a quadratic singularity..
Determine when a complex manifold is Kodaira-Spencer formal is generally difficult and
we actually know only a limited class of cases where this happen. Among such examples we have
Riemann surfaces, projective spaces, holomorphic Poisson manifolds with surjective anchor map
and every compact K"{a}hler manifold with trivial or torsion canonical
bundle.
In this short note we investigate the behavior of this property under finite products. Let be compact complex manifolds; we prove that whenever and are
K"{a}hler, then is Kodaira-Spencer formal if and only if the same
holds for and . A revisit of a classical example by Douady shows that the above result fails if the K"{a}hler assumption is droppe
Radiative polarization of electrons in a strong laser wave
We reanalyze the problem of radiative polarization of electrons brought into
collision with a circularly polarized strong plane wave. We present an
independent analytical verification of formulae for the cross section given by
D.\,Yu. Ivanov et al [Eur.\ Phys.\ J. C \textbf{36}, 127 (2004)]. By choosing
the exact electron's helicity as the spin quantum number we show that the
self-polarization effect exists only for the moderately relativistic electrons
with energy and only for a non-head-on collision
geometry. In these conditions polarization degree may achieve the values up to
65%, but the effective polarization time is found to be larger than 1\,s even
for a high power optical or infrared laser with intensity parameter (). This
makes such a polarization practically unrealizable. We also compare these
results with the ones of some papers where the high degree of polarization was
predicted for ultrarelativistic case. We argue that this apparent contradiction
arises due to the different choice of the spin quantum numbers. In particular,
the quantum numbers which provide the high polarization degree represent
neither helicity nor transverse polarization, that makes the use of them
inconvenient in practice.Comment: minor changes compared to v3; to appear in PR
Possible Implications of Asymmetric Fermionic Dark Matter for Neutron Stars
We consider the implications of fermionic asymmetric dark matter for a "mixed
neutron star" composed of ordinary baryons and dark fermions. We find examples,
where for a certain range of dark fermion mass -- when it is less than that of
ordinary baryons -- such systems can reach higher masses than the maximal
values allowed for ordinary ("pure") neutron stars. This is shown both within a
simplified, heuristic Newtonian analytic framework with non-interacting
particles and via a general relativistic numerical calculation, under certain
assumptions for the dark matter equation of state. Our work applies to various
dark fermion models such as mirror matter models and to other models where the
dark fermions have self interactions.Comment: 20 pages, 6 figure
Absence of structural correlations of magnetic defects in heavy fermion LiV2O4
Magnetic defects have pronounced effects on the magnetic properties of the
face-centered cubic compound LiV2O4. The magnetic defects arise from crystal
defects present within the normal spinel structure. High-energy x-ray
diffraction studies were performed on LiV2O4 single crystals to search for
superstructure peaks or any other evidence of periodicity in the arrangement of
the crystal defects present in the lattice. Entire reciprocal lattice planes
are mapped out with help of synchrotron radiation. No noticeable differences in
the x-ray diffraction data between a crystal with high magnetic defect
concentration and a crystal with low magnetic defect concentration have been
found. This indicates the absence of any long-range periodicity or short-range
correlations in the arrangements of the crystal/magnetic defects.Comment: 6 pages, 4 figure
Characterizing the Hofstadter butterfly's outline with Chern numbers
In this work, we report original properties inherent to independent particles
subjected to a magnetic field by emphasizing the existence of regular
structures in the energy spectrum's outline. We show that this fractal curve,
the well-known Hofstadter butterfly's outline, is associated to a specific
sequence of Chern numbers that correspond to the quantized transverse
conductivity. Indeed the topological invariant that characterizes the
fundamental energy band depicts successive stairways as the magnetic flux
varies. Moreover each stairway is shown to be labeled by another Chern number
which measures the charge transported under displacement of the periodic
potential. We put forward the universal character of these properties by
comparing the results obtained for the square and the honeycomb geometries.Comment: Accepted for publication in J. Phys. B (Jan 2009
Forcing function control of Faraday wave instabilities in viscous shallow fluids
We investigate the relationship between the linear surface wave instabilities
of a shallow viscous fluid layer and the shape of the periodic,
parametric-forcing function (describing the vertical acceleration of the fluid
container) that excites them. We find numerically that the envelope of the
resonance tongues can only develop multiple minima when the forcing function
has more than two local extrema per cycle. With this insight, we construct a
multi-frequency forcing function that generates at onset a non-trivial harmonic
instability which is distinct from a subharmonic response to any of its
frequency components. We measure the corresponding surface patterns
experimentally and verify that small changes in the forcing waveform cause a
transition, through a bicritical point, from the predicted harmonic
short-wavelength pattern to a much larger standard subharmonic pattern. Using a
formulation valid in the lubrication regime (thin viscous fluid layer) and a
WKB method to find its analytic solutions, we explore the origin of the
observed relation between the forcing function shape and the resonance tongue
structure. In particular, we show that for square and triangular forcing
functions the envelope of these tongues has only one minimum, as in the usual
sinusoidal case.Comment: 12 pages, 10 figure
Multiple Quantum NMR Dynamics in Dipolar Ordered Spin Systems
We investigate analytically and numerically the Multiple Quantum (MQ) NMR
dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole
interactions in the case of the dipolar ordered initial state. We suggest two
different methods of MQ NMR. One of them is based on the measurement of the
dipolar temperature in the quasi-equilibrium state which establishes after the
time of order T2 after the MQ NMR experiment. The other method uses an
additional resonance 45^0 -pulse after the preparation period of the standard
MQ NMR experiment in solids. Many-spin clusters and correlations are created
faster in such experiments than in the usual MQ NMR experiments and can be used
for the investigation of many-spin dynamics of nuclear spins in solids.Comment: 11 pages, 3 figures. accepted for publication in Physical Review
Energetics of Quantum Antidot States in Quantum Hall Regime
We report experiments on the energy structure of antidot-bound states. By
measuring resonant tunneling line widths as function of temperature, we
determine the coupling to the remote global gate voltage and find that the
effects of interelectron interaction dominate. Within a simple model, we also
determine the energy spacing of the antidot bound states, self consistent edge
electric field, and edge excitation drift velocity.Comment: 4 pages, RevTex, 5 Postscript figure
Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals
Ultracold fermions trapped in a honeycomb optical lattice constitute a
versatile setup to experimentally realize the Haldane model [Phys. Rev. Lett.
61, 2015 (1988)]. In this system, a non-uniform synthetic magnetic flux can be
engineered through laser-induced methods, explicitly breaking time-reversal
symmetry. This potentially opens a bulk gap in the energy spectrum, which is
associated with a non-trivial topological order, i.e., a non-zero Chern number.
In this work, we consider the possibility of producing and identifying such a
robust Chern insulator in the laser-coupled honeycomb lattice. We explore a
large parameter space spanned by experimentally controllable parameters and
obtain a variety of phase diagrams, clearly identifying the accessible
topologically non-trivial regimes. We discuss the signatures of Chern
insulators in cold-atom systems, considering available detection methods. We
also highlight the existence of topological semi-metals in this system, which
are gapless phases characterized by non-zero winding numbers, not present in
Haldane's original model.Comment: 30 pages, 12 figures, 4 Appendice
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