909 research outputs found
The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1
An analog of Gelfand-Levitan-Marchenko integral equations for multi-
dimensional Delsarte transmutation operators is constructed by means of
studying their differential-geometric structure based on the classical Lagrange
identity for a formally conjugated pair of differential operators. An extension
of the method for the case of affine pencils of differential operators is
suggested.Comment: 12 page
Broken parity and a chiral ground state in the frustrated magnet CdCr2O4
We present a model describing the lattice distortion and incommensurate
magnetic order in the spinel CdCr2O4, a good realization of the Heisenberg
"pyrochlore" antiferromagnet. The magnetic frustration is relieved through the
spin-Peierls distortion of the lattice involving a phonon doublet with odd
parity. The distortion stablizes a collinear magnetic order with the
propagation wavevector q=2\pi(0,0,1). The lack of inversion symmetry makes the
crystal structure chiral. The handedness is transferred to magnetic order by
the relativistic spin-orbit coupling: the collinear state is twisted into a
long spiral with the spins in the ac plane and q shifted to 2\pi(0,\delta,1).Comment: Incremental changes in response to referee report
Carrier dynamics and coherent acoustic phonons in nitride heterostructures
We model generation and propagation of coherent acoustic phonons in
piezoelectric InGaN/GaN multi-quantum wells embedded in a \textit{pin} diode
structure and compute the time resolved reflectivity signal in simulated
pump-probe experiments. Carriers are created in the InGaN wells by ultrafast
pumping below the GaN band gap and the dynamics of the photoexcited carriers is
treated in a Boltzmann equation framework. Coherent acoustic phonons are
generated in the quantum well via both deformation potential electron-phonon
and piezoelectric electron-phonon interaction with photogenerated carriers,
with the latter mechanism being the dominant one. Coherent longitudinal
acoustic phonons propagate into the structure at the sound speed modifying the
optical properties and giving rise to a giant oscillatory differential
reflectivity signal. We demonstrate that coherent optical control of the
differential reflectivity can be achieved using a delayed control pulse.Comment: 14 pages, 11 figure
Propagating Coherent Acoustic Phonon Wavepackets in InMnAs/GaSb
We observe pronounced oscillations in the differential reflectivity of a
ferromagnetic InMnAs/GaSb heterostructure using two-color pump-probe
spectroscopy. Although originally thought to be associated with the
ferromagnetism, our studies show that the oscillations instead result from
changes in the position and frequency-dependent dielectric function due to the
generation of coherent acoustic phonons in the ferromagnetic InMnAs layer and
their subsequent propagation into the GaSb. Our theory accurately predicts the
experimentally measured oscillation period and decay time as a function of
probe wavelength.Comment: 4 pages, 4 figure
Self-gravitating branes of codimension 4 in Lovelock gravity
We construct a familly of exact solutions of Lovelock equations describing
codimension four branes with discrete symmetry in the transverse space. Unlike
what is known from pure Einstein gravity, where such brane solutions of higher
codimension are singular, the solutions we find, for the complete Lovelock
theory, only present removable singularities. The latter account for a
localised tension-like energy-momentum tensor on the brane, in analogy with the
case of a codimension two self-gravitating cosmic string in pure Einstein
gravity. However, the solutions we discuss present two main distinctive
features : the tension of the brane receives corrections from the induced
curvature of the brane's worldsheet and, in a given Lovelock theory, the
spectrum of possible values of the tension is discrete. These solutions provide
a new framework for the study of higher codimension braneworlds.Comment: 22 page
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Characterizing the radiative effect of rain using a global ensemble of cloud resolving simulations
The effect of rain on radiative fluxes and heating rates is a process that is neglected in most of the large scale atmospheric models used for weather forecasting or climate prediction. Yet, to our knowledge, the magnitude of the resulting radiative bias remains unquantified. This study aims to quantify the rain radiative effect (RRE) at a range of temporal and spatial scales, as a step towards determining whether the radiation schemes in these models should include rain. Using offline radiative transfer calculations with input from an ensemble of cloud resolving model simulations, we find that rain has a negligible effect on global mean radiative fluxes (less than 0.2 W m‐2). Weekly mean RREs at specific locations may be larger (less than 4 W m−2). At the finest temporal and spatial resolutions, the RRE can occasionally be much larger again (greater than 100 W m‐2), but values exceeding 10 W m‐2 occur in less than 0.1% of cases. Using detailed analysis of case studies we demonstrate that the magnitude and direction of the RRE depend on the rain water path, its vertical location with respect to cloud and, for longwave radiation, the temperature at which it occurs. Large RREs generally only occur when the rain water path is large and the cloud water path is small. These cases are infrequent and intermittent. As the RREs are generally small, we conclude that this missing process is unlikely to be important for large scale atmospheric models
Conditional linearizability criteria for a system of third-order ordinary differential equations
We provide linearizability criteria for a class of systems of third-order
ordinary differential equations (ODEs) that is cubically semi-linear in the
first derivative, by differentiating a system of second-order quadratically
semi-linear ODEs and using the original system to replace the second
derivative. The procedure developed splits into two cases, those where the
coefficients are constant and those where they are variables. Both cases are
discussed and examples given
Classical Topological Order in Kagome Ice
We examine the onset of classical topological order in a nearest-neighbor
kagome ice model. Using Monte Carlo simulations, we characterize the
topological sectors of the groundstate using a non-local cut measure which
circumscribes the toroidal geometry of the simulation cell. We demonstrate that
simulations which employ global loop updates that are allowed to wind around
the periodic boundaries cause the topological sector to fluctuate, while
restricted local loop updates freeze the simulation into one topological
sector. The freezing into one topological sector can also be observed in the
susceptibility of the real magnetic spin vectors projected onto the kagome
plane. The ability of the susceptibility to distinguish between fluctuating and
non-fluctuating topological sectors should motivate its use as a local probe of
topological order in a variety of related model and experimental systems.Comment: 17 pages, 9 figure
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