2,957 research outputs found
On the disorder-driven quantum transition in three-dimensional relativistic metals
The Weyl semimetals are topologically protected from a gap opening against
weak disorder in three dimensions. However, a strong disorder drives this
relativistic semimetal through a quantum transition towards a diffusive
metallic phase characterized by a finite density of states at the band
crossing. This transition is usually described by a perturbative
renormalization group in of a Gross-Neveu model in the
limit . Unfortunately, this model is not multiplicatively
renormalizable in dimensions: An infinite number of relevant
operators are required to describe the critical behavior. Hence its use in a
quantitative description of the transition beyond one-loop is at least
questionable. We propose an alternative route, building on the correspondence
between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context
of high energy physics. It results in a model of Weyl fermions with a random
non-Gaussian imaginary potential which allows one to study the critical
properties of the transition within a expansion. We also
discuss the characterization of the transition by the multifractal spectrum of
wave functions.Comment: 5+8 pages, 1+5 figure
Minimal conductivity, topological Berry winding and duality in three-band semimetals
The physics of massless relativistic quantum particles has recently arisen in
the electronic properties of solids following the discovery of graphene. Around
the accidental crossing of two energy bands, the electronic excitations are
described by a Weyl equation initially derived for ultra-relativistic
particles. Similar three and four band semimetals have recently been discovered
in two and three dimensions. Among the remarkable features of graphene are the
characterization of the band crossings by a topological Berry winding, leading
to an anomalous quantum Hall effect, and a finite minimal conductivity at the
band crossing while the electronic density vanishes. Here we show that these
two properties are intimately related: this result paves the way to a direct
measure of the topological nature of a semi-metal. By considering three band
semimetals with a flat band in two dimensions, we find that only few of them
support a topological Berry phase. The same semimetals are the only ones
displaying a non vanishing minimal conductivity at the band crossing. The
existence of both a minimal conductivity and a topological robustness
originates from properties of the underlying lattice, which are encoded not by
a symmetry of their Bloch Hamiltonian, but by a duality
The k-parent spatial Lambda-Fleming-Viot process as a stochastic measure-valued model for an expanding population
We model spatially expanding populations by means of a spatial
-Fleming Viot process (SLFV) with selection : the k-parent SLFV. We
fill empty areas with type 0 "ghost" individuals, which have a strong selective
disadvantage against "real" type 1 individuals. This model is a special case of
the SLFV with selection introduced in [19, 22] : natural selection acts during
all reproduction events, and the fraction of individuals replaced during a
reproduction event is constant equal to 1. Letting the selective advantage k of
type 1 individuals over type 0 individuals grow to +, and without
rescaling time nor space, we obtain a new model for expanding populations, the
-parent SLFV. This model is reminiscent of the Eden growth model [13],
but with an associated dual process of potential ancestors, making it possible
to investigate the genetic diversity in a population sample. In order to obtain
the limit k + of the k-parent SLFV, we introduce an
alternative construction of the k-parent SLFV adapted from [38], which allows
us to couple SLFVs with different selection strengths
The Howe-Moore property for real and p-adic groups
We consider in this paper a relative version of the Howe-Moore Property,
about vanishing at infinity of coefficients of unitary representations. We
characterize this property in terms of ergodic measure-preserving actions. We
also characterize, for linear Lie groups or p-adic Lie groups, the pairs with
the relative Howe-Moore Property with respect to a closed, normal subgroup.
This involves, in one direction, structural results on locally compact groups
all of whose proper closed characteristic subgroups are compact, and, in the
other direction, some results about the vanishing at infinity of oscillatory
integrals.Comment: 25 pages, no figur
Dusty spirals triggered by shadows in transition discs
Context. Despite the recent discovery of spiral-shaped features in
protoplanetary discs in the near-infrared and millimetric wavelengths, there is
still an active discussion to understand how they formed. In fact, the spiral
waves observed in discs around young stars can be due to different physical
mechanisms: planet/companion torques, gravitational perturbations or
illumination effects. Aims. We study the spirals formed in the gaseous phase
due to two diametrically opposed shadows cast at fixed disc locations. The
shadows are created by an inclined non-precessing disc inside the cavity, which
is assumed to be optically thick. In particular, we analyse the effect of these
spirals on the dynamics of the dust particles and discuss their detectability
in transition discs. Methods. We perform gaseous hydrodynamical simulations
with shadows, then we compute the dust evolution on top of the gaseous
distribution, and finally we produce synthetic ALMA observations of the dust
emission based on radiative transfer calculations. Results. Our main finding is
that mm- to cm-sized dust particles are efficiently trapped inside the
shadow-triggered spirals. We also observe that particles of various sizes
starting at different stellocentric distances are well mixed inside these
pressure maxima. This dynamical effect would favour grain growth and affect the
resulting composition of planetesimals in the disc. In addition, our radiative
transfer calculations show spiral patterns in the disc at 1.6 {\mu}m and 1.3
mm. Due to their faint thermal emission (compared to the bright inner regions
of the disc) the spirals cannot be detected with ALMA. Our synthetic
observations prove however that shadows are observable as dips in the thermal
emission.Comment: 15 pages, 11 figures, accepted for publication in A&
Compensated Horner algorithm in K times the working precision
We introduce an algorithm to evaluate a polynomial with floating point coefficients as accurately as the Horner scheme performed in K times the working precision, for K an arbitrary integer. The principle is to iterate the error-free transformation of the compensated Horner algorithm and to accurately sum the final decomposition. We prove this accuracy property with an apriori error analysis. We illustrate its practical efficiency with numerical experiments on significant environments and IEEE-754 arithmetic. Comparing to existing alternatives we conclude that this K-times compensated algorithm is competitive for K up to 4, i.e. up to 212 mantissa bits
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