3,824 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
An exactly soluble noisy traveling wave equation appearing in the problem of directed polymers in a random medium
We calculate exactly the velocity and diffusion constant of a microscopic
stochastic model of evolving particles which can be described by a noisy
traveling wave equation with a noise of order . Our model can be
viewed as the infinite range limit of a directed polymer in random medium with
sites in the transverse direction. Despite some peculiarities of the
traveling wave equations in the absence of noise, our exact solution allows us
to test the validity of a simple cutoff approximation and to show that, in the
weak noise limit, the position of the front can be completely described by the
effect of the noise on the first particle.Comment: 5 page
A Geospatial Assessment of Social Vulnerability to Sea-Level Rise in Coastal San Luis Obispo
This project is an assessment of social vulnerability to sea-level rise in the unincorporated coastal area of the County of San Luis Obispo (County) using geospatial and statistical analysis. The intention of this assessment is to inform local climate adaptation efforts now required by state legislation. A social vulnerability index was generated at the Census block group level using 32 variables positively correlated with social vulnerability. The social vulnerability score for each block group is the sum of scores generated for the following principle components: (1) race/ethnicity and disability status, (2) social isolation and age, (3) income, and (4) housing quality and dependence on social services. This study uses Geographic Information Systems software to map social vulnerability scores and building footprints attributed each block group in the coastal planning area. To provide a preliminary assessment of exposure to sea-level rise hazards, social vulnerability and buildings are overlaid with existing spatial datasets for inundation, bluff erosion, dune erosion, and wetland migration induced by sea-level rise in the year 2100. Implications for existing plans and further research include the incorporation of sea-level rise vulnerability into the general plan (safety, land use, and environmental justice elements in particular), local hazard mitigation plan, and local coastal programs
Integrability of Dirac reduced bi-Hamiltonian equations
First, we give a brief review of the theory of the Lenard-Magri scheme for a
non-local bi-Poisson structure and of the theory of Dirac reduction. These
theories are used in the remainder of the paper to prove integrability of three
hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some
generalized Drinfeld-Sokolov hierarchies.Comment: 15 pages. Corrected some typos and added missing equations in Section
5 for g=sl_n, n>
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