6,876 research outputs found
Long-time behavior of MHD shell models
The long time behavior of velocity-magnetic field alignment is numerically
investigated in the framework of MHD shell model. In the stationary forced
case, the correlation parameter C displays a nontrivial behavior with long
periods of high variability which alternates with periods of almost constant C.
The temporal statistics of correlation is shown to be non Poissonian, and the
pdf of constant sign periods displays clear power law tails. The possible
relevance of the model for geomagnetic dynamo problem is discussed.Comment: 6 pages with 5 figures. In press on Europhysics Letter
Spin polarization and g-factor enhancement in graphene nanoribbons in magnetic field
We provide a systematic quantitative description of spin polarization in
armchair and zigzag graphene nanoribbons in a perpendicular magnetic field. We
first address spinless electrons within the Hartree approximation studying the
evolution of the magnetoband structure and formation of the compressible
strips. We discuss the potential profile and the density distribution near the
edges and the difference and similarities between armchair and zigzag edges.
Accounting for the Zeeman interaction and describing the spin effects via the
Hubbard term we study the spin-resolved subband structure and relate the spin
polarization of the system at hand to the formation of the compressible strips
for the case of spinless electrons. At high magnetic field the calculated
effective g-factor varies around a value of ~2.25 for armchair nanoribbons
and ~3 for zigzag nanoribbons. An important finding is that in zigzag
nanoribbons the zero-energy mode remains pinned to the Fermi-energy and becomes
fully spin-polarized for all magnetic fields, which, in turn, leads to a strong
spin polarization of the electron density near the zigzag edge.Comment: 9 pages, 4 figure
Universal finite size corrections and the central charge in non solvable Ising models
We investigate a non solvable two-dimensional ferromagnetic Ising model with
nearest neighbor plus weak finite range interactions of strength \lambda. We
rigorously establish one of the predictions of Conformal Field Theory (CFT),
namely the fact that at the critical temperature the finite size corrections to
the free energy are universal, in the sense that they are exactly independent
of the interaction. The corresponding central charge, defined in terms of the
coefficient of the first subleading term to the free energy, as proposed by
Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all
0<\lambda<\lambda_0 and \lambda_0 a small but finite convergence radius. This
is one of the very few cases where the predictions of CFT can be rigorously
verified starting from a microscopic non solvable statistical model. The proof
uses a combination of rigorous renormalization group methods with a novel
partition function inequality, valid for ferromagnetic interactions.Comment: 43 pages, 1 figur
Electron Correlations in Bilayer Graphene
The nature of electron correlations in bilayer graphene has been
investigated. An analytic expression for the radial distribution function is
derived for an ideal electron gas and the corresponding static structure factor
is evaluated. We also estimate the interaction energy of this system. In
particular, the functional form of the pair-correlation function was found to
be almost insensitive to the electron density in the experimentally accessible
range. The inter-layer bias potential also has a negligible effect on the
pair-correlation function. Our results offer valuable insights into the general
behavior of the correlated systems and serve as an essential starting-point for
investigation of the fully-interacting system.Comment: 4 pages, 3 figure
Convergence of density-matrix expansions for nuclear interactions
We extend density-matrix expansions in nuclei to higher orders in derivatives
of densities and test their convergence properties. The expansions allow for
converting the interaction energies characteristic to finite- and short-range
nuclear effective forces into quasi-local density functionals. We also propose
a new type of expansion that has excellent convergence properties when
benchmarked against the binding energies obtained for the Gogny interaction.Comment: 4 pages, 3 figure
Striped periodic minimizers of a two-dimensional model for martensitic phase transitions
In this paper we consider a simplified two-dimensional scalar model for the
formation of mesoscopic domain patterns in martensitic shape-memory alloys at
the interface between a region occupied by the parent (austenite) phase and a
region occupied by the product (martensite) phase, which can occur in two
variants (twins). The model, first proposed by Kohn and Mueller, is defined by
the following functional: where
is periodic in and almost everywhere.
Conti proved that if then the minimal specific
energy scales like ,
as . In the regime , we improve Conti's results, by computing exactly the
minimal energy and by proving that minimizers are periodic one-dimensional
sawtooth functions.Comment: 29 pages, 3 figure
Froth-like minimizers of a non local free energy functional with competing interactions
We investigate the ground and low energy states of a one dimensional non
local free energy functional describing at a mean field level a spin system
with both ferromagnetic and antiferromagnetic interactions. In particular, the
antiferromagnetic interaction is assumed to have a range much larger than the
ferromagnetic one. The competition between these two effects is expected to
lead to the spontaneous emergence of a regular alternation of long intervals on
which the spin profile is magnetized either up or down, with an oscillation
scale intermediate between the range of the ferromagnetic and that of the
antiferromagnetic interaction. In this sense, the optimal or quasi-optimal
profiles are "froth-like": if seen on the scale of the antiferromagnetic
potential they look neutral, but if seen at the microscope they actually
consist of big bubbles of two different phases alternating among each other. In
this paper we prove the validity of this picture, we compute the oscillation
scale of the quasi-optimal profiles and we quantify their distance in norm from
a reference periodic profile. The proof consists of two main steps: we first
coarse grain the system on a scale intermediate between the range of the
ferromagnetic potential and the expected optimal oscillation scale; in this way
we reduce the original functional to an effective "sharp interface" one. Next,
we study the latter by reflection positivity methods, which require as a key
ingredient the exact locality of the short range term. Our proof has the
conceptual interest of combining coarse graining with reflection positivity
methods, an idea that is presumably useful in much more general contexts than
the one studied here.Comment: 38 pages, 2 figure
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