6,670 research outputs found
The von Neumann entropy asymptotics in multidimensional fermionic systems
We study the von Neumann entropy asymptotics of pure translation-invariant
quasi-free states of d-dimensional fermionic systems. It is shown that the
entropic area law is violated by all these states: apart from the trivial
cases, the entropy of a cubic subsystem with edge length L cannot grow slower
than L^{d-1}ln L. As for the upper bound of the entropy asymptotics, the
zero-entropy-density property of these pure states is the only limit: it is
proven that arbitrary fast sub-L^d entropy growth is achievable.Comment: 10 page
On the automorphisms of moduli spaces of curves
In the last years the biregular automorphisms of the Deligne-Mumford's and
Hassett's compactifications of the moduli space of n-pointed genus g smooth
curves have been extensively studied by A. Bruno and the authors. In this paper
we give a survey of these recent results and extend our techniques to some
moduli spaces appearing as intermediate steps of the Kapranov's and Keel's
realizations of , and to the degenerations of Hassett's spaces
obtained by allowing zero weights.Comment: 15 pages. The material of version 1 has been reorganized and expanded
in this paper and in arXiv:1307.6828 on automorphisms of Hassett's moduli
space
On the sharpness of the zero-entropy-density conjecture
The zero-entropy-density conjecture states that the entropy density, defined
as the limit of S(N)/N at infinity, vanishes for all translation-invariant pure
states on the spin chain. Or equivalently, S(N), the von Neumann entropy of
such a state restricted to N consecutive spins, is sublinear. In this paper it
is proved that this conjecture cannot be sharpened, i.e., translation-invariant
states give rise to arbitrary fast sublinear entropy growth. The proof is
constructive, and is based on a class of states derived from quasifree states
on a CAR algebra. The question whether the entropy growth of pure quasifree
states can be arbitrary fast sublinear was first raised by Fannes et al. [J.
Math. Phys. 44, 6005 (2003)]. In addition to the main theorem it is also shown
that the entropy asymptotics of all pure shift-invariant nontrivial quasifree
states is at least logarithmic.Comment: 11 pages, references added, corrected typo
On the net reproduction rate of continuous structured populations with distributed states at birth
We consider a nonlinear structured population model with a distributed
recruitment term. The question of the existence of non-trivial steady states
can be treated (at least!) in three different ways. One approach is to study
spectral properties of a parametrized family of unbounded operators. The
alternative approach, on which we focus here, is based on the reformulation of
the problem as an integral equation. In this context we introduce a density
dependent net reproduction rate and discuss its relationship to a biologically
meaningful quantity. Finally, we briefly discuss a third approach, which is
based on the finite rank approximation of the recruitment operator.Comment: To appear in Computers and Mathematics with Application
Finite difference approximations for a size-structured population model with distributed states in the recruitment
In this paper we consider a size-structured population model where
individuals may be recruited into the population at different sizes. First and
second order finite difference schemes are developed to approximate the
solution of the mathematical model. The convergence of the approximations to a
unique weak solution with bounded total variation is proved. We then show that
as the distribution of the new recruits become concentrated at the smallest
size, the weak solution of the distributed states-at-birth model converges to
the weak solution of the classical Gurtin-McCamy-type size-structured model in
the weak topology. Numerical simulations are provided to demonstrate the
achievement of the desired accuracy of the two methods for smooth solutions as
well as the superior performance of the second-order method in resolving
solution-discontinuities. Finally we provide an example where supercritical
Hopf-bifurcation occurs in the limiting single state-at-birth model and we
apply the second-order numerical scheme to show that such bifurcation occurs in
the distributed model as well
Nonlinear preferential rewiring in fixed-size networks as a diffusion process
We present an evolving network model in which the total numbers of nodes and
edges are conserved, but in which edges are continuously rewired according to
nonlinear preferential detachment and reattachment. Assuming power-law kernels
with exponents alpha and beta, the stationary states the degree distributions
evolve towards exhibit a second order phase transition - from relatively
homogeneous to highly heterogeneous (with the emergence of starlike structures)
at alpha = beta. Temporal evolution of the distribution in this critical regime
is shown to follow a nonlinear diffusion equation, arriving at either pure or
mixed power-laws, of exponents -alpha and 1-alpha
Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
We formulate, and in some cases prove, three statements concerning the purity
or, more generally the naturality of the resolution of various rings one can
attach to a generic curve of genus g and a torsion point of order l in its
Jacobian. These statements can be viewed an analogues of Green's Conjecture and
we verify them computationally for bounded genus. We then compute the
cohomology class of the corresponding non-vanishing locus in the moduli space
R_{g,l} of twisted level l curves of genus g and use this to derive results
about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3}
is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is
greater than or equal to 19. In the last section we explain probabilistically
the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the
statement of Prop 2.
Magnetic field control of cycloidal domains and electric polarization in multiferroic BiFeO
The magnetic field induced rearrangement of the cycloidal spin structure in
ferroelectric mono-domain single crystals of the room-temperature multiferroic
BiFeO is studied using small-angle neutron scattering (SANS). The cycloid
propagation vectors are observed to rotate when magnetic fields applied
perpendicular to the rhombohedral (polar) axis exceed a pinning threshold value
of 5\,T. In light of these experimental results, a phenomenological model
is proposed that captures the rearrangement of the cycloidal domains, and we
revisit the microscopic origin of the magnetoelectric effect. A new coupling
between the magnetic anisotropy and the polarization is proposed that explains
the recently discovered magnetoelectric polarization to the rhombohedral axis
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