1,770 research outputs found
Trace for the Loewner Equation with Singular Forcing
The Loewner equation describes the time development of an analytic map into
the upper half of the complex plane in the presence of a "forcing", a defined
singularity moving around the real axis. The applications of this equation use
the trace, the locus of singularities in the upper half plane. This note
discusses the structure of the trace for the case in which the forcing
function, xi(t), is proportional to (-t)^beta with beta in the interval (0,
1/2). In this case, the trace is a simple curve, gamma(t), which touches the
real axis twice. It is computed by using matched asymptotic analysis to compute
the trajectory of the Loewner evolution in the neighborhood of the singularity,
and then assuming a smooth mapping of these trajectories away from the
singularity. Near the t=0 singularity, the trace has a shape given by
[ Re(gamma(t)-gamma(0)) ]^(1-beta) ~ [ beta*Im(gamma(t)) ]^beta ~
O(xi(t))^(1-beta).
A numerical calculation of the trace provides support for the asymptotic
theory.Comment: 21 pages, 6 figures, submitted to Nonlinearit
Early Thermal Evolution of Planetesimals and its Impact on Processing and Dating of Meteoritic Material
Radioisotopic ages for meteorites and their components provide constraints on
the evolution of small bodies: timescales of accretion, thermal and aqueous
metamorphism, differentiation, cooling and impact metamorphism. Realising that
the decay heat of short-lived nuclides (e.g. 26Al, 60Fe), was the main heat
source driving differentiation and metamorphism, thermal modeling of small
bodies is of utmost importance to set individual meteorite age data into the
general context of the thermal evolution of their parent bodies, and to derive
general conclusions about the nature of planetary building blocks in the early
solar system. As a general result, modelling easily explains that iron
meteorites are older than chondrites, as early formed planetesimals experienced
a higher concentration of short-lived nuclides and more severe heating.
However, core formation processes may also extend to 10 Ma after formation of
Calcium-Aluminum-rich inclusions (CAIs). A general effect of the porous nature
of the starting material is that relatively small bodies (< few km) will also
differentiate if they form within 2 Ma after CAIs. A particular interesting
feature to be explored is the possibility that some chondrites may derive from
the outer undifferentiated layers of asteroids that are differentiated in their
interiors. This could explain the presence of remnant magnetization in some
chondrites due to a planetary magnetic field.Comment: 24 pages, 9 figures, Accepted for publication as a chapter in
Protostars and Planets VI, University of Arizona Press (2014), eds. H.
Beuther, R. Klessen, C. Dullemond, Th. Hennin
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for
fermions with positive weights. In the example of the Hubbard model close to
half filling it fails to reproduce all the symmetries of the ground state
leading to systematic errors at low temperatures. In a previous work [Phys.
Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by
projecting the density matrix obtained from the simulation onto the ground
state symmetry sector. For ground state properties, the accuracy of this method
depends on a {\it large overlap} between the GQMC and exact density matrices.
Thus, the method is not rigorously exact. We present the limits of the approach
by a systematic study of the method for 2 and 3 leg Hubbard ladders for
different fillings and on-site repulsion strengths. We show several indications
that the systematic errors stem from non-vanishing boundary terms in the
partial integration step in the derivation of the Fokker-Planck equation.
Checking for spiking trajectories and slow decaying probability distributions
provides an important test of the reliability of the results. Possible
solutions to avoid boundary terms are discussed. Furthermore we compare results
obtained from two different sampling methods: Reconfiguration of walkers and
the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for
fermions with positive weights. In the example of the Hubbard model close to
half filling it fails to reproduce all the symmetries of the ground state
leading to systematic errors at low temperatures. In a previous work [Phys.
Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by
projecting the density matrix obtained from the simulation onto the ground
state symmetry sector. For ground state properties, the accuracy of this method
depends on a {\it large overlap} between the GQMC and exact density matrices.
Thus, the method is not rigorously exact. We present the limits of the approach
by a systematic study of the method for 2 and 3 leg Hubbard ladders for
different fillings and on-site repulsion strengths. We show several indications
that the systematic errors stem from non-vanishing boundary terms in the
partial integration step in the derivation of the Fokker-Planck equation.
Checking for spiking trajectories and slow decaying probability distributions
provides an important test of the reliability of the results. Possible
solutions to avoid boundary terms are discussed. Furthermore we compare results
obtained from two different sampling methods: Reconfiguration of walkers and
the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl
Spin Waves in Quantum Antiferromagnets
Using a self-consistent mean-field theory for the Heisenberg
antiferromagnet Kr\"uger and Schuck recently derived an analytic expression for
the dispersion. It is exact in one dimension () and agrees well with
numerical results in . With an expansion in powers of the inverse
coordination number () we investigate if this expression can be
{\em exact} for all . The projection method of Mori-Zwanzig is used for the
{\em dynamical} spin susceptibility. We find that the expression of Kr\"uger
and Schuck deviates in order from our rigorous result. Our method is
generalised to arbitrary spin and to models with easy-axis anisotropy \D.
It can be systematically improved to higher orders in . We clarify its
relation to the expansion.Comment: 8 pages, uuencoded compressed PS-file, accepted as Euro. Phys. Lette
Vector chiral order in frustrated spin chains
By means of a numerical analysis using a non-Abelian symmetry realization of
the density matrix renormalization group, we study the behavior of vector
chirality correlations in isotropic frustrated chains of spin S=1 and S=1/2,
subject to a strong external magnetic field. It is shown that the field induces
a phase with spontaneously broken chiral symmetry, in line with earlier
theoretical predictions. We present results on the field dependence of the
order parameter and the critical exponents.Comment: 8 pages, 9 figure
Discrete charges on a two dimensional conductor
We investigate the electrostatic equilibria of N discrete charges of size 1/N
on a two dimensional conductor (domain). We study the distribution of the
charges on symmetric domains including the ellipse, the hypotrochoid and
various regular polygons, with an emphasis on understanding the distributions
of the charges, as the shape of the underlying conductor becomes singular. We
find that there are two regimes of behavior, a symmetric regime for smooth
conductors, and a symmetry broken regime for ``singular'' domains. For smooth
conductors, the locations of the charges can be determined up to a certain
order by an integral equation due to Pommerenke (1969). We present a derivation
of a related (but different) integral equation, which has the same solutions.
We also solve the equation to obtain (asymptotic) solutions which show
universal behavior in the distribution of the charges in conductors with
somewhat smooth cusps. Conductors with sharp cusps and singularities show
qualitatively different behavior, where the symmetry of the problem is broken,
and the distribution of the discrete charges does not respect the symmetry of
the underlying domain. We investigate the symmetry breaking both theoretically,
and numerically, and find good agreement between our theory and the numerics.
We also find that the universality in the distribution of the charges near the
cusps persists in the symmetry broken regime, although this distribution is
very different from the one given by the integral equation.Comment: 46 pages, 46 figures, submitted to J. Stat. Phy
Thermal history modeling of the H chondrite parent body
The cooling histories of individual meteorites can be empirically
reconstructed by using ages from different radioisotopic chronometers with
distinct closure temperatures. For a group of meteorites derived from a single
parent body such data permit the reconstruction of the cooling history and
properties of that body. Particularly suited are H chondrites because precise
radiometric ages over a wide range of closure temperatures are available. A
thermal evolution model for the H chondrite parent body is constructed by using
all H chondrites for which at least three different radiometric ages are
available. Several key parameters determining the thermal evolution of the H
chondrite parent body and the unknown burial depths of the H chondrites are
varied until an optimal fit is obtained. The fit is performed by an 'evolution
algorithm'. Empirical data for eight samples are used for which radiometric
ages are available for at least three different closure temperatures. A set of
parameters for the H chondrite parent body is found that yields excellent
agreement (within error bounds) between the thermal evolution model and
empirical data of six of the examined eight chondrites. The new thermal model
constrains the radius and formation time of the H chondrite parent body
(possibly (6) Hebe), the initial burial depths of the individual H chondrites,
the average surface temperature of the body, the average initial porosity of
the material the body accreted from, and the initial 60Fe content of the H
chondrite parent body.Comment: 16 pages, 7 figure
Extended coherence time on the clock transition of optically trapped Rubidium
Optically trapped ensembles are of crucial importance for frequency
measurements and quantum memories, but generally suffer from strong dephasing
due to inhomogeneous density and light shifts. We demonstrate a drastic
increase of the coherence time to 21 s on the magnetic field insensitive clock
transition of Rb-87 by applying the recently discovered spin self-rephasing.
This result confirms the general nature of this new mechanism and thus shows
its applicability in atom clocks and quantum memories. A systematic
investigation of all relevant frequency shifts and noise contributions yields a
stability of 2.4E-11 x tau^(-1/2), where tau is the integration time in
seconds. Based on a set of technical improvements, the presented frequency
standard is predicted to rival the stability of microwave fountain clocks in a
potentially much more compact setup.Comment: 5 pages, 4 figure
Excitations in two-component Bose-gases
In this paper, we study a strongly correlated quantum system that has become
amenable to experiment by the advent of ultracold bosonic atoms in optical
lattices, a chain of two different bosonic constituents. Excitations in this
system are first considered within the framework of bosonization and Luttinger
liquid theory which are applicable if the Luttinger liquid parameters are
determined numerically. The occurrence of a bosonic counterpart of fermionic
spin-charge separation is signalled by a characteristic two-peak structure in
the spectral functions found by dynamical DMRG in good agreement with
analytical predictions. Experimentally, single-particle excitations as probed
by spectral functions are currently not accessible in cold atoms. We therefore
consider the modifications needed for current experiments, namely the
investigation of the real-time evolution of density perturbations instead of
single particle excitations, a slight inequivalence between the two
intraspecies interactions in actual experiments, and the presence of a
confining trap potential. Using time-dependent DMRG we show that only
quantitative modifications occur. With an eye to the simulation of strongly
correlated quantum systems far from equilibrium we detect a strong dependence
of the time-evolution of entanglement entropy on the initial perturbation,
signalling limitations to current reasonings on entanglement growth in
many-body systems
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