4,215 research outputs found
Efficient representation of fully many-body localized systems using tensor networks
We propose a tensor network encoding the set of all eigenstates of a fully
many-body localized system in one dimension. Our construction, conceptually
based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built
from two layers of unitary matrices which act on blocks of contiguous
sites.
We argue this yields an exponential reduction in computational time and
memory requirement as compared to all previous approaches for finding a
representation of the complete eigenspectrum of large many-body localized
systems with a given accuracy. Concretely, we optimize the unitaries by
minimizing the magnitude of the commutator of the approximate integrals of
motion and the Hamiltonian, which can be done in a local fashion. This further
reduces the computational complexity of the tensor networks arising in the
minimization process compared to previous work. We test the accuracy of our
method by comparing the approximate energy spectrum to exact diagonalization
results for the random field Heisenberg model on 16 sites. We find that the
technique is highly accurate deep in the localized regime and maintains a
surprising degree of accuracy in predicting certain local quantities even in
the vicinity of the predicted dynamical phase transition. To demonstrate the
power of our technique, we study a system of 72 sites and we are able to see
clear signatures of the phase transition. Our work opens a new avenue to study
properties of the many-body localization transition in large systems.Comment: Version 2, 16 pages, 16 figures. Larger systems and greater
efficienc
Towards a more realistic population of bright spiral galaxies in cosmological simulations
We present an update to the multiphase SPH galaxy formation code by
Scannapieco et al. We include a more elaborate treatment of the production of
metals, cooling rates based on individual element abundances, and a scheme for
the turbulent diffusion of metals. Our SN feedback model now transfers energy
to the ISM in kinetic and thermal form, and we include a prescription for the
effects of radiation pressure from massive young stars on the ISM. We calibrate
our new code on the well studied Aquarius haloes and then use it to simulate a
sample of 16 galaxies with halo masses between 1x10^11 and 3x10^12 M_sun. In
general, the stellar masses of the sample agree well with the stellar mass to
halo mass relation inferred from abundance matching techniques for redshifts
z=0-4. There is however a tendency to overproduce stars at z>4 and to
underproduce them at z<0.5 in the least massive haloes. Overly high SFRs at z<1
for the most massive haloes are likely connected to the lack of AGN feedback in
our model. The simulated sample also shows reasonable agreement with observed
star formation rates, sizes, gas fractions and gas-phase metallicities at
z=0-3. Remaining discrepancies can be connected to deviations from predictions
for star formation histories from abundance matching. At z=0, the model
galaxies show realistic morphologies, stellar surface density profiles,
circular velocity curves and stellar metallicities, but overly flat metallicity
gradients. 15 out of 16 of our galaxies contain disk components with kinematic
disk fraction ranging between 15 and 65 %. The disk fraction depends on the
time of the last destructive merger or misaligned infall event. Considering the
remaining shortcomings of our simulations we conclude that even higher
kinematic disk fractions may be possible for LambdaCDM haloes with quiet merger
histories, such as the Aquarius haloes.Comment: 26 pages, 20 figures, accepted for publication in MNRA
Statistical and Dynamical Downscaling of Numerical Climate Simulations : Enhancement and Evaluation for East Asia
The overall aim of this thesis is to present methods, which improve evaluating dynamical downscaling approaches or enhance statistical downscaling schemes. These methods are illustrated along examples of both approaches for the East Asian region. The transfer of information from a large scale to a smaller scale is referred to as downscaling. Two different approaches are employed in climate science for downscaling purposes, i.e. textit{dynamical downscaling} and textit{statistical downscaling}. In order to give a better description of the downscaled data, this thesis presents methods, which help evaluating and interpreting the data and results of further studies in a better way, for both approaches. Dynamical Downscaling is based on a spatially limited atmospheric general circulation model, a so-called regional climate model (RCM). At the boundaries of the RCM lateral boundary conditions (LBC) are provided by a climate simulation performed with a global general circulation model (GCM). This thesis proposes methods for evaluating RCM simulations. First, a qualitative evaluation, that investigates whether single atmospheric dynamics are resolved by the RCM, is presented. Second, a newly developed evaluation method, that investigates by cross-spectral analysis on which temporal scales a RCM is able to generate variability independently from the GCM defining the LBC, is introduced. To this end, cross-spectra are estimated point-to-point between the RCM and a bi-linearly interpolated version of the GCM defining the LBC. Both methods are illustrated along RCM simulations performed for a domain covering East Asia. The RCM COSMO-CLM has been adapted for this purpose, and was driven by climate simulations performed with ECHAM5 and the re-analysis ERA-40 at its boundaries. The qualitative evaluation shows that both summer monsoon and winter monsoon dynamics are resolved by COSMO-CLM. The cross-spectral analysis suggests that the potential of COSMO-CLM to generate variability independently from the GCM depends on both dynamical features, i.e. monsoons and inter-tropical convergence zone, and on numerical parameters, i.e. horizontal resolution and domain extension. Statistical downscaling is based on statistical transfer functions between the output of large scale climate simulations and observations on the local scale. While an abundance of statistical methods for this kind of purpose are available, it is crucial from case to case to find physically meaningful predictors, which allow further interpretations of the results. Deriving and applying such predictors is demonstrated along a statistical downscaling study for precipitation properties in the Poyang catchment in Eastern China. The dichotomous variable, if 24~h accumulated rainfall exceeds a certain threshold, is taken from local rain gauges for summer. Empirical orthogonal functions (EOF) are calculated for relative vorticity at 850~hPa and vertical velocity at 500~hPa taken from ERA-40 re-analysis data. Both information are linked by logistic regression. The most dominant EOF-predictor can be associated with meso--scale disturbances, which are part of the summer monsoon dynamics in this region. Downscaled data is often requested for further studies in climate science, but also in other disciplines. Thus, developing evaluation methods for assessing the quality of RCM simulations, and deriving physically interpretable predictors for statistical downscaling schemes are crucial enhancements for the downscaling procedure
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Like many other advanced imaging methods, x-ray phase contrast imaging and
tomography require mathematical inversion of the observed data to obtain
real-space information. While an accurate forward model describing the
generally nonlinear image formation from a given object to the observations is
often available, explicit inversion formulas are typically not known. Moreover,
the measured data might be insufficient for stable image reconstruction, in
which case it has to be complemented by suitable a priori information. In this
work, regularized Newton methods are presented as a general framework for the
solution of such ill-posed nonlinear imaging problems. For a proof of
principle, the approach is applied to x-ray phase contrast imaging in the
near-field propagation regime. Simultaneous recovery of the phase- and
amplitude from a single near-field diffraction pattern without homogeneity
constraints is demonstrated for the first time. The presented methods further
permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval
and tomographic inversion. We demonstrate the potential of this approach by
three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may
be made for personal use only. Systematic reproduction and distribution,
duplication of any material in this paper for a fee or for commercial
purposes, or modifications of the content of this paper are prohibite
- …