arXiv subjects

Michael Rumetshofer

Publications and source records attributed to Michael Rumetshofer.

5 recordsLinked to original sources

arXiv2019

Bayesian parametric analytic continuation of Green's functions

Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Green's function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the spectral function is inferred from a suitable set of parametrized basis functions. Bayesian model comparison then allows to assess the reliability of different parametrizations. The required evidence integrals of such a model comparison are determined by nested sampling. Compared to the maximum entropy method (MEM), routinely used for the analytic continuation of CTQMC data, the presented approach allows to infer whether the data support specific structures of the spectral function. We demonstrate the capability of BPAC in terms of CTQMC data for an Anderson impurity model (AIM) that shows a generalized Kondo scenario and compare the BPAC reconstruction to the MEM as well as to the spectral function obtained from the real-time fork tensor product state impurity solver where no analytic continuation is required. Furthermore, we present a combination of MEM and BPAC and its application to an AIM arising from the ab initio treatment of SrVO$_3$.

cond-mat.str-el↗

arXiv2019

Global Small-Angle Scattering Data Analysis of Inverted Hexagonal Phases

We have developed a global analysis model for randomly oriented, fully hydrated inverted hexagonal (H$_\text{II}$) phases formed by many amphiphiles in aqueous solution, including membrane lipids. The model is based on a structure factor for hexagonally packed rods and a compositional model for the scattering length density (SLD) enabling also the analysis of positionally weakly correlated H$_\text{II}$ phases. For optimization of the adjustable parameters we used Bayesian probability theory, which allows to retrieve parameter correlations in much more detail than standard analysis techniques, and thereby enables a realistic error analysis. The model was applied to different phosphatidylethanolamines including previously not reported H$_\text{II}$ data for diC14:0 and diC16:1 phosphatidylethanolamine. The extracted structural features include intrinsic lipid curvature, hydrocarbon chain length and area per lipid at the position of the neutral plane.

q-bio.BM↗

arXiv2019

First-principles quantum transport simulation of CuPc on Au(111) and Ag(111)

We investigate equilibrium and transport properties of a copper phthalocyanine (CuPc) molecule adsorbed on Au(111) and Ag(111) surfaces. The CuPc molecule has essentially three localized orbitals close to the Fermi energy resulting in strong local Coulomb repulsion not accounted for properly in density functional calculations. Hence, they require a proper many-body treatment within, e.g., the Anderson impurity model (AIM). The occupancy of these orbitals varies with the substrate on which CuPc is adsorbed. Starting from density functional theory calculations, we determine the parameters for the AIM embedded in a noninteracting environment that describes the residual orbitals of the entire system. While correlation effects in CuPc on Au(111) are already properly described by a single orbital AIM, for CuPc on Ag(111) the three orbital AIM problem can be simplified into a two orbital problem coupled to the localized spin of the third orbital. This results in a Kondo effect with a mixed character, displaying a symmetry between SU(2) and SU(4). The computed Kondo temperature is in good agreement with experimental values. To solve the impurity problem we use the recently developed fork tensor product state solver. To obtain transport properties, a scanning tunneling microscope (STM) tip is added to the CuPc molecule absorbed on the surface. We find that the transmission depends on the detailed position of the STM tip above the CuPc molecule in good agreement with differential conductance measurements.

cond-mat.str-el↗

arXiv2019

Bayesian Analysis of Femtosecond Pump-Probe Photoelectron-Photoion Coincidence Spectra with Fluctuating Laser Intensities

This paper employs Bayesian probability theory for analyzing data generated in femtosecond pump-probe photoelectron-photoion coincidence (PEPICO) experiments. These experiments allow investigating ultrafast dynamical processes in photoexcited molecules. Bayesian probability theory is consistently applied to data analysis problems occurring in these types of experiments such as background subtraction and false coincidences. We previously demonstrated that the Bayesian formalism has many advantages, amongst which are compensation of false coincidences, no overestimation of pump-only contributions, significantly increased signal-to-noise ratio, and applicability to any experimental situation and noise statistics. Most importantly, by accounting for false coincidences, our approach allows running experiments at higher ionization rates, resulting in an appreciable reduction of data acquisition times. In addition to our previous paper, we include fluctuating laser intensities, of which the straightforward implementation highlights yet another advantage of the Bayesian formalism. Our method is thoroughly scrutinized by challenging mock data, where we find a minor impact of laser fluctuations on false coincidences, yet a noteworthy influence on background subtraction. We apply our algorithm to data obtained in experiments and discuss the impact of laser fluctuations on the data analysis.

physics.atom-ph↗

arXiv2017

Nested sampling, statistical physics and the Potts model

We present a systematic study of the nested sampling algorithm based on the example of the Potts model. This model, which exhibits a first order phase transition for $q>4$, exemplifies a generic numerical challenge in statistical physics: The evaluation of the partition function and thermodynamic observables, which involve high dimensional sums of sharply structured multi-modal density functions. It poses a major challenge to most standard numerical techniques, such as Markov Chain Monte Carlo. In this paper we will demonstrate that nested sampling is particularly suited for such problems and it has a couple of advantages. For calculating the partition function of the Potts model with $N$ sites: a) one run stops after $O(N)$ moves, so it takes $O(N^{2})$ operations for the run, b) only a single run is required to compute the partition function along with the assignment of confidence intervals, c) the confidence intervals of the logarithmic partition function decrease with $1/\sqrt{N}$ and d) a single run allows to compute quantities for all temperatures while the autocorrelation time is very small, irrespective of temperature. Thermodynamic expectation values of observables, which are completely determined by the bond configuration in the representation of Fortuin and Kasteleyn, like the Helmholtz free energy, the internal energy as well as the entropy and heat capacity, can be calculated in the same single run needed for the partition function along with their confidence intervals. In contrast, thermodynamic expectation values of magnetic properties like the magnetization and the magnetic susceptibility require sampling the additional spin degree of freedom. Results and performance are studied in detail and compared with those obtained with multi-canonical sampling. Eventually the implications of the findings on a parallel implementation of nested sampling are outlined.

physics.comp-ph↗