arXiv subjects

Christian Schmidt

Publications and source records attributed to Christian Schmidt.

At least 73 records · Page 4Linked to original sources

arXiv2020

Higher order cumulants of net baryon-number distributions at non-zero $μ_B$

Using recent results on higher order cumulants of conserved charge fluctuations from lattice QCD, we construct mean, variance, skewness, kurtosis, hyper-skewness and hyper-kurtosis of net-baryon number distributions for small baryon chemical potentials $μ_B$. For the strangeness neutral case ($μ_S=0$) at fixed ratio of electric charge to baryon number density ($\frac{n_Q}{n_B}=0.4$), which is appropriate for a comparison with heavy ion collisions, we present results for $κ_B σ_B^2$, $S_B σ_B^3/M_B$, $κ^{H}_{B}σ_{B}^4$ and $S^{H}_{B}σ^5_{B}/M_{B}$ on the crossover line for the chiral transition, $T_{pc}(μ_B)$. Continuum extrapolations for this pseudo-critical transition line have recently been reported by HotQCD up to baryon chemical potentials $μ_B\simeq 300$ MeV [arXiv:1812.08235]. These cumulant ratios are of direct relevance for comparisons with corresponding ratios measured by STAR in the BES-I and II runs at beam energies $\sqrt{s_{NN}}\ge 20$ GeV. In particular, we point out that recent high statistics results on skewness and kurtosis of net-baryon number distributions obtained by STAR at $\sqrt{s_{NN}} = 54.4$ GeV put strong constraints on freeze-out parameters and are consistent with predictions from thermal QCD.

hep-lat↗

arXiv2020

Simulating gauge theories on Lefschetz thimbles

Lefschetz thimbles have been proposed recently as a possible solution to the complex action problem (sign problem) in Monte Carlo simulations. Here we discuss pure abelian gauge theory with a complex coupling $β$ and apply the concept of Generalized Lefschetz thimbles. We propose to simulate the theory on the union of the tangential manifolds to the thimbles. We construct a local Metropolis-type algorithm, that is constrained to a specific tangential manifold. We also discuss how, starting from this result, successive subleading tangential manifolds can be taken into account via a reweighting approach. We demonstrate the algorithm on $U(1)$ gauge theory in 1+1 dimensions and investigate the residual sign problem.

hep-lat↗

arXiv2019

Conserved charge fluctuations with smaller-than-physical quark masses

We present results from calculations of conserved charge fluctuations in $(2+1)$-flavor QCD using light quark masses in the range $m_s/80 \leq m_l \leq m_s/27$, with the strange quark mass ($m_s$) kept fixed at its physical value. This corresponds to a Goldstone pion mass in the range $80$ MeV $\leq m_π\leq 140$ MeV. The measurements have been done using HISQ fermion discretization and Symanzik improved gauge action. We discuss the quark mass dependence of up to 6th order cumulants and present first results on the separation of singular and regular contributions to these cumulants. From these results, we examine the nature of the chiral phase transition and the variation of the curvature of the crossover line as we approach the chiral limit.

hep-lat↗

arXiv2019

Uncertainty Modeling and Analysis of the European X-ray Free Electron Laser Cavities Manufacturing Process

This paper reports on comprehensive efforts on uncertainty quantification and global sensitivity analysis for accelerator cavity design. As a case study object the TESLA shaped superconducting cavities, as produced for the European X-ray Free Electron Laser (EXFEL), are selected. The choice for these cavities is explained by the available measurement data that can be leveraged to substantiate the simulation model. Each step of the manufacturing chain is documented together with the involved uncertainties. Several of these steps are mimicked on the simulation side, e.g. by introducing a random eigenvalue problem. The uncertainties are then quantified numerically and in particular the sensitivities give valuable insight into the systems behavior. We also compare these findings to purely statistical studies carried out for the manufactured cavities. More advanced, adaptive, surrogate modeling techniques are adopted, which are crucial to incorporate a large number of uncertain parameters. The main contribution is the detailed comparison and fusion of measurement results for the EXFEL cavities on the one hand and simulation based uncertainty studies on the other hand. After introducing the quantities of physical interest for accelerator cavities and the Maxwell eigenvalue problem, the details on the manufacturing of the EXFEL cavities and measurements are reported. This is followed by uncertainty modeling with quantification studies.

cs.CE↗

arXiv2019

Meson Screening Masses in (2+1)-Flavor QCD

We present lattice QCD results for mesonic screening masses in the temperature range 140 MeV $\lesssim T \lesssim$ 2500 MeV. Our calculations were carried out using (2+1)-flavors of the Highly Improved Staggered Quark (HISQ) action, with a physical value for the strange quark mass and two values of the light quark mass corresponding to pion masses of 160 MeV and 140 MeV. Continuum-extrapolated results were obtained using calculations with a variety of lattice spacings corresponding to temporal lattice extents $N_τ= 6 - 16$. We discuss the implications of these results for the effective restoration of various symmetries in the high temperature phase of QCD, as well as the approach toward the perturbative limit.

hep-lat↗

arXiv2019

Critical end points in (2+1)-flavor QCD with imaginary chemical potential

We present here the results from an ongoing determination of the critical quark mass in simulations of (2+1)-flavor QCD with an imaginary chemical potential. Studies with unimproved actions found the existence of a critical quark mass value at which the crossover transition ends on a second order phase transition and becomes first order for smaller values of the quark mass for the case of both vanishing and imaginary chemical potential. We use the Highly Improved Staggered Quark (HISQ) action and perform calculations in the Roberge-Weiss (RW) plane, where the value of the critical mass is expected to be largest. The lowest quark mass value used in our simulation corresponds to the pion mass $m_π$, down to $40$ MeV. Contrary to calculations performed with unimproved actions we find no evidence for the occurrence of first order transitions at the smallest quark mass values explored so far. Moreover we also show that the chiral observables are sensitive to the RW transition. Our results also indicate that the RW transition and chiral transition could coincide in the chiral limit.

hep-lat↗

arXiv2019

Phase structure of three flavor QCD in external magnetic fields using HISQ fermions

We study the phase structure of QCD with three degenerate flavors in the external magnetic fields using highly improved staggered quarks (HISQ). The simulations are performed on $16^3\times 6$ lattice. In order to investigate the quark mass dependence of the chiral transition we choose the values of the bare quark masses 0.015 and 0.0009375 in the lattice unit, corresponding to $m_π=320$ MeV and 80 MeV in the continuum limit. We found no indication of a first order phase transition in the current window of quark masses and external magnetic fields. Unlike to the case with standard staggered fermions inverse magnetic catalysis is always observed at about the critical temperature. The microscopic origin of this phenomena are further discussed by looking into the Dirac eigenvalue spectrum.

hep-lat↗

arXiv2018

QCD phase diagram for finite imaginary chemical potential with HISQ fermions

We present results from an ongoing study of the phase diagram of (2+1)-flavor QCD using the HISQ action with smaller than physical light quark masses in the Roberge-Weiss (RW) plane on lattices with temporal extent $N_τ=4$. We find that the endpoint of the $1^{st}$ order RW transition line remains $2^{nd}$ order at least down to light quark masses corresponding to Goldstone pion masses of $55$ MeV. Furthermore, we show that the chiral condensate is sensitive to the RW transition and may serve as a energy-like operator characterizing universal behavior close to the RW endpoint.

hep-lat↗

arXiv2018

On Minimal Sets to Destroy the $k$-Core in Random Networks

We study the problem of finding the smallest set of nodes in a network whose removal results in an empty $k$-core; where the $k$-core is the sub-network obtained after the iterative removal of all nodes of degree smaller than $k$. This problem is also known in the literature as finding the minimal contagious set. The main contribution of our work is an analysis of the performance of the recently introduced corehd algorithm [Scientific Reports, 6, 37954 (2016)] on random networks taken from the configuration model via a set of deterministic differential equations. Our analyses provides upper bounds on the size of the minimal contagious set that improve over previously known bounds. Our second contribution is a new heuristic called the weak-neighbor algorithm that outperforms all currently known local methods in the regimes considered.

physics.soc-ph↗

arXiv2018

Dense Limit of the Dawid-Skene Model for Crowdsourcing and Regions of Sub-optimality of Message Passing Algorithms

Crowdsourcing is a strategy to categorize data through the contribution of many individuals. A wide range of theoretical and algorithmic contributions are based on the model of Dawid and Skene [1]. Recently it was shown in [2,3] that, in certain regimes, belief propagation is asymptotically optimal for data generated from the Dawid-Skene model. This paper is motivated by this recent progress. We analyze the dense limit of the Dawid-Skene model. It is shown that it belongs to a larger class of low-rank matrix estimation problems for which it is possible to express the asymptotic, Bayes-optimal, performance in a simple closed form. In the dense limit the mapping to a low-rank matrix estimation problem provides an approximate message passing algorithm that solves the problem algorithmically. We identify the regions where the algorithm efficiently computes the Bayes-optimal estimates. Our analysis refines the results of [2,3] about optimality of message passing algorithms by characterizing regions of parameters where these algorithms do not match the Bayes-optimal performance. We further study numerically the performance of approximate message passing, derived in the dense limit, on sparse instances and carry out experiments on a real world dataset.

stat.ML↗

arXiv2017

Chiral phase transition of three flavor QCD with nonzero magnetic field using standard staggered fermions

Lattice simulations for (2+1)-flavor QCD with external magnetic field demonstrated that the quark mass is one of the important parameters responsible for the (inverse) magnetic catalysis. We discuss the dependences of chiral condensates and susceptibilities, the Polyakov loop on the magnetic field and quark mass in three degenerate flavor QCD. The lattice simulations are performed using standard staggered fermions and the plaquette action with spatial sizes Ns = 16 and 24 and a fixed temporal size Nt = 4. The value of the quark masses are chosen such that the system undergoes a first order chiral phase transition and crossover with zero magnetic field. We find that in light mass regime, the quark chiral condensate undergoes magnetic catalysis in the whole temperature region and the phase transition tend to become stronger as the magnetic field increases. In crossover regime, deconfinement transition temperature is shifted by the magnetic field when quark mass ma is less than 0.4. The lattice cutoff effects are also discussed.

hep-lat↗

arXiv2017

Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological Tissues

Uncertainty quantification plays an important role in biomedical engineering as measurement data is often unavailable and literature data shows a wide variability. Using state-of-the-art methods one encounters difficulties when the number of random inputs is large. This is the case, e.g., when using composite Cole-Cole equations to model random electrical properties. It is shown how the number of parameters can be significantly reduced by the Karhunen-Loeve expansion. The low-dimensional random model is used to quantify uncertainties in the axon activation during deep brain stimulation. Numerical results for a Medtronic 3387 electrode design are given.

cs.CE↗

arXiv2017

Adaptive Estimation of the Neural Activation Extent in Computational Volume Conductor Models of Deep Brain Stimulation

Objective: The aim of this study is to propose an adaptive scheme embedded into an open-source environment for the estimation of the neural activation extent during deep brain stimulation and to investigate the feasibility of approximating the neural activation extent by thresholds of the field solution. Methods: Open-source solutions for solving the field equation in volume conductor models of deep brain stimulation and computing the neural activation are embedded into a Python package to estimate the neural activation dependent on the dielectric tissue properties and axon parameters by employing a spatially adaptive scheme. Feasibility of the approximation of the neural activation extent by field thresholds is investigated to further reduce the computational expense. Results: The varying extents of neural activation for different patient-specific dielectric properties were estimated with the adaptive scheme. The results revealed the strong influence of the dielectric properties of the encapsulation layer in the acute and chronic phase after surgery. The computational time required to determine the neural activation extent in each studied model case was substantially reduced. Conclusion: The neural activation extent is altered by patient-specific parameters. Threshold values of the electric potential and electric field norm facilitate a computationally efficient method to estimate the neural activation extent. Significance: The presented adaptive scheme is able to robustly determine neural activation extents and field threshold estimates for varying dielectric tissue properties and axon diameters while reducing substantially the computational expense.

q-bio.NC↗

arXiv2017

Uncertainty Quantification of Oscillation Suppression during DBS in a Coupled Finite Element and Network Model

Models of the cortico-basal ganglia network and volume conductor models of the brain can provide insight into the mechanisms of action of deep brain stimulation (DBS). In this study, the coupling of a network model, under parkinsonian conditions, to the extracellular field distribution obtained from a three dimensional finite element model of a rodent's brain during DBS is presented. This coupled model is used to investigate the influence of uncertainty in the electrical properties of brain tissue and encapsulation tissue, formed around the electrode after implantation, on the suppression of oscillatory neural activity during DBS. The resulting uncertainty in this effect of DBS on the network activity is quantified using a computationally efficient and non-intrusive stochastic approach based on the generalized Polynomial Chaos. The results suggest that variations in the electrical properties of brain tissue may have a substantial influence on the level of suppression of oscillatory activity during DBS. Applying a global sensitivity analysis on the suppression of the simulated oscillatory activity showed that the influence of uncertainty in the electrical properties of the encapsulation tissue had only a minor influence, in agreement with previous experimental and computational studies investigating the mechanisms of current-controlled DBS in the literature.

q-bio.NC↗

arXiv2017

Simulating low dimensional QCD with Lefschetz thimbles

Non-perturbative lattice QCD calculations at non vanishing baryon number density are hampered by the QCD sign problem. The path integral, that in lattice QCD is calculated numerically, becomes highly oscillating. One possible solution is the Lefschetz thimble approach. It requires a deformation of the original integration domain into a manifold embedded in complex space. For properly chosen integration manifolds ("thimbles") the sign problem is drastically alleviated. For some bosonic and fermionic models this approach has been shown to work. Here we apply the thimble disretization to (0+1)-dimensional QCD with standard staggerd quarks and disscuss issues that may arrise in higher dimensions.

hep-lat↗

arXiv2017

The phase structure of QCD

We review recent results on the phase structure of QCD and bulk QCD thermodynamics. In particular we discuss how universal critical scaling related to spontaneous breaking of the chiral symmetry manifests itself in recent lattice QCD simulations and how the knowledge on non-universal scaling parameter can be utilized in the exploration of the QCD phase diagram. We also show how various (generalized) susceptibilities can be employed to characterize properties of QCD matter at low and hight temperatures, related to deconfining aspects of the QCD transition. Finally, we address the input these lattice QCD calculation can provide for our under standing of the matter created in heavy ion collisions and in particular on the freeze-out conditions met in the hydrodynamic evolution of this matter.

hep-lat↗

arXiv2016

On unitary reconstruction of linear optical networks

Linear optical elements are pivotal instruments in the manipulation of classical and quantum states of light. The vast progress in integrated quantum photonic technology enables the implementation of large numbers of such elements on chip while providing interferometric stability. As a trade-off these structures face the intrinsic challenge of characterizing their optical transformation as individual optical elements are not directly accessible. Thus the unitary transformation needs to be reconstructed from a dataset generated with having access to the input and output ports of the device only. Here we present a novel approach to unitary reconstruction that significantly improves upon existing approaches. We compare its performance to several approaches via numerical simulations for networks up to 14 modes. We show that an adapted version of our approach allows to recover all mode-dependent losses and to obtain highest reconstruction fidelities under such conditions.

quant-ph↗

arXiv2016

Optical Activation of Germanium Plasmonic Antennas in the Mid Infrared

Impulsive interband excitation with femtosecond near-infrared pulses establishes a plasma response in intrinsic germanium structures fabricated on a silicon substrate. This direct approach activates the plasmonic resonance of the Ge structures and enables their use as optical antennas up to the mid-infrared spectral range. The optical switching lasts for hundreds of picoseconds until charge recombination red-shifts the plasma frequency. The full behavior of the structures is modeled by the electrodynamic response established by an electron-hole plasma in a regular array of antennas.

cond-mat.mes-hall↗