arXiv subjects

Alexander Rothkopf

Publications and source records attributed to Alexander Rothkopf.

At least 37 records · Page 2Linked to original sources

arXiv2022

Static quark anti-quark interactions at non-zero temperature from lattice QCD

We present results on the in-medium interactions of static quark anti-quark pairs using realistic 2+1 HISQ flavor lattice QCD. Focus is put on the extraction of spectral information from Wilson line correlators in Coulomb gauge using four complementary methods. Our results indicate that on HISQ lattices, the position of the dominant spectral peak associated with the real-part of the interquark potential remains unaffected by temperature. This is in contrast to prior work in quenched QCD and we present follow up comparisons to newly generated quenched ensembles.

hep-lat↗

arXiv2022

Open-quantum-systems approach to in-medium heavy quarkonium dynamics

Heavy quarkonium continues to play a central role in the study of nuclear matter under extremes of temperature and density in relativistic heavy-ion collisions. In this talk I report on recent developments in the theoretical description of quarkonium in-medium dynamics using the open-quantum systems approach. Not only does it provide a clear interpretation of the imaginary part of the complex heavy-quark potential but also reveals that a subtle interplay between screening and wavefunction decoherence is responsible for the melting of heavy quarkonium states.

hep-ph↗

arXiv2022

Towards symmetric discretization schemes via weak boundary conditions

The Szymanzik improvement program for gauge theories is most commonly implemented using forward finite difference corrections to the Wilson action. Central symmetric schemes naively applied, suffer from a doubling of degrees of freedom, identical to the well known fermion doubling phenomenon. And while adding a complex Wilson term remedies the problem for fermions, it does not easily transfer to real-valued gauge fields. In this talk I report on recent progress in formulating symmetric discretization schemes for classical actions of simple one-dimensional problems. They avoid doubling by exploiting the weak imposition of initial/boundary conditions. Inspired by recent work in the field of numerical analysis of partial differential equations, I construct a regularized summation-by-parts finite difference operator using boundary data based on affine coordinates. Application to a classical initial value problems with second order derivatives are presented.

hep-lat↗

arXiv2022

Kernel controlled real-time Complex Langevin simulation

This study explores the utility of a kernel in complex Langevin simulations of quantum real-time dynamics on the Schwinger-Keldysh contour. We give several examples where we use a systematic scheme to find kernels that restore correct convergence of complex Langevin. The schemes combine prior information we know about the system and the correctness of convergence of complex Langevin to construct a kernel. This allows us to simulate up to $1.5β$ on the real-time Schwinger-Keldysh contour with the $0+1$ dimensional anharmonic oscillator using $m=1,λ=24$, which was previously unattainable using the complex Langevin equation.

hep-lat↗

arXiv2022

Inverse problems, real-time dynamics and lattice simulations

The determination of real-time dynamics of strongly coupled quantum fields is a central goal of modern nuclear and particle physics, which requires insight into quantum field theory beyond the weak-coupling approximation. While lattice QCD has provided vital insights into the non-perturbative static properties of quarks and gluons it hides their real-time dynamics behind an ill-posed inverse problem. In this proceeding I will discuss developments in tackling the inverse problem on the lattice and touch upon progress in the direct simualtion of real-time dynamics.

hep-lat↗

arXiv2022

The effective complex heavy-quark potential in an anisotropic quark-gluon plasma

We introduce a method for reducing anisotropic heavy-quark potentials to isotropic potentials by using an effective screening mass that depends on the quantum numbers $l$ and $m$ of a given state. We demonstrate that, using the resulting 1D effective potential model, one can solve a 1D Schrödinger equation and reproduce the full 3D results for the energies and binding energies of low-lying heavy-quarkonium bound states to relatively high accuracy. This includes the splitting of different p-wave polarizations. The resulting 1D effective model provides a way to include momentum anisotropy effects in open quantum system simulations of heavy-quarkonium dynamics in the quark-gluon plasma.

hep-ph↗

arXiv2022

The complex heavy-quark potential in an anisotropic quark-gluon plasma -- Statics and dynamics

We generalize a complex heavy-quark potential model from an isotropic QCD plasma to an anisotropic one by replacing the Debye mass $m_D$ with an anisotropic screening mass depending on the quark pair alignment with respect to the direction of anisotropy. Such an angle-dependent mass is determined by matching the perturbative contributions in the potential model to the exact result obtained in the Hard-Thermal-Loop resummed perturbation theory. An advantage of the resulting potential model is that its angular dependence can be effectively described by using a set of angle-averaged screening masses as proposed in our previous work. Consequently, one could solve a one-dimensional Schrödinger equation with a potential model built by changing the anisotropic screening masses into the corresponding angle-averaged ones, and reproduce the full three-dimensional results for the binding energies and decay widths of low-lying quarkonium bound states to very high accuracy. Finally, turning to dynamics, we demonstrate that the one-dimensional effective potential can accurately describe the time evolution of the vacuum overlaps obtained using the full three-dimensional anisotropic potential. This includes the splitting of different p-wave polarizations.

hep-ph↗

arXiv2022

Bayesian inference of real-time dynamics from lattice QCD

The computation of dynamical properties of nuclear matter, ranging from parton distribution functions of nucleons and nuclei to transport properties in the quark-gluon plasma, constitutes a central goal of modern theoretical physics. This real-time physics often defies a perturbative treatment and the most successful strategy so far is to deploy lattice QCD simulations. These numerical computations are based on Monte-Carlo sampling and formulated in an artificial Euclidean time. Real-time physics is most conveniently formulated in terms of spectral functions, which are hidden in lattice QCD behind an ill-posed inverse problem. I will discuss the current methods state-of-the art in the extraction of spectral functions from lattice QCD simulations, based on Bayesian inference and emphasize the importance of prior domain knowledge, vital to regularizing the otherwise ill-posed extraction task. With Bayesian inference allowing us to make explicit the uncertainty in both observations and in our prior knowledge, a systematic estimation of the total uncertainties in the extracted spectral functions is nowadays possible. Two implementations of the Bayesian Reconstruction (BR) method for spectral function extraction, one for MAP point estimates and one based on an open access Monte-Carlo sampler are provided.I will briefly touch on the use of machine learning for spectral function reconstruction and discuss some new insight it has brought to the Bayesian community.

hep-lat↗

arXiv2022

Static quark anti-quark interactions at non-zero temperature from lattice QCD

We study the interactions of a static quark antiquark pair at non-zero temperature using realistic 2+1 flavor lattice QCD calculations. The study consists of two parts: the first investigates the properties of Wilson line correlators in Coulomb gauge and compares to predictions of hard-thermal loop perturbation theory. As a second step we extract the spectral functions underlying the correlators using four conceptually different methods: spectral function fits, a HTL inspired fit for the correlation function, Padé rational approximation and the Bayesian BR spectral reconstruction. We find that our high statistics Euclidean lattice data are amenable to different hypotheses for the shapes of the spectral function and we compare the implications of each analysis method for the existence and properties of a well defined ground state spectral peak.

hep-lat↗

arXiv2022

The QCD Equation of State in Small Systems

We present first results on finite system size corrections to the equation of state, trace anomaly, and speed of sound for two model systems: 1) free, massless scalar theory and 2) quenched QCD with periodic boundary conditions (PBC). We further present work-in-progress results for quenched QCD with Dirichlet boundary conditions.

hep-ph↗

arXiv2021

The complex potential from 2+1 flavor QCD using HTL inspired approach

We have studied finite temperature complex static quark-antiquark potentials for 2+1 flavor QCD using highly improved staggered action with physical strange quark masses and light quark masses corresponding to a pion mass of 161 MeV. We calculated the potential using Wilson line correlators fixed in Coulomb gauge. For the extraction, we have used HTL motivated parametrization of the correlators. We found that the real part of the potential is screened above the crossover temperature and it's close to singlet free energies, whereas the imaginary part is increasing with both distance and temperature.

hep-lat↗

arXiv2021

In-medium static quark potential from spectral functions on realistic HISQ ensembles

We explore the interactions between a quark anti-quark pair in a thermal medium based on lattice QCD ensembles with $N_f = 2+1$ dynamical HISQ flavors. Our dataset spans the phenomenologically relevant temperature range between T=140MeV-2GeV based on lattice sizes $N_τ=10,12$ and $16$, with an aspect ratio of $N_σ/N_τ=4$. The peak position $Ω$ and the width $Γ$ of the spectral function of Wilson-line correlators in Coulomb gauge is computed. We assess the information content in the correlation functions and deploy three complementary strategies to reconstruct spectral information: model fits, Padé approximation and the Bayesian BR method. Limitations of each approach are carefully assessed.

hep-lat↗

arXiv2021

Conserving Lattice Gauge Theory for Finite Systems

In this contribution I discuss a recent proposal of a novel action for lattice gauge theory for finite systems, which accommodates non-periodic spatial boundary conditions. Drawing on the summation-by-parts formulation of finite differences and finite volume strategies of computational electrodynamics, an action is constructed that implements the proper integral form of Gauss' law and exhibits an inherently symmetric energy momentum tensor, all while realizing automatic ${\cal O}(a)$ improvement. Its central ingredients are illustrated using Abelian gauge theory as example.

hep-lat↗

arXiv2021

Stable solvers for real-time Complex Langevin

This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue of runaway solution moot, but they also allow us to simulate at comparatively largeLangevin time steps, leading to lower computational cost. We compare different ways of regularizing the underlying path integral and estimate the errors introduced due to the finite Langevin time. Based on that insight, we implement benchmark (non-)thermal simulations of the quantum anharmonic oscillator on the canonical Schwinger-Keldysh contour of short real-time extent.

hep-lat↗

arXiv2021

Conserving Lattice Gauge Theory for Finite Systems

In this study I develop a novel action for lattice gauge theory for finite systems, which accommodates non-periodic boundary conditions, implements the proper integral form of Gauss' law and exhibits an inherently symmetric energy momentum tensor, all while realizing automatic ${\cal O}(a)$ improvement. Taking the modern summation-by-parts formulation for finite differences as starting point and combining it with insight from the finite volume strategies of computational electrodynamics I show how the concept of a conserving discretization can be realized for non-Abelian lattice gauge theory. Major steps in the derivation are illustrated using Abelian gauge theory as example.

hep-lat↗

arXiv2021

Spectral Reconstruction with Deep Neural Networks

We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which prior knowledge is encoded in the training data and the inverse transformation manifold is explicitly parametrised through a neural network. We systematically investigate this novel reconstruction approach, providing a detailed analysis of its performance on physically motivated mock data, and compare it to established methods of Bayesian inference. The reconstruction accuracy is found to be at least comparable, and potentially superior in particular at larger noise levels. We argue that the use of labelled training data in a supervised setting and the freedom in defining an optimisation objective are inherent advantages of the present approach and may lead to significant improvements over state-of-the-art methods in the future. Potential directions for further research are discussed in detail.

physics.comp-ph↗

arXiv2020

Proper static potential in classical lattice gauge theory at finite T

We compute the proper real-time interaction potential between a static quark and antiquark in classical lattice gauge theory at finite temperature. Our central result is the determination of the screened real-part of this potential, and we reconfirm the presence of an imaginary part. The real part is intimately related to the back-reaction of the static sources onto the gauge fields, incorporated via Gauss's law. Differences in the treatment of static sources in quantum and classical lattice gauge theory are discussed.

hep-lat↗

arXiv2020

Bryan's Maximum Entropy Method -- diagnosis of a flawed argument and its remedy

The Maximum Entropy Method (MEM) is a popular data analysis technique based on Bayesian inference, which has found various applications in the research literature. While the MEM itself is well-grounded in statistics, I argue that its state-of-the-art implementation, suggested originally by Bryan, artificially restricts its solution space. This restriction leads to a systematic error often unaccounted for in contemporary MEM studies. The goal of this paper is to carefully revisit Bryan's train of thought, point out its flaw in applying linear algebra arguments to an inherently nonlinear problem, and suggest possible ways to overcome it.

physics.data-an↗