Past Talks (2020-2022)

13.12.2022 {$\hspace{1cm}$} Thimo Preis (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Stable and unstable perturbations in universal scaling phenomena far from equilibrium

Abstract: It is a great challenge to understand the emergent stability properties in self-organized scaling phenomena from the underlying quantum dynamics. For an N-component scalar quantum field theory, I will present a study of the dynamics of perturbations around nonthermal fixed points associated to universal scaling phenomena in quantum many-body systems far from equilibrium. While the approach to universal scaling behavior of this system is known to be observed from a wide range of far-from-equilibrium initial conditions without fine-tuning, we find both stable and unstable perturbations around the scaling solution to be present. With the help of linear response theory, I will discuss how unstable dynamics arises from a competition between elastic scattering processes among the quasi-particle states. We find that the fixed point is rendered dynamically attractive at any non-zero momentum due to universal scaling of the unstable regime towards the infrared by virtue of a self-similar quasi-particle cascade.

29.11.2022 {$\hspace{1cm}$} Daniel Spitz (ITP Heidelberg) {$\hspace{0.1cm}$} Slides

Title: Confinement in non-Abelian lattice gauge theory via persistent homology

Abstract: Finding order parameters for the detection of critical phenomena can be a challenging endeavour in non-Abelian gauge theories. Tailored to detect topological structures in noisy data and accompanied by stability and limit theorems, persistent homology allows for the construction of sensible and sensitive observables. Based on state-of-the-art hybrid Monte Carlo simulations of SU(2) lattice gauge theory I will show how the persistent homology of filtrations by chromoelectric- and -magnetic fields, topological densities and Polyakov loops can be used to gauge-invariantly uncover interpretable features of the confinement-deconfinement phase transition. This includes signatures of instanton-dyons and Debye screening.

22.11.2022 {$\hspace{1cm}$} Moritz Reh (KIP Heidelberg)

Title: Solving quantum many-body dynamics and PDEs with neural networks

Abstract: Quantum mechanics suffers from the curse of dimensionality, prohibiting the study of large scale quantum systems. We develop a variational approach that is based on the recently developed "Neural Network Quantum States" that allow for a compressed representation of the quantum state using artificial neural networks as ansatz functions, mitigating this curse of dimensionality. Particularly, our approach is aimed at dissipative dynamics of Lindbladian type, which we model using a classical probability description of the quantum state. In a second part, we show how the developed formalism can be adapted to solve PDEs of probability densities in high dimensions when grid based solutions fail. Here we employ a neural network representation of the density and use our general solver to study the special case of Fokker-Planck type dynamics.

08.11.2022 {$\hspace{1cm}$} Stephan Hagel (Universität Gießen) {$\hspace{0.1cm}$} Slides

Title: Light meson spectrum from functional methods beyond rainbow-ladder

Abstract: A novel approach to construct an expression for the quark self-energy from a Bethe-Salpeter kernel is presented. The equation for the scalar part of the quark-propagator is directly constructed from the axialvector Ward-Takahashi identity, ensuring chiral symmetry breaking is correctly entailed in this approach. It will also be outlined, how the vector part of the propagator can be obtained from the vector Ward identity. The combined equations will be used to calculate the quark propagator and solve the corresponding Bethe-Salpeter equation for light mesons.

25.10.2022 {$\hspace{1cm}$} Georg Wolschin (ITP Heidelberg) {$\hspace{0.1cm}$} Slides

Title: Thermalization and Bose-Einsten condensation in ultracold atoms

Abstract: To account for the thermalization of, and the time-dependent Bose-Einstein condensate (BEC) formation in ultracold quantum gases, a nonlinear boson diffusion equation (NBDE) is presented. It is one of the few nonlinear partial differential equations that can be solved analytically. The solution method is explained, and the outcome is shown to agree with numerical results. The model results are compared with time-dependent BEC formation data from MIT (Na-23) and – more recently – Cambridge University (K-39) at various interaction strengths (s-wave scattering lengths), confirming the validity and usefulness of the nonlinear diffusion model, which has also been applied to the fast thermalization of gluons at relativistic energies.

24.05.2022 {$\hspace{1cm}$} Peter Lowdon (Universität Frankfurt) {$\hspace{0.1cm}$} Slides

Title: Local quantum field theory in extreme environments

Abstract: Local quantum field theory (QFT) provides a framework for establishing the non-perturbative constraints imposed on finite-temperature correlation functions. In this talk I will discuss how the locality of fields has significant implications for the spectral properties of finite-temperature QFTs, in particular that the peak-broadening effects experienced by particle states can be directly extracted from imaginary-time correlation functions. As an application, I will discuss the calculation of the pion spectral function peak from Euclidean data.

11.05.2022 {$\hspace{1cm}$} Alaric Erschfeld (Universität Jena) {$\hspace{0.1cm}$} Slides

Title: Functional methods for cosmic large-scale structure formation

Abstract: The formation of cosmic large-scale structures can be formulated in a functional approach for a statistical field theory of dark matter. Functional methods such as the Dyson—Schwinger equation and the functional renormalisation group provide generically non-perturbative methods to study the statistical properties of dark matter in the small-scale regime, where cosmic structure formation is non-linear. In particular, utilising the underlying symmetries of the theory, such as conservation laws and an extended version of Galilean invariance, allows to pursue non-perturbative approximations necessary to capture the relevant physics at small scales. Dark matter correlation functions carrying signatures of phenomena beyond the perfect pressureless fluid approximation are presented, utilising the Dyson—Schwinger equation and the functional renormalisation group.

26.04.2022 {$\hspace{1cm}$} Lillian de Bruin (Universität Heidelberg) {$\hspace{0.1cm}$} Slides

Title: Exploring the IR sector of QCD out of equilibrium

Abstract: High energy nuclear collisions produce a large density of gluons at initial times, which can lead to the formation of a “condensate.” It’s been demonstrated that the condensate can be studied using the gauge-invariant spatial Wilson loop as an order parameter. We argue that the spatial “Polyakov loop” is a neater order parameter for condensation and is related to a gauge-invariant scalar field. Such a scalar field can be used to make contact with condensation behavior in other highly-occupied systems far from equilibrium. Based on work in progress.

11.01.2022 {$\hspace{1cm}$} Carl Zelle (Universität Köln) {$\hspace{0.1cm}$} Slides

Title: Non-Equilibrium Criticality at an Exceptional Point

Abstract: We study a classical U(1) nonequilibrium field theory with non conservative interactions. We show that a new phase with constantly rotating order parameter that breaks Z_2 conjugation symmetry and has no equilibrium counterpart emerges in the steady state phase diagram. An exceptional point marks the phase transition from the statically ordered into rotating phase. We analyse the dynamical scaling of response and correlation functions at this phase transition and employ a perturbative RG scheme to derive the corresponding universal critical exponents.

07.12.2021 {$\hspace{1cm}$} Federica Capellino (GSI Darmstadt) {$\hspace{0.1cm}$} Slides

Title: Hydrodynamic approach to heavy-quark diffusion in the quark-gluon plasma

Abstract: Exciting experimental results on the flow of charmonia and bottomonia, which have nowadays an unprecedented level of precision, pose the important physics question about the possible heavy-quark thermalization in the QGP. In this work, a new hydrodynamic approach to the transport of heavy quarks in the quark-gluon plasma (QGP) is presented. We exploit the conservation of the number of heavy quark--antiquark pairs within the evolution of the QGP to construct causal second-order hydrodynamic equations of motion. The hydrodynamic transport coefficients associated with the heavy-quark diffusion current are then compared with the momentum-diffusion coefficients obtained in transport theory (Fokker-Planck equation). By investigating the relation between the two approaches, we provide new insights concerning the level of local thermalization of charm and bottom quarks inside the expanding QGP.

09. 11. 2021 {$\hspace{1cm}$} Lingxiao Wang (FIAS) {$\hspace{0.1cm}$} Slides

Title: Automatic differentiation approach for reconstructing spectral functions with neural networks

Abstract: Reconstructing spectral functions from Euclidean Green’s functions is an important inverse problem in physics. The prior knowledge for specific physical systems routinely offers essential regularization schemes for solving the ill-posed problem approximately. Aiming at this point, we propose an automatic differentiation framework as a generic tool for the reconstruction from observable data. We represent the spectra by neural networks and set chi-square as loss function to optimize the parameters with backward automatic differentiation unsupervisedly. In the training process, there is no explicit physical prior embedding into neural networks except the positive-definite form. The reconstruction accuracy is assessed through Kullback–Leibler divergence and mean square error at multiple noise levels. It should be noted that the automatic differential framework and the freedom of introducing regularization are inherent advantages of the present approach and may lead to improvements of solving inverse problem in the future.

20. 07. 2021 {$\hspace{1cm}$} Martina Zündel (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Nonperturbative approach to dark matter structure growth

Abstract: Kinetic field theory (KFT) applied to cosmic structure formation is designed to overcome the intrinsic limitation of the single stream approximation that is inherent in the most common approaches to describe the growth of dark matter structures, but fails on small scales. Based on a reformulation of KFT {https://arxiv.org/abs/1809.06942} in terms of macroscopic fields, in this talk we examine a nonperturbative ansatz to probe the non-linear regime of dark matter structure growth in the density contrast power spectrum. As the power spectrum can be perturbatively described on large scales by RKFT, I implemented an out-of-equilibrium flow equation under a vertex expansion towards smaller scales.

06.07.2021 {$\hspace{1cm}$} Lukas Kades (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Towards sampling complex actions

Abstract: For many physical systems, the computation of observables amounts to solving an integral over a strongly oscillating complex-valued function. This so-called sign problem renders the numerical evaluation of these integrals a hard computational problem. Complex Langevin dynamics is one numerical method for tackling the sign problem. In this talk, I introduce a generalized framework for this method, providing explicit access to problems hindering a general applicability of complex Langevin dynamics.One of the key problems of complex Langevin dynamics is a potential convergence to unphysical solutions. Starting from first principles, I establish constraints on sampling processes facilitating a sampling of the physically correct solutions. The constraints are built on firm grounds by techniques of Markov chain Monte Carlo methods which warrant, as opposed to complex Langevin dynamics, explicit control of the underlying sampling process. The approach opens up a perspective for tackling the sign problem by means of taylor-made sampling schemes.

11. 05. 2021 {$\hspace{1cm}$} Gregor Fauth (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Collisional strong-field QED kinetic equations from quantum field theory

Abstract: Many different modern experiments such as involving highly charged condensed matter systems, off-central heavy-ion collisions or laser systems feature strong electromagnetic fields. The long time behaviour of such fields and their effect on the process of thermalization in isolated systems is still poorly understood. No practicable strong-field description that remains valid for late times is established. Aiming to improve this situation, I present my recent work on deriving collisional strong-field QED kinetic equations from nonequilibrium quantum field theory. Our complete leading order O(e^2) equations capture a plenitude of effects in one description ranging from early time vacuum (Schwinger) pair production to the onset of collisional equilibration in the presence of a strong field at later times. The collision kernels emerge with strong-field scattering amplitudes that are familiar from particle-in-cell descriptions. On a technical level this is achieved by combining the 2PI formulation of QED with Wigner function ideas.

13. 04. 2021 {$\hspace{1cm}$} Daniel Spitz (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Universal dynamics in quantum many-body systems via persistent homology

Abstract: Surprisingly, the dynamics of quantum systems far from equilibrium can show self-similar behavior which is the same across different physical systems and energy scales. Typically, such universal features are discussed for correlation functions. Inspired by topological data analysis techniques, we introduce persistent homology observables. As a prototype application, we consider data from a classical-statistical simulation of a two-dimensional Bose gas far from equilibrium. We discover a continuous spectrum of dynamical scaling exponents, which provides a refined classification of nonequilibrium universal phenomena. We find that the persistent homology scaling exponents are inherently linked to the geometry of the system, as the derivation of a packing relation reveals. The approach opens new ways to understand far-from-equilibrium dynamics.

02. 02. 2021 {$\hspace{1cm}$} Martin Brass (Heidelberg University)

Title: Ab initio calculation of the electron capture spectrum in Holmium

Abstract: The rest masses of neutrinos emerging from electron capture decay affect the shape of the atomic excitation spectrum of the created daughter atom. Determination of neutrino masses from such spectra relies on a precise theoretical understanding of the spectral shape. This shape is dominated by resonances due to local atomic multiplet states with core holes. Coulomb scattering between electrons couple the discrete atomic states, via Auger-Meitner decay, to final states with free electrons. I discuss these mechanisms and how they lead to these spectral features. Numerical ab initio methods to calculate the spectral shape are presented and results are compared to experimental data.

12. 01. 2021 {$\hspace{1cm}$} Gurtej Kanwar (Massachusetts Institute of Technology) {$\hspace{0.1cm}$} Slides

Title: "Observifolds": Deforming the Path Integral to Improve Noisy Observables

Abstract: Lattice field theory path integrals in many cases integrate over holomorphic functions of the field variables. When the path integral defining an observable has severe phase fluctuations, i.e. a sign problem, statistical noise can overwhelm attempts to estimate the expectation value. I present recent work on applying complex contour deformation to lattice gauge theory path integrals, in particular in the case where the action is real and observables are the sole source of sign problems. I will discuss our approach to deforming integration over SU(N) variables and results showing significant noise reduction in Wilson loop observables in 1+1D gauge theory.

02. 11. 2020 {$\hspace{1cm}$} Maximilian Rupprecht (The University of Edinburgh) {$\hspace{0.1cm}$} Slides

Title: The full S-matrix of N=4 super-Yang-Mills theory at tree-level

Abstract: While functional, the classical Feynman diagram approach used to obtain physical observables of scattering processes requires an immense computational effort apart for the simplest of processes. In this talk, I review more modern techniques in the study of scattering amplitudes. Using three ingredients, MHV amplitudes, the so-called BCFW recursion relations and twistor theory, I demonstrate how one can express the full S-matrix of N=4 super-Yang-Mills theory at tree-level. This striking result, known as the RSVW formula, is just one of a much broader class of novel formulae for full tree-level S-matrices.

07. 07. 2020 {$\hspace{1cm}$} Passant Ali (University of Cologne) {$\hspace{0.1cm}$} Slides

Title: Natural Mass Hierarchy in Potts-Yukawa Systems and Its Implementations in Asymptotic Safety

Abstract: A different approach to mass hierarchy generation in scalar sectors is investigated. This is conducted by analyzing the Potts-Yukawa system featuring a scalar potential with discrete Z_n -symmetric minima with n > 4. Using a functional renormalization group approach, this leads to a mass hierarchy generation in the scalar sector towards the IR scales, owing to the irrelevance of the symmetry- breaking coupling, along with the spontaneous symmetry-breaking induction via the Yukawa coupling. Additionally, the possibility of a UV completion of the Potts-Yukawa system via an asymptotically-safe quantum gravity inclusion is further investigated. This culminates in an extension of the scalar sector to multiple-flavoured fields, where a search for an interacting, UV-attractive fixed point is conducted.

30. 06. 2020 {$\hspace{1cm}$} Robert Ott (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Quantum Simulation of a U(1) lattice gauge theory

Abstract: Understanding the nonequilibrium evolution of gauge theories is in general a hard task. Quantum simulators may give a new promising route towards this challenge, by using highly controllable quantum technologies to experimentally engineer quantum systems with local gauge symmetry. In this talk I first give an introduction to this concept and the Hamiltonian formulation of gauge theories. Then I present recent results on the quantum simulation of a U(1) lattice gauge theory in the quantum link formulation.

23. 06. 2020 {$\hspace{1cm}$} Ryusuke Jinno (DESY, Hamburg) {$\hspace{0.1cm}$} Slides

Title: Gravitational waves from first-order phase transitions: some developments in ultra-supercooled transitions

Abstract: Gravitational waves (GWs) offer a unique probe to the early Universe. One of the interesting targets is the ultra-supercooled transition, in which the amount of the released energy dominates over the plasma energy before the transition. Despite its theoretical and observational importance, there still remains a huge uncertainty in the amount and the spectral shape of the GWs produced in this type of transition. In this talk I first review GW production in relatively weak first-order phase transitions, and explain several difficulties associated with ultra-supercooled transitions. Then I explain our (semi-analytic) approaches to understand GW production in these transitions.

26. 05. 2020 {$\hspace{1cm}$} Aleksandr Mikheev (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Prescaling in a far-from-equilibrium Bose gas

Abstract: Non-equilibrium conditions give rise to classes of universally evolving configurations of quantum-many body systems at non-thermal fixed points. While the fixed point and thus full scaling in space and time is generically reached at very long evolution times, we propose that systems can show prescaling much earlier in time, in particular, on experimentally accessible time scales. During the prescaling evolution, some well-measurable properties of spatial correlations already scale with the universal exponents of the fixed point while others still show scaling violations. As an example of such a behavior, we consider far-from-equilibrium dynamics of a U(3)-symmetric spatially uniform three-dimensional Bose gas.

12. 05. 2020 {$\hspace{1cm}$} Jan Horak (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Real-time physics from Dyson-Schwinger Equations via Spectral Renormalisation

Abstract: We set-up a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems via analytic continuation. The framework is based on the spectral representation of correlation functions and dimensional regularisation. Therefore, the non-perturbative spectral renormalisation set-up here respects all symmetries of the theories at hand. In particular this includes space-time symmetries as well as internal symmetries such as chiral symmetry, and gauge symmetries. Spectral renormalisation can be applied within general functional approaches such as the functional renormalisation group, Dyson-Schwinger equations, and two- or n-particle irreducible approaches. First, this is applied to a scalar φ4-theory, where renormalised spectral DSEs are derived. Numerical results include the full, non-perturbative spectral function of the scalar filed. Aiming at QCD on the long run, preliminary results indicate the existence of spectral representation of the gluon in Yang-Mills theory. There, a numerical gluon spectral function has been computed, which obeys the the analytically known IR- und UV-asymptotics.

21. 04. 2020 {$\hspace{1cm}$} Christian Bertoni (ETH Zürich) {$\hspace{0.1cm}$} Slides

Title: Entropic time-energy uncertainty relations: An algebraic approach

Abstract: While it is clear that uncertainty relations between time and energy should exist, they are difficult to obtain using the standard methods. In this talk I will introduce new entropic time-energy uncertainty relations based on a novel approach. After having introduced entropic uncertainty relations in general, I will present an operational approach in terms of games between adversaries, which leads to entropic uncertainties between time and energy without needing to mention time observables. I will then present new bounds on these uncertainties in two scenarios and explain how they were obtained by extending a recent algebraic approach to standard entropic uncertainty relations.

11. 02. 2020 {$\hspace{1cm}$} Davide Rindori (Università di Firenze) {$\hspace{0.1cm}$} Slides

Title: Extensivity and entropy current at thermodynamic equilibrium with acceleration

Abstract: We derive a sufficient condition for the existence of the entropy current of a fluid at local thermodynamic equilibrium using relativistic quantum statistical mechanics, and put forward a general method to calculate it. We also work out a specific calculation in a non-trivial case of interest, namely a system at global thermodynamic equilibrium with proper acceleration of constant magnitude along the flow lines in Minkowski spacetime, whose lowest possible proper temperature is the Unruh temperature. In this case, we show that the integral of the entropy current in the right Rindler wedge is the entanglement entropy with the left Rindler wedge.

28. 01. 2020 {$\hspace{1cm}$} Lukas Rammelmueller (LMU Munich) {$\hspace{0.1cm}$} Slides

Title: Exploring imbalanced Fermi gases with stochastic quantization

Abstract: Experiments with ultracold Fermi gases continue to provide us with invaluable insight into the nature of strongly correlated systems. However, the theoretical description of such systems is challenging as analytic solutions are not available for general cases. On the numerical side progress is slowed down by the infamous sign-problem that causes Monte Carlo approaches to be exponentially expensive for increasing system sizes. To address this issue in a non-relativistic setting, we can learn from methodological advances made by the high-energy community. Specifically, we adapt the so-called complex Langevin (CL) approach to ultracold quantum gases which turns out to be a valuable tool in this context. In this talk, I will briefly introduce the method and report on recent progress that has been made with the CL method in the regime of strongly interacting Fermi gases. In particular, I will focus on recent results for the unitary Fermi gas in the presence of a finite spin-asymmetry and discuss equations of state as well as thermodynamic response functions. Further, I will briefly discuss the effect of mismatched Fermi surfaces and masses on pairing in one-dimensional systems.

21. 01. 2020 {$\hspace{1cm}$} Linda Shen (Heidelberg University) {$\hspace{0.1cm}$} Slides

Title: Dynamical thermalisation in the quark-meson model

Abstract: We investigate the non-equilibrium time-evolution of the quark-meson model using 2PI effective action techniques. Our numerical simulations, which include the full dynamics of the order parameter of chiral symmetry, show how the model dynamically thermalizes into different regions of its phase diagram. In particular, by studying quark and meson spectral functions, we shed light on the real-time dynamics approaching the crossover transition, revealing e.g. the emergence of light effective fermionic degrees of freedom in the infrared. At late times in the evolution, the fluctuation-dissipation relation emerges naturally among both meson and quark d.o.f., confirming that the simulation successfully reaches the universal thermal fixed point.