Sommerfeld Theory Colloquium (ASC)

Ultra-High-Energy Cosmic Rays (UHECRs) are particles with energies up to $3times 10^20 eV$, originating from unknown sources and producing extensive air showers in Earth's atmosphere. In this talk, I will review the current status of UHECR observations, including the energy spectrum, mass composition, and anisotropy in their arrival directions. I will highlight how the knowledge of the Galactic Magnetic Field (GMF) of the Milky Way is crucial for identifying UHECR sources. Additionally, I will review recent models of the GMF. Finally, I will discuss the propagation of UHECRs from their sources through both intergalactic and galactic magnetic fields, and I will explore the prospects for future source identification.

In a simple, constant environment does evolution continue forever? Does extensive diversification via small genetic and ecological differences? What are general evolutionary consequences of organismic complexity? Hints from long term laboratory evolution experiments and findings from genomic data of extensive within-species bacterial diversity motivate considering these questions. Several simple models of evolution with ecological feedback will be introduced, with the high dimensionality of phenotype space enabling analysis by statistical physics approaches.

In driven open quantum matter, coherent many-body quantum dynamics, drive, and dissipation play equally significant roles. These systems span a wide range of examples, including cold atomic gases, exciton-polaritons in solid state, and quantum devices designed for quantum information applications. These setups break the conditions of thermodynamic equilibrium on the microscopic scale, prompting questions about how this impacts macroscopic behavior, such as phases and phase transitions. We examine two key points: First, we showcase that a minor out-of-equilibrium perturbation on the microscopic level can lead to substantial macroscopic effects, including the emergence of novel non-equilibrium universality classes. This paves the way to active quantum matter scenarios in solid state physics. Second, we argue that drive and dissipation can be used constructively to maintain or even create fragile quantum mechanical correlations such as phase coherence, entanglement or topological order by carefully engineering the system. A topological quantum phase transition far from equilibrium can be induced in this way, exhibiting intriguing analogies to the problem of directed percolation.

This talk will overview the history of primordial black hole (PBH) research from the first papers around 50 years ago to the present time. I will first discuss their possible formation mechanisms, including critical collapse from inflationary fluctuations and various types of phase transition. I will then describe the numerous constraints on the number of PBHs from various quantum and astrophysical processes, this being the main focus of PBH research until recently. In the last decade there has been a shift of emphasis to the search for evidence for PBHs 13 what I term the bright side. So the final part of my talk will present this evidence, with particular emphasis on their possible role as dark matter candidates, sources of gravitational waves and seeds for supermassive black holes and early cosmic structures.

We will review the beginning of experimental and theoretical studies of moire systems and their evolution up to present. We will show how thousands of p orbitals in a moire unit cell of graphene can create single Heavy fermion at moire scale, and how the interaction between such fermions can lead to a perfect quantum simulator of an Anderson model. We will then present a catalogue of possible twistable materials and show how a huge variety of strongly interacting models can be realized in twisted homo and hetero twiste bilayers and multilayers of these materials.

In this talk, I will explore the fascinating connections between string theory and quantum field theory, focusing on what we have learned from studying string scattering amplitudes. These insights have not only deepened our understanding of particle interactions but have also led to significant advancements in quantum field theory itself. To set the stage, I will introduce string theory, highlighting its foundational principles and its relationship to low-energy quantum field theories that describe the fundamental forces of nature. Building on this, I will delve into three key concepts 14massive gravity, the double copy framework, and twisted cohomology 14all of which have roots in string theory or have been profoundly influenced by it. I will explain how massive gravity emerges as a natural extension in the context of string theory and how the double copy framework elegantly connects gauge theories with gravity, offering a unifying perspective. Twisted cohomology, a sophisticated mathematical tool, will be discussed in relation to the structure of scattering amplitudes and its role in uncovering deeper symmetries. Finally, I will illustrate how these ideas impact our understanding of scattering amplitudes in quantum field theories and how they are applied to describe physics across a wide range of energy scales 14from the low-energy behavior of known particles to the high-energy frontier. Through these examples, I aim to show how string theory serves as a powerful lens for reimagining and advancing our understanding of particle physics.

I will discuss Effective Field Theories that can originate from microscopic unitary theories, and their relation to moment theory. I will show that massive gravity, theories with isolated massive higher-spin particles, and theories with very irrelevant interactions, don't posses healthy UV completions, and I will show how Vector Meson Dominance follows from such first principles.

Our search for a quantum theory of gravity is aided by a unique and perplexing feature of the classical theory: General Relativity already knows" about its own quantum states (the entropy of a black hole), and about those of all matter (via the covariant entropy bound). The results we are able to extract from classical gravity are inherently nonperturbative and increasingly sophisticated. Recent breakthroughs include a derivation of the entropy of Hawking radiation, a computation of the exact integer number of states of some black holes, and the construction of gravitational holograms in our universe using techniques from single-shot quantum communication protocols.

Gravitational waves open a new window into our universe. In this colloquium we discuss particle theorists' perspective on calculations directly relevant for gravitational-wave emission from compact objects, which is rooted in quantum field theory and builds on the idea that gravitational interactions are mediated by spin-2 particles. After reviewing some of the remarkable advances in our understanding of scattering amplitudes and in our ability to evaluate them, we show how these ideas produce state of the art results in weak-field fully-relativistic calculations for gravitational wave observables, including for the astrophysical binary black hole inspiral problem.

Understanding dark energy and black holes remain a great challenge to fundamental physics. In this talk I will review the difficulties and explore some new and speculative approaches.

I will describe recent developments on the (numerical) computation of energy levels of various systems by the quantum mechanical bootstrap. The main way the bootstrap works is by using constraints that arise from positive matrices. Part of the goal is to turn the bootstrap problem into a problem that can be solved by semi-definite programming methods. I will describe how this method leads to solutions of the spectrum of various systems and will describe some additional applications of this way of solving problems to the study of quantum spin chains.

Interesting erasure phenomena arise from interactions between lower-dimensional and higher-dimensional objects and impact cosmology and fundamental physics. In the first part of the colloquium, I will examine the case for topological defects, revealing insights into the interactions of magnetic monopoles, cosmic strings, and domain walls. For objects like cosmic or QCD flux strings, encounters with domain walls or D-branes result in erasure through coherence loss during collisions, introducing a new string break-up mechanism. The collisions between magnetic monopoles and domain walls in an SU(2) gauge theory lead to monopole erasure, which is pivotal in post-inflationary phase transitions and potentially solves the cosmological monopole problem. Simulations show that strings or monopoles cannot penetrate domain walls. Entropy-based arguments highlight the significance of the erasure phenomena that can produce correlated gravitational waves and electromagnetic radiation, impacting cosmology and astrophysics. The second part of the colloquium focuses on the saturation of unitarity and the emergence of Saturons. These self-sustained objects, which reach the maximal entropy allowed by unitarity, resemble black holes. I discuss a "black hole-saturon" correspondence in a renormalizable SU(N) invariant theory. Despite lacking gravity, saturons show features like an information horizon, Bekenstein-Hawking entropy, thermal evaporation, and a characteristic information retrieval time. This correspondence has significant implications for black hole physics and saturated systems. We will examine recent results on saturon mergers, vortices in black holes, and primordial black holes, offering new perspectives on fundamental theory and observations.

One of the major problems of computational chemistry is the ab initio prediction of energies and properties of molecules. The electronic Schrödinger equations provides the in-principle solution, but because of intrinsic difficulties associated with the singular and long-ranged Coulomb interaction, this remains an extremely challenging task numerically. Here we outline a formalism called transcorrelation which provides a route out of the difficulties, whilst itself creating new problems (which have stumped the community for decades). We outline our work of the past few years in tackling these new problems, and show that the formalism has the potential to transform our ability to solve the Schrödinger problem in a general manner. In particular, by eliminating the Coulomb singularities, we show we can achieve both basis-set converged results, as well as thermodynamic limit results, with far fewer resources and less sophisticated many-body theories. Prospects to extend this methodology in the context of quantum computing will also be mentioned.

One of the simplest ways to make gauge fields massive is to add them a mass "by hand". Intuitively, one could expect that the corresponding massless theory would then be easy to recover. Yet, conventional methods indicate that such a limit is singular. In this talk, we will explore the massless limits of several massive gauge theories. We will identify the source of the apparent discontinuities and show that they are, in fact, simply an artifact of the perturbative approach. Then, we will discuss the consequences of this study on the relations between different gauge fields. Finally, we will conclude with a comment on the latest insights about these theories and their prospects.

Learning algorithms using deep neural networks are currently having a major impact on basic sciences. The physics of complex quantum systems is no exception, with multiple applications that constitute a new field of research. Examples include the representation and optimization of wave functions of quantum systems with large numbers of degrees of freedom (neural quantum states), the determination of wave functions from measurements (quantum tomography), and applications to the electronic structure of materials, such as the determination of more precise density functionals or the learning of force fields to accelerate molecular dynamics simulations. I will survey some of these applications, with an emphasis on neural quantum states.

I will discuss recent progress in the study of cosmological applications of string compactifications with stabilised moduli, focusing in particular on inflation, reheating and dark energy.

Since the discovery of the first binary black-hole merger in 2015, analytical and numerical solutions to the relativistic two-body problem have been essential for the detection and interpretation of more than 100 gravitational-wave signals from compact-object binaries. Future experiments will detect black holes at cosmic dawn, probe the nature of gravity and reveal the composition of neutron stars with exquisite precision. Theoretical advances (of up to two orders of magnitude in the precision with which we can predict relativistic dynamics) are needed to turn gravitational-wave astronomy into precision laboratories of astrophysics, cosmology, and gravity. In this talk, I will discuss recent advances in modeling the two-body dynamics and gravitational radiation, review the science that accurate waveform models have enabled with LIGO-Virgo gravitational-wave observations, and highlight the theoretical challenges that lie ahead to fully exploit the discovery potential of increasingly sensitive detectors on the ground, such as the Einstein Telescope and Cosmic Explorer, and in space, such as the Laser Interferometer Space Antenna (LISA).

Throughout the century that has passed since Ernst Ising submitted his PhD thesis in 1924, the Ising (-Lenz) model has provided an incredibly fruitful challenge that gave rise to entirely new branches of physics and mathematics. In this colloquium I will focus on the conformal bootstrap program which was designed by Polyakov in 1974 as a mathematical method to access non-perturbative aspects of critical systems/fixed points of the renormalization groups. In the light of holography, such systems are also relevant for the study of quantum gravity. In my presentation I will review some of the milestone achievements of the modern conformal bootstrap and outline current frontiers. The advances will be benchmarked mostly within the context of the 3D Ising model.

Perturbation theory remains one of the main tools in physics, in particular in quantum theories. However, most perturbative series diverge factorially, and it is not obvious how to extract information from them. Their divergence also suggests that, in order to obtain accurate results, one might need additional non-perturbative information. The theory of resurgence has been proposed as a general framework to address these issues. In this talk I will give an introduction to this theory and will illustrate it with applications -old and new- in quantum mechanics, quantum field theory and string theory.

String theory is around 50 years old and for much of that time it has been proclaimed as a quantum theory of gravity unified with all forces and matter. However, we still don't know its fundamental formulation, although we do now know it is not just a theory of strings. Nonetheless, it has led to many new and surprising insights, with concepts that were once seen as absolute now seen as dependent on the “duality frame". In this talk I survey some of these insights and discuss their implications for physics and the fundamental formulation of string theory.

Strongly correlated electron systems, i.e. systems where the interaction between electrons cannot be treated as an effective potential, are an extremely fascinating, but also very challenging topic in modern solid state physics. The challenge arises in parts due to the simultaneous importance of non-local kinetic and local correlation effects, which make it important to treat both at equal footing. For this reason Dynamical Mean Field Theory (DMFT) has in the last decades become the state of the art method for electronic structure caluclations of strongly correlated electrons as it includes local correlation effects exactly, but also respects kinetic effects in terms of an embedding approach. In this talk, we will first motivate our interest in strongly correlated materials by giving an example regarding the fascinating properties that these materials can exhibit. This will be followed by an intuitive introduction to DMFT. Finally we present results from our DMFT studies of two strongly correlated systems: BaOsO3 [1] and tetragonal CuO (t-CuO) [2]. [1] MB, Jernej Mravlje, Martin Grundner, Ulrich Schollwoeck, and Manuel Zingl, Phys. Rev. B. 103, 165133 (2021) [2] MB, B. Bacq-Labreuil, M. Grundner, S. Biermann, U. Schollwoeck, S. Paeckel, and B. Lenz, SciPost Phys., 14, 010 (2023)

Electron-positron pair production in ultra-strong electric fields, the Sauter-Schwinger effect, is a long-standing theoretical prediction. In this talk the Sauter-Schwinger effect will be introduced and the related field-strength and energy scales as well as the possibility to verify this effect in upcoming multi-petawatt laser facilities will be discussed. The Dirac-Heisenberg-Wigner formalism provides a fully Poincaré-covariant, non-perturbative phase space description of the Sauter-Schwinger effect, and therefore its key quantities will be introduced. Some respective numerical results will be shown and discussed. An interpretation of a particle distribution at finite (non-asymptotic) times will be provided via a Gedankenexperiment. This in turn enables one to isolate and, therefore, identify the relevant time scales of particle formation. The resulting generic aspects for particle creation in quantum physics beyond perturbation theory will be elucidated.

The life of a protein, from birth till death, is complex and challenging. At times, because of stresses or bad luck, it might take the wrong conformation and start aggregating. This process is intrinsic to the physics of proteins, and life has had to cope with it since its early days. The solution devised by evolution comes in the form of chaperone protein, a broad class of machines, present in all organisms on Earth, that repair conformationally damaged proteins, making them functional again, at an energy cost. In this talk I will provide a view of our present understanding of the molecular mechanism of function of Hsp70, possibly the most central of all chaperones, and of its consequences on proteins.

We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory (RMT) to reveal their underlying structure. We focus on the feature-feature covariance matrix, analyzing both its local and global eigenvalue statistics. Our main observations are: (i) The power-law scalings that the bulk of its eigenvalues exhibit are vastly different for uncorrelated random data compared to real-world data, (ii) this scaling behavior can be completely recovered by introducing long range correlations in a simple way to the synthetic data, (iii) both generated and real-world datasets lie in the same universality class from the RMT perspective, as chaotic rather than integrable systems, (iv) the expected RMT statistical behavior already manifests for empirical covariance matrices at dataset sizes significantly smaller than those conventionally used for real-world training, and can be related to the number of samples required to approximate the population power-law scaling behavior, (v) the Shannon entropy is correlated with local RMT structure and eigenvalues scaling, and substantially smaller in strongly correlated datasets compared to uncorrelated synthetic data, and requires fewer samples to reach the distribution entropy. These findings can have numerous implications to the characterization of the complexity of data sets, including differentiating synthetically generated from natural data, quantifying noise, developing better data pruning methods and classifying effective learning models utilizing these scaling laws.

The Nobel Prize in Physics in 1930 was awarded to Raman for the discovery of the effect named after him. The next time physics prizes were announced was in November 1933, which makes this the longest peace-time gap in the history of the Nobel Prize in Physics. Considering that the 1932 year's prize was awarded in 1933 to Heisenberg and the 1933 year's prize to Schrödinger and Dirac for their contributions to the new quantum mechanics, this gap is the more puzzling. I will describe, based on archive material, the struggle facing the Nobel Committee during those years, and how it eventually arrived at a name combination comprising three of the greatest physicists of the twentieth century. I will also describe briefly the three Nobel Prizes concerning quantum mechanics that followed later, in 1945, 1954 and 2022.

Topology is one of the most recent branches of mathematics and has entered fully into the most modern aspects of theoretical physics: quantum computation. In this colloquium an elementary approach to the role of topology in quantum physics and its implications for exotic states of quantum matter is provided. Topology helps to solve the essential problem of quantum computation: to battle its fragility in order to benefit from its enormous potential possibilities. After showing topological color codes and their experimental realization, future challenges are addressed by fracton models involving the discovery of new quantum phases of matter beyond the well-known topological phases that were recognized with the Nobel Prize in Physics in 2016.

The bootstrap program leverages symmetry and positivity to carve out the space of consistent quantum theories. In this talk I will highlight some of its recent successes, ranging from the numerical solution of statistical models at criticality to universal constraints on quantum gravity.

The observation of metallic ground states in a variety of two-dimensional electronic systems poses a fundamental challenge for the theory of electron fluids. I will analyze evidence for the existence of a regime, which we call the “anomalous metal regime," in diverse 2D superconducting systems driven through a quantum superconductor to metal transition by tuning physical parameters such as the magnetic field, the gate voltage in the case of systems with a MOSFET geometry, or the degree of disorder. The principal phenomenological observation is that in the anomalous metal, as a function of decreasing temperature, the resistivity first drops as if the system were approaching a superconducting ground state, but then saturates at low temperatures to a value that can be orders of magnitude smaller than the Drude value. The anomalous metal also shows a giant positive magneto-resistance. This behavior is observed in a broad range of parameters. I will exhibit, by theoretical solution of a model of superconducting grains embedded in a metallic matrix, that as a matter of principle such anomalous metallic behavior can occur in the neighborhood of a quantum superconductor-metal transition. However, I will also argue that the robustness and ubiquitous nature of the observed phenomena are difficult to reconcile with any existing theoretical treatment and speculate about the character of a more fundamental theoretical framework.

The cells of our body are divided up into separate subcompartments by fluid membranes with a thickness of only a few nanometers. Even though these membranes provide robust barriers for the exchange of molecules between different compartments, they can easily remodel their shape and topology. [1] A particularly interesting example of shape remodeling is the formation of multispherical shapes which represent constant- mean-curvature surfaceswith two values of the mean curvature. [2] The individual spheres are connected by membrane necks which are crucial for topology remodeling by membrane fission and fusion. Multispherical shapes can attain many distinct patterns with multispherical junctions. The latter geometry is reminiscent of the endoplasmic reticulum, a fascinating organelle that forms a large network of membrane nanotubes connected by three-way junctions. [1] R. Lipowsky. Remodeling of Membrane Shape and Topology by Curvature Elasticity and Membrane Tension. Adv. Biology 6, 2101020 (2022) [2] R. Lipowsky. Multispherical shapes of vesicles highlight the curvature elasticityof biomembranes. Adv. Colloid Interface Sci. 301, 102613 (2022)

The (unique) maximally extended D=11 supermembrane theory stands out as a candidate for the non-perturbative unification of superstring theory. In this talk I will review some basic features, in particular the light-cone gauge reformulation of the theory as the N-->infty limit of the maximally supersymmetric SU(N) matrix model, and present new evidence for the existence of the N-->infty limit, using a path integral formulation. I will also touch on several open issues, such as the construction of supermembrane vertex operators.

Wetting of liquid phases, such as water drops condensing at the surface of plant leaves, is ubiquitous in our daily life. Interestingly, the physics of wetting also plays a crucial role in our cells. Droplets composed of proteins can wet specific target sites in living cells and locally enrich biomolecules for specific chemical processes. Many droplet-forming proteins can also bind to membrane surfaces. Binding in cells is often chemically active since it is maintained away from equilibrium by supplying energy and matter. This non-equilibrium setting suggests a plethora of physical phenomena of soft condensed phases at biological interfaces. To investigate such phenomena, we derive the non-equilibrium thermodynamic theory of active wetting. By means of this theory, we show that active binding significantly alters the wetting behavior leading to non-equilibrium steady states with condensate shapes reminiscent of a fried egg or a mushroom. We further show that condensate shapes can switch upon changing the strength of active binding. The origin of such anomalous condensate shapes can be explained by an electrostatic analogy, where binding sinks and sources correspond to electrostatic dipoles along the triple line. This analogy suggests a general analogy between chemically active systems and electrodynamics.

Understanding how fluctuations propagate across spatial scales is central to our understanding of inanimate matter from turbulence to critical phenomena. In contrast to these systems, many non-equilibrium systems are organised into a spatial hierarchy of nested processes on different spatial scales, including biological and robotic systems. In this talk, I will discuss physical principles underlying the propagation of fluctuations in these multi-scale systems. I will also show how manipulating probability fluxes across spatial scales is used to perform biological signal processing.

Living systems interact with their environment by exerting mechanical forces and exchanging chemical substances. By fueling nonequilibrium reactions and driven molecular transport, cells dynamically create internal protein patterns (symmetry breaking) which, in turn, control cell mechanics and force generation. Here, we discuss some examples and consequences of such a mechanochemical coupling, ranging from proteins that cooperatively bind and bend membranes, to protein patterns that elicit nonspecific cargo transport via driven diffusive fluxes on planar membranes. Finally, on much larger scales, we discuss how active cells can control tissue shape via their broken symmetry and, specifically, through their orientation.

The cosmic microwave background contains a wealth of information about cosmology as well as high energy physics. It tells us about the composition and geometry of the universe, the properties of neutrinos, dark matter, and even the conditions in our universe long before the cosmic microwave background was emitted. After a general introduction, I will turn to the search for primordial gravitational waves with CMB observations and gravitational wave observatories.

I will discuss the statistical physics of random growth processes which, on the one hand, model the non-perturbative gauge dynamics, emergence of space geometry in string theory on the other, yet could also model the evolution of language(s).

After a short introduction to the swampland program and the challenges one faces in explicit tests of some conjectures, this talk will focus on the computation of periods and their application to the swampland program. A detailed understanding of periods allows to answer questions about the existence of solutions or the finiteness of the string landscape, as well as explicit constructions of models. Moreover, applications of periods outside of string compactifications are discussed, such as the computation of Feynman integrals, the tameness of QFTs and the appearance of periods in many other physical systems.

Feynman integrals are indispensable for precision calculations, not only for high-energy particle physics experiments, but also for example for QED precision experiments at lower energies or precision studies in gravitational wave physics. In recent years there has been a significant progress in our abilities to compute Feynman integrals, revealing a rich and fascinating mathematical structure, relating Feynman integrals to (algebraic) geometry. In this talk I will review these recent developments.

The asymptotic structure of gravity in the asymptotically flat case will be described in four and higher spacetime dimensions by making central use of the Hamiltonian formalism. Special emphasis will be paid to the case D=5. How the relevant infinite-dimensional asymptotic symmetry group (BMS group) emerges at spatial infinity will be explained. Non-linear structures which appear in five (and higher) spacetime dimensions will be discussed.

Machine learning using artificial neural networks is revolutionizing many areas of science and technology. This increases the urgency for exploring alternatives to artificial neural networks running on digital hardware. These alternatives might eventually be faster and/or more power-efficient. With this in mind, we ask the question whether one can identify a general principle that would enable a nonlinear physical system to become a self-learning machine - i.e. a physical information-processing device where internal degrees of freedom self-adjust by physical interactions to learn a desired input-output relation. In this talk, I will present our recent idea on how this might be achieved for arbitrary time-reversal-invariant Hamiltonian systems. I will introduce the principle of 'Hamiltonian Echo Backpropagation', and demonstrate how efficient learning could be possible in a wide class of physical systems. See: Self-learning Machines based on Hamiltonian Echo Backpropagation, Victor Lopez-Pastor, Florian Marquardt, arXiv 2103.04992 (2021)

Sommerfeld Theory Colloquium

It has long been expected that the symmetry structure of quantum gravity is highly constrained. In particular it has been conjectured that global symmetries do not exist, and also that there must exist objects carrying all possible gauge charges. Until recently however there has been no systematic way of deriving such statements. In this talk I'll explain how these two conjectures can be derived in the special case of quantum gravity with negative cosmological constant, and also argue they are true more generally in any theory of quantum gravity where the evaporation of black holes is a unitary process. Along the way I'll clarify what is really meant by ``global'' and ``gauge'' symmetries, consider possible implications of these conjectures for particle physics, and present a new formula counting how many microstates of a black hole transform in each representation of a finite gauge group.

Sommerfeld Theory Colloquium

Sommerfeld Theory Colloquium

Sommerfeld Theory Colloquium

Sommerfeld Theory Colloquium

Sommerfeld Theory Colloquium

The question, whether a local, realistic theory can be a valid description of nature led to Bell's formulation of a clear cut experimental test. In spite of the many measurements performed and the numerous violation of Bell's inequality, all these tests relied on assumptions opening loopholes for local realistic theories. We present experiments which attempted to close as many as possible loopholes during the recent years, and what still might be left to do. In the experiment, as Bell's inequality limits preshared knowledge about possible measurement results, it can be used on the one hand to now confirm random numbers deduced from measurement results or the security of the devices used for quantum key distribution. On the other hand we can use the techniques developed for this experiment as the basic link for future quantum networks distributing entanglement efficiently over larger distances.

Quantum mechanical potentials with multiple classically degenerate minima lead to spectra that are determined by the pertaining tunneling amplitudes. For the strong interactions, these classical minima correspond to configurations of a given Chern-Simons number. The tunneling amplitudes are then given by instanton transitions, and the associated gauge invariant eigenstates are the theta-vacua. Under charge-parity (CP) reversal theta changes its sign, and so it is believed that CP-violating observables such as the electric dipole moment of the neutron or the decay of the eta-prime meson into two pions are proportional to theta. Here we argue that this is not the case. This conclusion is based on the assumption that the path integral is dominated by saddle points of finite action and fluctuations around these. In spacetimes of infinite volume, this leads to the requirement of vanishing physical fields at the boundaries. For the gauge fields, this implies topological quantization corresponding to homotopy classes for all integers. We consequently calculate quark correlations by first taking the spacetime volume to infinity and then summing over the sectors. This leads to an absence of CP violation in the quark correlations, in contrast to the conventional way of taking the limits the other way around. While there is an infinite number of homotopy classes in the strong interactions, there is only a finite number of classical vacua for quantum mechanical systems. For the latter the order of taking time to infinity and summing over the transitions is therefore immaterial.

The dynamics of the early universe and black holes are fundamental reflections of the interplay between general relativity and quantum fields. The essential physical processes occur in situations that are difficult to observe and impossible to experiment with: when gravitational interactions are strong, quantum effects are important, and theoretical predictions for these regimes are based on major extrapolations of laboratory-tested physics. We will discuss the possibility to study these processes in experiments by employing analogue classical/quantum simulators. Their high degree of tunability, in terms of dynamics, effective geometry, and field theoretical description, allows one to emulate a wide range of elusive physical phenomena in a controlled laboratory setting. We will discuss recent developments in this area of research.

I will first define the stochastic gravitational-wave background (SGWB) and highlight the method we are using to detect it in the presence of correlated magnetic noise. I will then discuss astrophysical (compact binary coalescences) and cosmological (cosmic strings, first-order phase transitions) sources and report on the current constraints imposed from a non-detection during the last observing run of the LIGO/Virgo/KAGRA collaboration. I will also address the question of a simultaneous estimation of astrophysical and cosmological SGWB. Then I will present a search for circularly polarised SGWB and its relation to early universe cosmology. Finally, I will discuss how the SGWB can provide tests for gravity theories, including quantum gravity proposals.

Topological phases were discovered in condensed matter physics and recently extended to classical physics such as topological mechanical metamaterials. Their study and realization in soft-matter and biological systems has only started to develop. In this talk we discuss how topological phases may determine the behavior of nonlinear dynamical systems that arise, for example, in population dynamics. We have shown that topological phases can be realized with the anti-symmetric Lotka-Volterra equation (ALVE). The ALVE is a paradigmatic model system in population dynamics and governs, for example, the evolutionary dynamics of zero-sum games, such as the rock-paper-scissors game [1], but also describes the condensation of non-interacting bosons in driven-dissipative set-ups [2]. We have shown that for the ALVE, defined on a one-dimensional chain of rock-paper-scissors cycles, robust polarization emerges at the chain’s edge [3]. The system undergoes a transition from left to right polarization as the control parameter passes through a critical value. At the critical point, solitary waves are observed. We found that the polarization states are topological phases and that this transition is indeed a topological phase transition. Remarkably, this phase transition falls into symmetry class D within the “ten-fold way” classification scheme of gapped free-fermion systems, which also applies, for example, to one-dimensional topological superconductors. Beyond the observation of topological phases in the ALVE, it might be possible to generalize the approach of our work to other dynamical systems in biological physics whose attractors are nonlinear oscillators or limit cycles. [1] J. Knebel, T. Krüger, M. F. Weber, and E. Frey, Phys. Rev. Lett. 110, 168106 (2013). [2] J. Knebel, M. F. Weber, T. Krüger, and E. Frey, Nature Communications 6, 6977 (2015). [3] J. Knebel, P. M. Geiger, and E. Frey, Phys. Rev. Lett. (in press) [arXiv:2009.01780].