Sommerfeld Theory Colloquium (ASC)

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].

Many particle physics theories beyond the Standard Model (BSM) admit topologically stable cosmic string solutions. If Nature is described by such a theory, a network of strings will form in the early universe and persist to the present time. The strings carry energy and hence lead to characteristic signatures in many observational windows. Searching for signals of strings in the sky can lead to new constraints on BSM models. Conversely, cosmic strings may also help solve some current mysteries in astrophysics, e.g. the origin of super-massive black holes.

Particle physics is at the crossroads. The last particle firmly predicted by the Standard Model (SM) has been discovered. In recent years many of its interactions with other known particles have been experimentally studied, again confirming the SM's predictions in large detail. However, despite this impressive success, we are sure that the SM is incomplete. The Standard Model can not explain dark matter, neutrino masses, and matter-antimatter asymmetry of the Universe, and we do know what particles are responsible for these phenomena — their masses, interaction strength, life time etc. I will discuss how the synergy with Cosmology and Astrophysics can help to limit these uncertainties and discuss several concrete examples which can drastically change the situation in particle physics in the next 5-7 years.

Type Ia supernovae are standard (isable) candles so observing them out to cosmological distances reveals the change of the Hubble parameter with redshift. Such observations have been interpreted to mean that the expansion rate of the universe is accelerating, as if driven by a Cosmological Constant. However reanalysis of the data shows that the inferred cosmic acceleration is anisotropic and aligned with the CMB dipole - so is likely an artefact due to our being untypical observers embedded in a local non-Hubble `bulk flow’. Moreover the usual kinematic interpretation of the CMB dipole is rejected at 4.9 sigma as the corresponding dipole in the distribution of distant quasars is much bigger than expected. The implications of these surprising findings will be discussed.