Statistics are an important tool in many fields of physics. They can not only be found in calculations regarding huge ensembles of particles (e.g. gases) but also describing random movements of small objects in more microscopic invironments (e.g. diffusion). Methods like mean square displacement or autocorrelation functions help us to better understand the nature of such random movements. In order to focus on objects of interest, the human eye exhibits fixational eye movments (FEMs) with sub- and superdiffusive movement patterns. These can be described via self avoiding walk simulations to provide a better understanding of their origin.
Literature: Carl J.J. Herrmann et al., "A self-avoiding walk with neural delays as a model of fixational eye movements", Sci. Rep. 7, 12958 (2017).

The climate change and fake news on its scientific background are among the biggest problems humanity faces in the beginning of the 21st century. In this talk the contribution of CO₂ to the natural greenhouse effect and the direct warming by doubling the atmospheric CO₂ concentration (without taking feedbacks into account) will be estimated based on physical laws and basic mathematics.
Literature: Derrek J. Wilson and Julio Gea-Banacloche, "Simple model to estimate the contribution of atmospheric CO₂ to the Earth's greenhouse effect", Am. J. Phys. 80, 306 (2012).

When disturbing a thermally equilibrated system in an irreversible way, the second law of thermodynamics is usually expressed as an inequality. The difference of free energy before and after the disturbance will remain smaller than the average work necessary to create the disturbance. Hence, the Jarzynski equality may provide a surprise by introducing an equal sign relating simple functions of free energy differences and nonequilibrium work amounts. Its validity and scaling constraints are illustrated by deriving from the equality two findings of Einstein: first, the relation between diffusion coefficient, temperature, and drag coefficient in Brownian motion, and second, the necessity for stimulated emission in light-absorbing two-state systems.
Literature: F. Gittes, "Two famous results of Einstein derived from the Jarzynski equality", Am. J. Phys. 86(1), 31–35 (2018).

The thermodynamics of a hurricane is presented in comparison of that of a normal steam engine. The paper states a hurricane has "super-Carnot" efficiency and this is consistent with the 2nd law of thermodynamics. How this is (or is not) possible will be calculated and discussed.
Literature: Jack Denur, "The apparent 'super-Carnot' efficiency of hurricanes: Nature's steam engine versus the steam locomotive", Am. J. Phys. 79(6), 631–43 (2010).

In 1935, eight years after the Copenhagen interpretation (1927) A. Einstein, B. Podolski and N. Rosen published a paper where they showed that the quantum mechanical description of physical reality is not complete. That conclusion rested on the seemingly reasonable assumptions of locality and realism. Almost thirty years later, in 1964, Bell showed theoretically that quantum mechanics cannot be real and local at the same time, so that one of the assumptions must be wrong. Only eight years later, the first Bell inequality ever tested was the simple version derived by S. Freedman. By using the Freedman's inequality, students can contradict the philosophical assumption of local realism in correlated photon experiments.
Literature: J. Brody and C. Selton, "Quantum entanglement with Freedman's inequality", Am. J. Phys. 86, 412–16 (2018).

Usually stochastic trajectories are studied in terms of their mean squared displacements. An alternative evaluation is based on the power spectral density (PSD). The paper analyzes what information on the PSD can be extracted from a single trajectory for a finite observation time. The authors have mathematically proven that the scaling exponent for the frequency-dependence of the ensemble-averaged PSD can be already obtained from a single trajectory for continuous-time Brownian motion. The distribution of its amplitude is calculated exactly identifying the appropriate frequency window. They show that the diffusion coefficient can be extracted by averaging over a small number of trajectories. These analytical results are verified by numerical simulations and experiments.
Literature: Diego Krapf et al., "Power spectral density of a single Brownian trajectory: what one can and cannot learn from it", New J. Phys. 20, 023029 (2018).

In 2015, the LIGO and VIRGO detectors observed for the first time gravitational waves emitted by two merging black holes. Einstein predicted the existence of gravitational waves using his theory of general relativity, but other suggestions had been made before. In the paper, the properties of gravitational waves emitted by orbiting binary objects are calculated using analogies with electromagnetic radiation, as a physicist might have done prior to 1915. The calculations are using Newtonian mechanics, electromagnetic theory and the technique of retarded time. The results will be compared with the observed signal.
Literatur: R. C. Hilborn, "Gravitational waves from orbiting binaries without general relativity", Am. J. Phys. 86(3), 186 (2018).

One of the most powerful methods in physics is based on symmetries and groups. The analysis of the symmetry group of the Hamilton operator often predicts the physical behavior of the system. When this symmetry is violated, the dynamics of the system change and a (quantum) anomaly occurs. We analyse a two-dimensional gas in a harmonic potential with a delta-function interaction potential. In classical and in quantum mechanics, such a trapped gas shows a collective oscillation, a so-called "breathing mode" at exactly twice the trap frequency. This is justified by an underlying symmetry group isomorphic to the two-dimensional Lorentz group SO(2,1). The careful further study of the particle interaction requires a regularization that breaks the scale invariance of the Hamilton operator. This shifts the breathing frequency by about one percent, indicating a quantum anomaly.
Literatur: L. P. Pitaevskii and A. Rosch, "Breathing modes and hidden symmetry of trapped atoms in two dimensions", Phys. Rev. A 55, R853 (1997); M. Olshanii, H. Perrin and V. Lorent, "Example of a Quantum Anomaly in the Physics of Ultracold Gases", Phys. Rev. Lett. 105, 095302 (2010).

The study of nonlinear dynamics has blossomed in the past few decades and it has been developed and used extensively, with many different applications. In this talk the basic concepts of the theory of nonlinear dynamical systems will be presented, starting from the definition of an ordinary differential equation/dynamical system and the linearization about a fixed point, ending with the definition of chaos. Apart from the mathematical theory behind the topic, I will also emphasize the possibility of application of this theory through different examples.
Literature: Steven H. Strogratz, "Nonlinear dynamics and chaos", Perseus (1985). J. C. Sprott, "Simple models of complex chaotic systems", Am. J. Phys. 76, 474 (2008)

According to Quantum field Theory (QFT), empty space is not really empty and contains zero-point fluctuations. This results in a large energy density for the vacuum which should have gravitational effects. By using Quantum theory, I will discuss this issue for the electromagnetic field and also briefly for other fields. In addition, one of the important manifestations of vacuum energy will be shown, the Casimir effect which demonstrates that the energy density of the vacuum is real. At the end, by using classical gravitational theory and also observations, I will estimate an upper limit of the energy density in the Universe which is less than predicted from QFT by 120 orders of magnitude.
Literatur: Ronald J. Adler, Brenden Casey, and Ovid C. Jacob, "Vacuume catastrophe: an elementary exposition of the cosmological constant problem", American Journal of Physics, 63(7), 620-26 (1995).

The rings of Saturn were first observed in 1655. They are separated by gaps the largest of which is called the Cassini Division. It is thought they originate from the disintegration of moons of Saturn, perhaps by scattering with comets or asteroids. In this talk, a non-linear diffusion model for gaps in planetary rings is developed. By looking at the gravitational scattering of the ring particles and an embedded moon, the density profile around the moon is examined. The models are applied to the gaps of the moons Pan and Daphnis which are located in the outer A ring of Saturn.
Literatur: F. Grätz, M. Seiß & F. Spahn, "Formation of Moon-induced Gaps in Dense Planetary Rings: Application to the Rings of Saturn", The Astrophysical Journal, 862(2), 157 (2018).

General relativity is a very important field for understanding how the universe works on a fundamental level. Simplified models (such as nonlinear Newtonian gravity) are often used in courses and textbooks to make it conceptually easier to grasp and less computationally intensive, even though they are ultimately flawed. The goal of this talk is to present an example of such a simplified model in action. Using a nonlinear version of Newtonian gravity that allows for black holes to exist, upper limits are derived on how much a black hole can be charged via bombardment by high- or low-energy charged particles. The result is then compared to the one obtained using general relativity, and the differences are reflected upon.
Literature: Michael R. R. Good, "On a nonlinear Newtonian gravity and charging a black hole", Am. J. Phys. 86(6), 453-59 (2018).

Nanofabricated Hyperbolic Media give rise to interesting new physics because of their unique way of interacting with light. For example, having a hyperbolic dispersion relation they offer an increased amount of decay channels compared to the vacuum for emitters in their immediate environment, effectively increasing its rate of emission. This effect is called the Purcell Effect. In this lecture I will give an overview about the theory of metamaterials and their properties and applications. Also I will show how Fermi's Golden Rule can be used to understand how the engineering of the density of states can produce enhanced photon sources that emit in a highly directional fashion.
Literature: Zubin Jacob, Igor I. Smolyaninov, Evgenii E. Narimanov, "Broadband Purcell effect: Radiative decay engineering with metamaterials", Appl. Phys. Lett. 100, 181105 (2012).

The laws of Quantum Mechanics (QM) allow for correlations between particles that have no equivalent in the classical world. Experiments based on spatially separated particles seem to predict "spooky actions at a distance". Bell's theorem give a precise limit between predictions from a Classical Mechanics and that from QM, stating that "The predictions of QM cannot be reproduced by any locally causal realistic description". The assumption that causality and QM hold both true simultaneously leads to contradictions with Relativity. An attempt is made to relieve the tension between QM, causality and Relativity by considering the implications of a retro-causal toy model, which appears to violate causality in the "past", rather than "at a distance".
Literature: N. Argaman, "Bell's theorem and the causal arrow of time," Am. J. Phys. 78, 1007-13 (2010).

Die Physik kann man in verschiedene Gebiete aufteilen, darin ist die Gravitation eine der vier Wechselwirkungen, die sich mit der Anziehung zwischen Massen beschäftigt. Durch das Quantisieren wurde aus der klassischen Physik die Quantenphysik, mit deren Hilfe verschiedene Effekte korrekt beschrieben oder vorhergesagt werden können (Energieniveaus von Atomen, Welle-Teilchen-Dualismus). Eine Verbindung zwischen Quantenphysik und Gravitationstheorie ist erstrebenswert, aber bislang noch Gegenstand der Forschung. M. Bronstein hat bereits im Jahr 1936 die Einstein'sche Gravitationstheorie für schwache Felder quantisiert. Im Vortrag diskutieren wir ein paar Formeln und stellen ein Gedankenexperiment vor, das sich mit der Messung von Gravitationsfeldern beschäftigt. Zum Schluss bringen wir eine "Quanten-Herleitung" des Newtonschen Gravitationsgesetzes.
Matvei Bronstein, "Quantentheorie Schwacher Gravitationsfelder", Physikalische Zeitschrift d. Sowjetunion 9, 140-57 (1936)