Department of Physics • University of Cologne

No, we can’t. The time at which the growth in the number of infected individuals halts and starts decreasing cannot be calculated with certainty before the turning point is actually attained. This assertion is illustrated by adding to a standard SIR model a new class for confined individuals. A Bayesian fit to the on-going COVID-19 pandemic in Spain shows that a slow-down in the number of newly infected individuals during the expansion phase allows to infer neither the precise position of the maximum nor whether the measures taken will bring the propagation to the inhibition regime. Our study warns against precise forecasts of the evolution of epidemics based on mean-field, effective models, and supports that only probabilities of different outcomes can be confidently given.

Systems consisting of a large number of interacting bosons or fermions in two dimensions can in some situations form anyonic quasiparticles that are neither bosons, nor fermions. Such systems are topologically ordered, and they have many special properties. They are, for instance, not characterized by a local order parameter, which makes it challenging to detect the phases. Here, we demonstrate that anyons are an interesting tool to detect topological order in new types of systems and to detect phase transitions involving topological phases. The phase transitions are detected based on the idea that the system does not support the same types of quasiparticles on the two sides of the transition. We test the method on three rather different examples, and in all cases we find that it is sufficient to study a simple property of the anyons, requiring low numerical costs, to accurately detect the phase transition point. A further advantage of the method is that it does not require particular boundary conditions, and we utilize this to demonstrate that topological order can also occur in fractal dimensions and on quasicrystals. References: arXiv:1909.02046, arXiv:1907.03193, PRB 101, 115413 (2020).