Large Fluctuations in Anti-Coordination Games on Scale-Free Graphs

We study the influence of the complex topology of scale-free graphs on the dynamics of anti-coordination games (e.g. snowdrift games). These reference models are characterized by the coexistence (evolutionary stable mixed strategy) of two competing species, say 'cooperators' and 'defectors', and, in finite systems, by metastability and large-fluctuation-driven fixation. In this work, we use extensive computer simulations and an effective diffusion approximation (in the weak selection limit) to determine under which circumstances, depending on the individual-based update rules, the topology drastically affects the long-time behavior of anti-coordination games. In particular, we compute the variance of the number of cooperators in the metastable state and the mean fixation time when the dynamics is implemented according to the voter model (death-first/birth-second process) and the link dynamics (birth/death or death/birth at random). For the voter update rule, we show that the scale-free topology effectively renormalizes the population size and as a result the statistics of observables depend on the network's degree distribution. In contrast, such a renormalization does not occur with the link dynamics update rule and we recover the same behavior as on complete graphs

Hawking fragmentation and Hawking attenuation in Weyl semimetals

We study black and white hole analogues in Weyl semimetals with inhomogenous nodal tilts. We study how the presence of a microscopic lattice, giving rise to low-energy fermion doubler states at large momenta that are not present for elementary particles, affects the analogy between Weyl Hamiltonians and general relativity. Using a microscopic tight-binding lattice model, we find the doubler states to give rise to Hawking fragmentation and Hawking attenuation of wavepackets by the analogue event horizon. These phenomena depend on an analogue Hawking temperature, and can be measured in metamaterials and solids, as we confirm by numerical simulations.Comment: 12 pages, 6 figure

Bending strain in 3D topological semi-metals

Abstract We present an experimental set-up for the controlled application of strain gradients by mechanical piezoactuation on 3D crystalline microcantilevers that were fabricated by focused ion beam machining. A simple sample design tailored for transport characterization under strain at cryogenic temperatures is proposed. The topological semi-metal Cd3As2 serves as a test bed for the method, and we report extreme strain gradients of up to 1.3 %   μ m−1 at a surface strain value of ≈ 0.65 % at 4 K. Interestingly, the unchanged quantum transport of the cantilever suggests that the bending cycle does not induce defects via plastic deformation. This approach is a first step towards realizing transport phenomena based on structural gradients, such as artificial gauge fields in topological materials.</jats:p