Congestion phenomena caused by matching pennies in evolutionary games

Evolutionary social dilemma games are extended by an additional matching-pennies game that modifies the collected payoffs. In a spatial version players are distributed on a square lattice and interact with their neighbors. Firstly, we show that the matching-pennies game can be considered as the microscopic force of the Red Queen effect that breaks the detailed balance and induces eddies in the microscopic probability currents if the strategy update is analogous to the Glauber dynamics for the kinetic Ising models. The resulting loops in probability current breaks symmetry between the chessboard-like arrangements of strategies via a bottleneck effect occurring along the four-edge loops in the microscopic states. The impact of this congestion is analogous to the application of a staggered magnetic field in the Ising model, that is, the order-disorder critical transition is wiped out by noise. It is illustrated that the congestion induced symmetry breaking can be beneficial for the whole community within a certain region of parameters.Comment: 7 pages, 6 figure

Diverging fluctuations in a spatial five-species cyclic dominance game

A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is governed by site exchange and invasion between the neighboring predator-prey pairs, where the cyclic symmetry can be characterized by two different invasion rates. The mean-field analysis has indicated periodic oscillations in the species densities with a frequency becoming zero for a specific ratio of invasion rates. When varying the ratio of invasion rates, the appearance of this zero-eigenvalue mode is accompanied by neutrality between the species associations. Monte Carlo simulations of the spatial system reveal diverging fluctuations at a specific invasion rate, which can be related to the vanishing dominance between all pairs of species associations.Comment: accepted for publication in Physical Review

Being in a new community possibilities for refugees to become actors of the political community in Hungary and the United Kingdom

The paper compares the possibilities of refugees and beneficiaries of subsidiary protection toward their political integration in two countries, Hungary and the United Kingdom. The aim of this comparison is not judge which country is better in this sense but to present and explain a few relevant dimensions of the political integration of refugees and beneficiaries of subsidiary protection. The scrutinized dimensions are the fundamental right of being recognized as a refugee; the right to stay, including legal residency, social support, education, right for employment and right to vote; the right to the free movement furthermore direct political rights as the right to vote; the freedom of expression; the freedom of association and the freedom of assembly and finally possibilities for preferential naturalization. Obviously, there is no possibility to analyse and evaluate the whole integration process but at least, its legal dimensions are presented in the paper. In the conclusion, the author will make a few suggestions what should be considered when thinking about these questions

Mocking quantum mechanics: Semiclassical and machine-learning approaches to frustrated magnetism

Many-body quantum mechanics is the fundamental theory behind many areas of modern science, such as condensed-matter physics, nuclear physics, and quantum chemistry. It is also notoriously hard: the classical picture of particles with well-defined positions and velocities is replaced by an intricate interference pattern between all their possible trajectories, captured by the quantum wave function. The exponentially large information content of wave functions makes direct simulation of large, strongly interacting quantum systems impossible, and necessitates strategies to manage the complexity in an analytically or computationally tractable manner. The bulk of this thesis explores two such strategies in the context of quantum spin liquids. In these materials, competition between incompatible interactions results in robust, massive entanglement, down to zero temperature. Such ground states give rise to a range of exotic behaviour, such as topological order and fractionalised excitations: understanding these is a central challenge in the physics of strongly correlated materials. Several quantum-spin-liquid phases are underpinned by strict local conservation laws, which give rise to lattice gauge theories with exotic quasiparticle excitations, such as emergent photons or magnetic monopoles. We developed a systematic approach, based on a large-S bosonisation formalism, to extract gauge-theoretic descriptions from such constrained Hamiltonians automatically, and thus make them amenable to the powerful techniques of quantum field theory. The same field theories also allow us to simulate quantum-spin-liquid systems semiclassically, that is, to replace spin-1/2 operators with classical ``compass needles,'' removing the computational complexity of quantum entanglement without losing the physical behaviour. We demonstrated this approach on quantum spin ice, a paradigmatic and experimentally relevant model of quantum spin liquids and, by simulating it on unprecedented large system sizes, obtained novel insights about its quasiparticles. The success of neural networks in a range of machine-learning problems makes them a natural candidate for representing highly entangled quantum states, allowing in principle an accurate simulation of large, challenging quantum systems with modest computational resources. However, most current approaches using such neural quantum states suffer from the infamous Monte-Carlo sign problem, making deep neural networks unable to learn ground states in antiferromagnetic and fermionic systems. We studied the possible origins of this sign problem and proposed a neural-network ansatz that is able to overcome the sign problem for unfrustrated antiferromagnets. In addition to this main theme, I have been part of an experiment--theory collaboration on understanding the unique magnetoresistance properties of the classical frustrated magnet Ho2Ir2O7. We discovered a mechanism by which antiferromagnetic domains can be coupled to an external magnetic field via an intercalated spin-ice system: such control is highly desirable for spintronics applications. We have also identified scattering channels through which magnetic monopoles give rise to a significant contribution to the resistivity of Ho2Ir2O7: this allows us to directly measure their density in a simple and flexible experiment. Finally, I report studies on the localisation properties of quasicrystals; namely, the discovery of thermodynamic universality not described by the usual power laws in one-dimensional quasiperiodic models, and of a two-dimensional quasicrystal in which localised and partially extended states coexist without a mobility edge.Vice Chancellor's Award, University of Cambridg