Institute for Technical Physics and Materials Science

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation $(\ensuremath{\eta})$ added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $|{\mathbf{v}}_{a}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous, since $|{\mathbf{v}}_{a}|$ is found to scale as $({\ensuremath{\eta}}_{c}\ensuremath{-}\ensuremath{\eta}{)}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}\ensuremath{\simeq}0.45$.

Abstract The Fermi gas model of one-dimensional conductors is reviewed. The exact solutions known for particular values of the coupling constants in a single chain problem (Tomonaga model, Luther-Emery model) are discussed. Renormalization group arguments are used to extend these solutions to arbitrary values of the couplings. The instabilities and possible ground states are studied by investigating the behaviour of the response functions. The relationship between this model and others is discussed and is used to obtain further information about the behaviour of the system. The model is generalized to a set of coupled chains to describe quasi-one-dimensional systems. The crossover from one-dimensional to three-dimensional behaviour and the type of ordering are discussed.

Atomic-scale control and manipulation of the microstructure of polycrystalline thin films during kinetically limited low-temperature deposition, crucial for a broad range of industrial applications, has been a leading goal of materials science during the past decades. Here, we review the present understanding of film growth processes—nucleation, coalescence, competitive grain growth, and recrystallization—and their role in microstructural evolution as a function of deposition variables including temperature, the presence of reactive species, and the use of low-energy ion irradiation during growth.

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate $(C)$ or to defect $(D)$ unconditionally. The players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques, we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect. In the limits $\stackrel{\ensuremath{\rightarrow}}{c}0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.

This paper adopts the hypothesis that the absence of macroscopic quantum fluctuations is due to a certain universal mechanism. Such a mechanism has recently been proposed by Ghirardi et al. [Phys. Rev. D 34, 470 (1986)], and here we recapitulate a compact version of it. K\'arolyh\'azy [Nuovo Cimento 52, 390 (1966)] showed earlier the possible role of gravity and, along this line, we construct here a new parameter-free unification of micro- and macrodynamics. We apply gravitational measures for reducing macroscopic quantum fluctuations of the mass density. This model leads to classical trajectories in the macroscopic limit of translational motion. For massive objects, unwanted macroscopic superpositions of quantum states become destroyed in very short times. The relation between state-vector and density-operator formalisms has also been discussed. We only anticipate the need for elaborating characteristic predictions of the model in the region separating micro- and macroscopic properties.

This article reviews our present knowledge of universality classes in nonequilibrium systems defined on regular lattices. The first section presents the most important critical exponents and relations, as well as the field-theoretical formalism used in the text. The second section briefly addresses the question of scaling behavior at first-order phase transitions. In Sec. III the author looks at dynamical extensions of basic static classes, showing the effects of mixing dynamics and of percolation. The main body of the review begins in Sec. IV, where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. Section V considers such nonequilibrium classes in coupled, multicomponent systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion-type systems. However, by mapping they can be related to the universal behavior of interface growth models, which are treated in Sec. VI. The review ends with a summary of the classes of absorbing-state and mean-field systems and discusses some possible directions for future research.

Abstract Our aim is to present further evidence supporting a recent suggestion by Anderson (1973) that the ground state of the triangular antiferromagnet is different from the conventional three-sublattice Néel state. The anisotropic Heisenberg model is investigated. Near the Ising limit a peculiar, possibly liquid-like state is found to be energetically more favourable than the Néel-state. It seems to be probable that this type of ground state prevails in the anisotropy region between the Ising model and the isotropic Heisenberg model. The implications for the applicability of the resonating valence bond picture to the S = ½ antiferromagnets are also discussed.

The diversity in wealth and social status is present not only among humans, but throughout the animal world. We account for this observation by generating random variables that determine the social diversity of players engaging in the prisoner's dilemma game. Here the term social diversity is used to address extrinsic factors that determine the mapping of game payoffs to individual fitness. These factors may increase or decrease the fitness of a player depending on its location on the spatial grid. We consider different distributions of extrinsic factors that determine the social diversity of players, and find that the power-law distribution enables the best promotion of cooperation. The facilitation of the cooperative strategy relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to prevail against the defectors even when there is a large temptation to defect. To confirm this, we also study the impact of spatially correlated social diversity and find that cooperation deteriorates as the spatial correlation length increases. Our results suggest that the distribution of wealth and social status might have played a crucial role by the evolution of cooperation amongst egoistic individuals.

We present a simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation in public goods games. This natural extension leads to "rock-scissors-paper"-type cyclic dominance of the three strategies, cooperate, defect, and loner. In spatial settings with players arranged on a regular lattice, this results in interesting dynamical properties and intriguing spatiotemporal patterns. In particular, variations of the value of the public good leads to transitions between one-, two-, and three-strategy states which either are in the class of directed percolation or show interesting analogies to Ising-type models. Although volunteering is incapable of stabilizing cooperation, it efficiently prevents successful spreading of selfish behavior.

The promise of punishment and reward in promoting public cooperation is debatable. While punishment is traditionally considered more successful than reward, the fact that the cost of punishment frequently fails to offset gains from enhanced cooperation has lead some to reconsider reward as the main catalyst behind collaborative efforts. Here we elaborate on the "stick versus carrot" dilemma by studying the evolution of cooperation in the spatial public goods game, where besides the traditional cooperators and defectors, rewarding cooperators supplement the array of possible strategies. The latter are willing to reward cooperative actions at a personal cost, thus effectively downgrading pure cooperators to second-order free-riders due to their unwillingness to bear these additional costs. Consequently, we find that defection remains viable, especially if the rewarding is costly. Rewards, however, can promote cooperation, especially if the synergetic effects of cooperation are low. Surprisingly, moderate rewards may promote cooperation better than high rewards, which is due to the spontaneous emergence of cyclic dominance between the three strategies.

The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner's dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive. Using Monte Carlo simulations and the generalized mean-field approximations we have determined the phase boundaries (critical points) separating the two phases on the plane of the temperature (noise) and temptation to choose defection. In the zero temperature limit the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs.

Evolutionary game theory is designed to capture the essentials of the characteristic interactions among individuals. Its most prominent application is the quest for the origins and evolution of cooperation. The effects of population structures on the performance of behavioral strategies became apparent only in recent years and marks the advent of an intriguing link between apparently unrelated disciplines. Evolutionary game theory in structured populations reveals critical phase transitions that fall into the universality class of directed percolation on square lattices and mean-field-type transitions on regular small world networks and random regular graphs. We employ the prisoner’s dilemma to discuss new insights gained in behavioral ecology using methods from physics.

We study the evolution of cooperation in public goods games on different regular graphs as a function of the noise level underlying strategy adoptions. We focus on the effects that are brought about by different group sizes of public goods games in which individuals participate, revealing that larger groups of players may induce qualitatively different behavior when approaching the deterministic limit of strategy adoption. While by pairwise interactions an intermediate uncertainty by strategy adoptions may ensure optimal conditions for the survival of cooperators at a specific graph topology, larger groups warrant this only in the vicinity of the deterministic limit independently from the underlying graph. These discrepancies are attributed to the indirect linkage of otherwise not directly connected players, which is brought about by joint memberships within the larger groups. Thus, we show that increasing the group size may introduce an effective transition of the interaction topology, and that the latter shapes the noise dependence of the evolution of cooperation in case of pairwise interactions only.

Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of the two pure strategies (cooperation or defection) are distributed on a two-dimensional lattice. The rate of strategy adoption from a randomly chosen neighbors are controlled by the payoff difference and a two-value pre-factor $w$ characterizing the players whom the strategy learned from. The reduced teaching activity of players is distributed randomly with concentrations $\nu$ at the beginning and fixed further on. Numerical and analytical calculations are performed to study the concentration of cooperators as a function of $w$ and $\nu$ for different noise levels and connectivity structures. Significant increase of cooperation is found within a wide range of parameters for this dynamics. The results highlight the importance of asymmetry characterizing the exchange of master-follower role during the strategy adoptions.

The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool punishers as the three competing strategies. Fines and costs of pool punishment are considered as the two main parameters determining the stationary distributions of strategies on the square lattice. Each player collects a payoff from five five-person public goods games, and the evolution of strategies is subsequently governed by imitation based on pairwise comparisons at a low level of noise. The impact of pool punishment on the evolution of cooperation in structured populations is significantly different from that reported previously for peer punishment. Representative phase diagrams reveal remarkably rich behavior, depending also on the value of the synergy factor that characterizes the efficiency of investments payed into the common pool. Besides traditional single- and two-strategy stationary states, a rock-paper-scissors type of cyclic dominance can emerge in strikingly different ways.

We study the evolution of cooperation in spatial public goods games where, besides the classical strategies of cooperation (C) and defection (D), we consider punishing cooperators (PC) or punishing defectors (PD) as an additional strategy. Using a minimalist modeling approach, our goal is to separately clarify and identify the consequences of the two punishing strategies. Since punishment is costly, punishing strategies loose the evolutionary competition in case of well-mixed interactions. When spatial interactions are taken into account, however, the outcome can be strikingly different, and cooperation may spread. The underlying mechanism depends on the character of the punishment strategy. In case of cooperating punishers, increasing the fine results in a rising cooperation level. In contrast, in the presence of the PD strategy, the phase diagram exhibits a reentrant transition as the fine is increased. Accordingly, the level of cooperation shows a non-monotonous dependence on the fine. Remarkably, punishing strategies can spread in both cases, but based on largely different mechanisms, which depend on the cooperativeness (or not) of punishers.

Situations where individuals have to contribute to joint efforts or share scarce resources are ubiquitous. Yet, without proper mechanisms to ensure cooperation, the evolutionary pressure to maximize individual success tends to create a tragedy of the commons (such as over-fishing or the destruction of our environment). This contribution addresses a number of related puzzles of human behavior with an evolutionary game theoretical approach as it has been successfully used to explain the behavior of other biological species many times, from bacteria to vertebrates. Our agent-based model distinguishes individuals applying four different behavioral strategies: non-cooperative individuals ("defectors"), cooperative individuals abstaining from punishment efforts (called "cooperators" or "second-order free-riders"), cooperators who punish non-cooperative behavior ("moralists"), and defectors, who punish other defectors despite being non-cooperative themselves ("immoralists"). By considering spatial interactions with neighboring individuals, our model reveals several interesting effects: First, moralists can fully eliminate cooperators. This spreading of punishing behavior requires a segregation of behavioral strategies and solves the "second-order free-rider problem". Second, the system behavior changes its character significantly even after very long times ("who laughs last laughs best effect"). Third, the presence of a number of defectors can largely accelerate the victory of moralists over non-punishing cooperators. Fourth, in order to succeed, moralists may profit from immoralists in a way that appears like an "unholy collaboration". Our findings suggest that the consideration of punishment strategies allows one to understand the establishment and spreading of "moral behavior" by means of game-theoretical concepts. This demonstrates that quantitative biological modeling approaches are powerful even in domains that have been addressed with non-mathematical concepts so far. The complex dynamics of certain social behaviors become understandable as the result of an evolutionary competition between different behavioral strategies.

We suggest that the polar heliospheric magnetic field, at large heliocentric distances, may deviate considerably from the generally accepted Archimedean spiral. Instead, we suggest that the large‐scale field near the poles may be dominated by randomly‐oriented transverse magnetic fields with magnitude much larger than the average spiral. The average vector field is still the spiral, but the average magnitude may be much larger. In addition, the field direction is transverse to the radial direction most of the time instead of being nearly radial. This magnetic‐field structure has important consequences for the transport of cosmic rays. Preliminary model calculations suggest changes in the radial gradient of galactic cosmic rays which may improve agreement with observations.

A comprehensive study by high-resolution transmission electron microscopy (TEM) and X-ray diffraction (XRD) was carried out on Ga2O3 epilayers grown at low temperature (650 °C) by vapor phase epitaxy in order to investigate the real structure at the nanoscale. Initial XRD measurements showed that the films were of the so-called ε phase; i.e. they exhibited hexagonal P63mc space group symmetry, characterized by disordered and partial occupation of the Ga sites. This work clarifies the crystal structure of Ga2O3 layers deposited at low temperature at the nanoscale: TEM investigation demonstrates that the Ga atoms and vacancies are not randomly distributed, but actually possess ordering, with (110)-twinned domains of 5–10 nm size. Each domain has orthorhombic structure with Pna21 space group symmetry, referred to as κ-Ga2O3. Further XRD analysis carried out on thicker samples (9–10 μm) confirmed this finding and provided refined structural parameters. The six (110)-type twinned ordered domains together – if the domain size falls below the actual resolution of the probing techniques – can be misinterpreted as the disordered structure with its P63mc space group symmetry usually referred to as ε-Ga2O3 in the current literature. The crystal structure of these Ga2O3 layers consists of an ABAC oxygen close-packed stacking, where Ga atoms occupy octahedral and tetrahedral sites in between, forming two types of polyhedral layers parallel to (001). The edge-sharing octahedra and the corner-sharing tetrahedra form zig-zag ribbons along the [100] direction. Anti-phase boundaries are common inside the domains. The polar character of the structure is confirmed, in agreement with the characteristics of the Pna21 space group and previous observations.

Abstract. Evolutionary games are studied where the teaching activity of players can evolve in time. Initially all players following either the cooperative or defecting strategy are distributed on a square lattice. The rate of strategy adoption is determined by the payoff difference and a teaching activity characterizing the donor’s capability to enforce its strategy on the opponent. Each successful strategy adoption process is accompanied with an increase in the donor’s teaching activity. By applying an optimum value of the increment this simple mechanism spontaneously creates relevant inhomogeneities in the teaching activities that support the maintenance of cooperation for both the prisoner’s dilemma and the snowdrift game. PACS numbers: 02.50.Le, 87.23.Ge, 89.75.FbCoevolution of teaching activity promotes cooperation 2 1.