Silvio R. Dahmen

Yang–Lee zeros for a nonequilibrium phase transition

Equilibrium systems which exhibit a phase transition can be studied by investigating the complex zeros of the partition function. This method, pioneered by Yang and Lee, has been widely used in equilibrium statistical physics. We show that an analogous treatment is possible for a nonequilibrium phase transition into an absorbing state. By investigating the complex zeros of the survival probability of directed percolation processes we demonstrate that the zeros provide information about universal properties. Moreover we identify certain nontrivial points where the survival probability for bond percolation can be computed exactly.

Similarity in the statistics of prime numbers

We present numerical evidence for regularities in the distribution of gaps between primes when these are divided into congruence families (in Dirichlets classification). The histograms for the distribution of gaps of families are scale invariant.

Quantum phase transitions in an interacting atom-molecule boson model

We study the quantum phase transitions of a model that describes the interconversion of interacting bosonic atoms and molecules. Using a classical analysis, we identify a threshold coupling line separating a molecular phase and a mixed phase. Through studies of the energy gap, von Neumann entanglement entropy, and fidelity, we give evidence that this line is associated with a boundary line in the ground-state phase diagram of the quantum system.

Static versus dynamic friction: the role of coherence

A simple model for solid friction is analysed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal strain the springs break irreversibly. Initially all springs are assumed to have zero strain, because at static contact local elastic stresses are expected to relax. Relative tangential motion of the two solids leads to a loss of coherence of the initial state: the springs get out of phase due to differences in their sizes. This mechanism alone is shown to lead to a difference between static and dynamic friction forces already. We find that in this case the ratio of the static and dynamic coefficients decreases with increasing relative width of the probability distribution, and has a lower bound of 1 and an upper bound of 2.

Emerging collective behavior in a simple artificial financial market

We consider a simple model for a society of economic agents, where each can invest a discrete quantity. Interactions among agents happen in a neighborhood and depend on the motivation level (insider information, economy prospects, etc.). The profit of the group fluctuates stochastically and is used to update individual motivations. We analyze the behavior, as a function of time, of the global persistence, given the initial quantity of money invested. Our simulations show that this quantity -- a measure of the probability that the amount of money of the entire group remains at least equal to the initial amount -- has a power law updating behavior. We have also performed simulations with heterogeneous agents, including deceiver and conservative agents. We show that, although there is no regular pattern regarding the average wealth, robust power laws for persistence exist, indicating that this can be used to model the emerging collective behavior. Besides, the updating of motivation and the presence of conservatives and deceivers is remarkable and has an influence on the persistence.

Phase diagram of the non-Hermitian asymmetric XXZ spin chain

The low-lying excitations of the asymmetric XXZ spin chain are derived explicitly in the antiferromagnetic regime through the Bethe ansatz. It is found that a massless and conformal invariant phase with central charge c = 1 is separated from a massive phase by a line on which the low-lying excitations surprisingly scale with the lattice length as . The mass gap vanishes with an exponent as one approaches the massless phase. The connection with the asymmetric six-vertex model and some physical consequences are discussed.

Magnetic vortices induced by a moving tip

A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicular with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. Due to the symmetry of the dipolar field of the tip, in addition to the collinear structure a magnetic vortex structure becomes stable. It is robust against excitations caused by the motion of the tip. We show that for high excitations the system may perform a transition between the two states. The influence of domain walls, which may also induce this transition, is examined.A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicular with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. Due to the symmetry of the dipolar field of the tip, in addition to the collinear structure a magnetic vortex structure becomes stable. It is robust against excitations caused by the motion of the tip. We show that for high excitations the system may perform a transition between the two states. The influence of domain walls, which may also induce this transition, is examined.

A obra de Boltzmann em Física

The goal of the present work is to present an overview of Boltzmanns work in Physics. Some of his most significant contributions are discussed and contextualized.

Dynamics of a Public Investment Game: from Nearest-Neighbor Lattices to Small-World Networks

In this work we analyze the time evolution of the wealth of a group of agents in a public-investment-game scenario. These are part of a small-world network, where connections depend on a probability p and investment depends on a binary variable σ (motivation). This variable tries to emulate one’s perception of other players’ actions. We study the effect of the connectivity on the wealth of the group as well as the dynamics when idyosincratic types are introduced in the game.

Long-range epidemic spreading with immunization

We study the phase transition between survival and extinction in an epidemic process with long-range interactions and immunization. This model can be viewed as the well-known general epidemic process in which nearest-neighbor interactions are replaced by Levy flights over distances r which are distributed as P(r) ~ r−d−σ. By extensive numerical simulations, we confirm previous field-theoretical results obtained by Janssen et al (1999 Eur. Phys. J. B 7 137).