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.

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 (GEP) in which nearestneighbor 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 fieldtheoretical results obtained by Janssen et al.

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 non-trivial points where the survival probability for bond percolation can be computed exactly.

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A simple model for solid friction is analyzed. 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.While the facts that dry solid friction is proportional to the normal load at the contact and does not depend on the apparent contact area were established experimentally at least as early as in the 16th century by Leonardo da Vinci and are now known under the names of Amonton (1699) or Coulomb (1781) [1], it was probably Euler (1750) who first distinguished between static and dynamic friction [2]. This difference has been explained in several, conceptually different ways. The reason was identified as: A collective depinning phenomenon [3], the time strengthening of individual pinning sites [4,5], the shear melting of a lubrication film [6], mobile impurities at the interface [7], or the formation and healing of microcracks [8]. The fact that all these mechanisms lead to the same macroscopic phenomenology raises the question whether they can be classified in terms of more abstract concepts.An attempt in this direction was made by Caroli and Nozières [9], who proposed a model for dry solid friction based on the following physical picture: The surfaces have randomly distributed asperities which get interlocked. These interlocked asperities act as pinning sites resisting tangential motion. Under tangential load they are deformed up to a threshold

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We study temporal networks of characters in literature focusing on Alice's Adventures in Wonderland (1865) by Lewis Carroll and the anonymous La Chanson de Roland (around 1100). The former, one of the most influential pieces of nonsense literature ever written, describes the adventures of Alice in a fantasy world with logic plays interspersed along the narrative. The latter, a song of heroic deeds, depicts the Battle of Roncevaux in 778 A.D. during Charlemagne's campaign on the Iberian Peninsula. We apply methods recently developed by Taylor et al. [26] to find time-averaged eigenvector centralities, Freeman indices and vitalities of characters. We show that temporal networks are more appropriate than static ones for studying stories, as they capture features that the time-independent approaches fail to yield.

The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schrödinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain. Within this approach we search for all 3-state integrable quantum chains whose spectra are known and which are related to diffusive-reactive systems. Two integrable models are found to appear naturally in this context: the U q SU (2)-invariant model with external fields and the 3-state U q SU (P/M )-invariant Perk-Schultz models with external fields. A nonlocal similarity transformation which brings the Hamiltonian governing the chemical processes to the known standard forms is described, leading in the case of periodic boundary conditions to a generalization of the Dzialoshinsky-Moriya interaction.