We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two nonequivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the eigenstates of the Hamiltonian. An analysis of finite size effects reveals that quantum chaos and eigenstate thermalization occur in those systems whenever the fields are nonvanishing and not too large.

We discuss a model of random segmented wire, with linear segments of two-dimensional wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all segments are of similar length. The resonant behavior is present with one and also with several propagating modes. The probability distributions evolve from diffusive to localized regimes when increasing the number of segments in a similar way for long and short localization lengths. As a function of the energy, a finite segmented wire typically evolves from localized to diffusive to ballistic behavior in each conductance plateau.

We consider the transient behavior of globally coupled systems of identical pulse-coupled oscillators. Synchrony develops through an aggregation phenomenon, with clusters of synchronized oscillators forming and growing larger in time. Previous work derived expressions for these time dependent clusters, when each oscillator obeyed a linear charging curve. We generalize these results to cases where the charging curves have nonlinearities.

In this paper we present a general framework for solving the stationary nonlinear Schrödinger equation (NLSE) on a network of one-dimensional wires modeled by a metric graph with suitable matching conditions at the vertices. A formal solution is given that expresses the wave function and its derivative at one end of an edge (wire) nonlinearly in terms of the values at the other end. For the cubic NLSE this nonlinear transfer operation can be expressed explicitly in terms of Jacobi elliptic functions. Its application reduces the problem of solving the corresponding set of coupled ordinary nonlinear differential equations to a finite set of nonlinear algebraic equations. For sufficiently small amplitudes we use canonical perturbation theory, which makes it possible to extract the leading nonlinear corrections over large distances.

Quasibrittle behavior, where macroscopic failure is preceded by stable damaging and intensive cracking activity, is a desired feature of materials because it makes fracture predictable. Based on a fiber-bundle model with global load sharing we show that blending strength and stiffness disorder of material elements leads to the stabilization of fracture, i.e., samples that are brittle when one source of disorder is present become quasibrittle as a consequence of blending. We derive a condition of quasibrittle behavior in terms of the joint distribution of the two sources of disorder. Breaking bursts have a power-law size distribution of exponent $5/2$ without any crossover to a lower exponent when the amount of disorder is gradually decreased. The results have practical relevance for the design of materials to increase the safety of constructions.

In this paper, we propose a moving part-free fluidic diode for simple fluids using nested nanochannels, which contain inner and outer channels of different lengths. Molecular dynamics simulations show that the fluidic diode accepts water flows in the forward direction and blocks flows in the backward direction in a wide range of pressure drops. The anisotropic flow rates are generated by the distinct activation pressures in different directions. In the forward direction, the activation pressure is low, which is determined by the infiltration pressure of the inner channel. In the backward direction, the activation pressure is quite high due to the capillary effects when flows are released from the inner to the outer channel. The pressure drop range for the fluidic diode can be varied by changing the channel size or surface wettability. The fluidic diode offers an alternative way for flow control in integrated micro- and nanofluidic devices.

Fluctuation theorems have become an important tool in single-molecule biophysics to measure free-energy differences from nonequilibrium experiments. When significant coarse-graining or noise affect the measurements, the determination of the free energies becomes challenging. In order to address this thermodynamic inference problem, we propose improved estimators of free-energy differences based on fluctuation theorems, which we test on a number of examples. The effect of the noise can be described by an effective temperature, which only depends on the signal-to-noise ratio, when the work is Gaussian distributed and uncorrelated with the error made on the work. The notion of effective temperature appears less useful for non-Gaussian work distributions or when the error is correlated with the work, but nevertheless, as we show, improved estimators can still be constructed for such cases. As an example of nontrivial correlations between the error and the work, we also consider measurements with delay, as described by linear Langevin equations.

We introduce a general contagionlike model for competing opinions that includes dynamic resistance to alternative opinions. We show that this model can describe candidate vote distributions, spatial vote correlations, and a slow approach to opinion consensus with sensible parameter values. These empirical properties of large group dynamics, previously understood using distinct models, may be different aspects of human behavior that can be captured by a more unified model, such as the one introduced in this paper.

We study how the thermodynamic properties of the triangular plaquette model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in kinetically constrained models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model the random-diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the “random first-order” kind. Finally, we give support to our conjectures studying the finite-temperature phase diagram of the random-diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free energy and configurational entropy can be computed by means of the cavity equations.

We investigate a class of agent-based models of self-propelled particles (SPP) that interact according to a Morse potential in the presence of friction, a class which was able to reproduce many of the intriguing patterns of collective motion observed in nature. Specifically, we compare two closely related SPP models in the literature that differ by their prescription of particle drag and self-propulsion. Writing both models in terms of nondimensional parameters allows us to show that the dynamics in the highly viscous regime is independent of the precise forms of drag and propulsion. In contrast to what is indicated in the literature both models yield the same low-energy self-organized states: the coherent flock and the rigid rotation states which are highly ordered in both the coordinate and the velocity spaces and a velocity-disordered droplet state where particles are confined to rings which pass through the lattice points of the underlying Lagrange configuration. In contrast to the first two states which are stable, the third state is found to be a long-lived transient. In the regime studied, relaxing to one of the ordered steady states is inevitable, but how and when the transition occurs and what is the probability of ending in one state rather than the other are functions of the model parameters. Two types of transitions are characterized and first passage times are computed. Eventually, the evolution of the order parameter is explored in the framework of a Langevin-type equation, and the possible metastability of the random droplet state is discussed.

Derivation of the dynamic structure factor, an important parameter linking experimental and theoretical work in dense plasmas, is possible starting from hydrodynamic equations. Here we obtain, by modifying the governing hydrodynamic equations, a new form of the dynamic structure factor which includes radiative terms. The inclusion of such terms has an effect on the structure factor at high temperatures, which suggests that its effect must be taken into consideration in such regimes.

We have made a simple and natural modification of a recent quantum refrigerator model presented by Cleuren et al. [Phys. Rev. Lett. 108, 120603 (2012)]. The original model consist of two metal leads acting as heat baths and a set of quantum dots that allow for electron transport between the baths. It was shown to violate the dynamic third law of thermodynamics (the unattainability principle, which states that cooling to absolute zero in finite time is impossible). By taking into consideration the finite energy level spacing $\mathrm{\Delta }$, in metals we restore the third law while keeping all of the original model's thermodynamic properties intact down to the limit of $k_{B}T\sim \mathrm{\Delta }$, where the cooling rate is quenched. The spacing $\mathrm{\Delta }$ depends on the confinement of the electrons in the lead and therefore, according to our result larger samples (with smaller level spacing), could be cooled efficiently to lower absolute temperatures than smaller ones. However, a large lead makes the assumption of instant equilibration of electrons implausible; in reality one would only cool a small part of the sample and we would have a nonequilibrium situation. This property is expected to be model independent and raises the question whether we can find an optimal size for the lead that is to be cooled.

We consider two coupled populations of leaky integrate-and-fire neurons. Depending on the coupling strength, mean fields generated by these populations can have incommensurate frequencies or become frequency locked. In the observed 2:1 locking state of the mean fields, individual neurons in one population are asynchronous with the mean fields, while in another population they have the same frequency as the mean field. These synchronous neurons form a chimera state, where part of them build a fully synchronized cluster, while other remain scattered. We explain this chimera as a marginal one, caused by a self-organized neutral dynamics of the effective circle map.

Locating the source that triggers a dynamical process is a fundamental but challenging problem in complex networks, ranging from epidemic spreading in society and on the Internet to cancer metastasis in the human body. An accurate localization of the source is inherently limited by our ability to simultaneously access the information of all nodes in a large-scale complex network. This thus raises two critical questions: how do we locate the source from incomplete information and can we achieve full localization of sources at any possible location from a given set of observable nodes. Here we develop a time-reversal backward spreading algorithm to locate the source of a diffusion-like process efficiently and propose a general locatability condition. We test the algorithm by employing epidemic spreading and consensus dynamics as typical dynamical processes and apply it to the H1N1 pandemic in China. We find that the sources can be precisely located in arbitrary networks insofar as the locatability condition is assured. Our tools greatly improve our ability to locate the source of diffusion in complex networks based on limited accessibility of nodal information. Moreover, they have implications for controlling a variety of dynamical processes taking place on complex networks, such as inhibiting epidemics, slowing the spread of rumors, pollution control, and environmental protection.

In multiplex networks with a large number of layers, the nodes can have different activities, indicating the total number of layers in which the nodes are present. Here we model multiplex networks with heterogeneous activity of the nodes and we study their robustness properties. We introduce a percolation model where nodes need to belong to the giant component only on the layers where they are active (i.e., their degree on that layer is larger than zero). We show that when there are enough nodes active only in one layer, the multiplex becomes more resilient and the transition becomes continuous. We find that multiplex networks with a power-law distribution of node activities are more fragile if the distribution of activity is broader. We also show that while positive correlations between node activity and degree can enhance the robustness of the system, the phase transition may become discontinuous, making the system highly unpredictable.

Simple growth mechanisms have been proposed to explain the emergence of seemingly universal network structures. The widely studied model of preferential attachment assumes that new nodes are more likely to connect to highly connected nodes. Preferential attachment explains the emergence of scale-free degree distributions within complex networks. Yet it is incompatible with many network systems, particularly bipartite systems in which two distinct types of agents interact. For example, the addition of new links in a host-parasite system corresponds to the infection of hosts by parasites. Increasing connectivity is beneficial to a parasite and detrimental to a host. Therefore, the overall network connectivity is subject to conflicting pressures. Here we propose a stochastic network growth model of conflicting attachment, inspired by a particular kind of parasite-host interaction: that of viruses interacting with microbial hosts. The mechanism of network growth includes conflicting preferences to network density as well as costs involved in modifying the network connectivity according to these preferences. We find that the resulting networks exhibit realistic patterns commonly observed in empirical data, including the emergence of nestedness, modularity, and nested-modular structures that exhibit both properties. We study the role of conflicting interests in shaping network structure and assess opportunities to incorporate greater realism in linking growth process to pattern in systems governed by antagonistic and mutualistic interactions.

We study experimentally a short chain of $N(\le 8)$ loosely connected spheres bouncing against a horizontal surface that vibrates sinusoidally at intensity $\mathrm{\Gamma }$. Distinct states are identified: a base state of uniform bouncing in-sync with the substrate prevails at low values of $\mathrm{\Gamma }$, whereas increasing $\mathrm{\Gamma }$ can induce transitions to two excited states with appreciable storage of energy around one or both ends of the chain. We find that, in a transitional window of $\mathrm{\Gamma }$, the chain can even switch spontaneously among states, resolving the mystery why different modes of motion can be initiated at the same position in our previous work along a gradient of vibration [Phys. Rev. Lett. 112, 058001 (2014)]. Preliminary interpretations on the parametric dependences and the optimal frequency window for seeing these transitions are offered, based on the microscopic and statistical evidence in our experiments up to date.

Plasticity in amorphous silica is unusual: The yield stress decreases with hydrostatic pressure, in contrast to the Mohr-Coulomb response commonly found in more compact materials such as bulk metallic glasses. To better understand this response, we have carried out molecular dynamics simulations of plastic response in a model glass with open structure. The simulations reproduce the anomalous dependence of yield stress with pressure and also correctly predict that the plastic response turns to normal once the material has been fully compacted. We also show that the overall shape of the yield surface is consistent with a quadratic behavior predicted assuming local buckling of the structure, a point of view that fits well into the present understanding of the deformation mechanisms of amorphous silica. The results also confirm that free volume is an adequate internal variable for a continuum scale description of the plastic response of amorphous silica. Finally, we also investigate the long-range correlations between rearrangement events. We find that strong intermittency is observed when the structure remains open, while compaction results in more homogeneous rearrangements. These findings are in agreement with recent results on the effect of compression on the middle range order in silicate glasses and also suggest that the well-known volume recovery of densified silica at relatively low temperatures is in fact a form of aging.