The statistics of the heat exchanged between two quantum $\mathit{XX}$ spin chains prepared at different temperatures is studied within the assumption of weak coupling. This provides simple formulas for the average heat and its corresponding characteristic function, from which the probability distribution may be computed numerically. These formulas are valid for arbitrary sizes and therefore allow us to analyze the role of the thermodynamic limit in this nonequilibrium setting. It is found that all thermodynamic quantities are extremely sensitive to the quantum phase transition of the $\mathit{XX}$ chain.

We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida–Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida–Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida–Thouless transition even though it is absent.

The dynamics of ultrafast energy transfer to water clusters and to bulk water by a highly intense, subcycle THz pulse of duration $\approx 150$ fs is investigated in the context of force-field molecular dynamics simulations. We focus our attention on the mechanisms by which rotational and translational degrees of freedom of the water monomers gain energy from these subcycle pulses with an electric field amplitude of up to about 0.6 V/Å. It has been recently shown that pulses with these characteristics can be generated in the laboratory [C. Vicario, B. Monoszlai, and C. P. Hauri, Phys. Rev. Lett. 112, 213901 (2014)]. Through their permanent dipole moment, water molecules are acted upon by the electric field and forced off their preferred hydrogen-bond network conformation. This immediately sets them in motion with respect to one another as energy quickly transfers to their relative center of mass displacements. We find that, in the bulk, the operation of these mechanisms is strongly dependent on the initial temperature and density of the system. In low density systems, the equilibration between rotational and translational modes is slow due to the lack of collisions between monomers. As the initial density of the system approaches $1 \text{g}/{\text{cm}}^3$, equilibration between rotational and translational modes after the pulse becomes more efficient. In turn, low temperatures hinder the direct energy transfer from the pulse to rotational motion owing to the resulting stiffness of the hydrogen bond network. For small clusters of just a few water molecules we find that fragmentation due to the interaction with the pulse is faster than equilibration between rotations and translations, meaning that the latter remain colder than the former after the pulse. In contrast, clusters with more than a few tens of water molecules already display energy gain dynamics similar to water in condensed phases owing to inertial confinement of the internal water molecules by the outer shells. In these cases, a complete equilibration becomes possible.

We study rational solutions of continuous wave backgrounds with the critical frequencies of the Sasa-Satsuma equation, which can be used to describe the evolution of the optical field in a nonlinear fiber with some high-order effects. We find a striking dynamical process that two W-shaped solitons are generated from a weak modulation signal on the continuous wave backgrounds. This provides a possible way to obtain stable high-intensity pulses from a low-intensity continuous wave background. The process involves both modulational instability and modulational stability regimes, in contrast to the rogue waves and W-shaped solitons reported before which involve modulational instability and stability, respectively. Furthermore, we present a phase diagram on a modulational instability spectrum plane for the fundamental nonlinear localized waves obtained already in the Sasa-Satsuma equation. The interactions between different types of nonlinear localized waves are discussed based on the phase diagram.

In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks “soft” or “probabilistic” connection models have recently been introduced, involving a “connection function” $H\left(r\right)$ that gives the probability that two nodes at distance $r$ are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.

We consider a general criterion to discern the nature of the threshold in epidemic models on scale-free (SF) networks. Comparing the epidemic lifespan of the nodes with largest degrees with the infection time between them, we propose a general dual scenario, in which the epidemic transition is either ruled by a hub activation process, leading to a null threshold in the thermodynamic limit, or given by a collective activation process, corresponding to a standard phase transition with a finite threshold. We validate the proposed criterion applying it to different epidemic models, with waning immunity or heterogeneous infection rates in both synthetic and real SF networks. In particular, a waning immunity, irrespective of its strength, leads to collective activation with finite threshold in scale-free networks with large degree exponent, at odds with canonical theoretical approaches.

Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical $d$-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor $s=-1,0,1$ (NGF) describing simplicial complexes defined in arbitrary dimension $d$ and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality $d$. In $d=1$ NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension $d>1$ it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time $t$ encodes all possible NGF evolutions up to time $t$. Interestingly the NGF remains fully classical but its statistical properties reveal the relation to its quantum mechanical description. In fact the $\delta$-dimensional faces of the NGF have generalized degrees that follow either the Fermi-Dirac, Boltzmann, or Bose-Einstein statistics depending on the flavor $s$ and the dimensions $d$ and $\delta$.

Transport of mass and energy across the vapor-liquid interface of water is of central importance in a variety of contexts such as climate models, weather forecasts, and power plants. We provide a complete description of the transport properties of the vapor-liquid interface of water with the framework of nonequilibrium thermodynamics. Transport across the planar interface is then described by 3 interface transfer coefficients where 9 more coefficients extend the description to curved interfaces. We obtain all coefficients in the range 260–560 K by taking advantage of water evaporation experiments at low temperatures, nonequilibrium molecular dynamics with the TIP4P/2005 rigid-water-molecule model at high temperatures, and square gradient theory to represent the whole range. Square gradient theory is used to link the region where experiments are possible (low vapor pressures) to the region where nonequilibrium molecular dynamics can be done (high vapor pressures). This enables a description of transport across the planar water interface, interfaces of bubbles, and droplets, as well as interfaces of water structures with complex geometries. The results are likely to improve the description of evaporation and condensation of water at widely different scales; they open a route to improve the understanding of nanodroplets on a small scale and the precision of climate models on a large scale.

Microorganisms develop coordinated beating patterns on surfaces lined with cilia known as metachronal waves. For a chain of cilia attached to a flat ciliate, it has been shown that hydrodynamic interactions alone can lead the system to synchronize. However, several microorganisms possess a curve-shaped ciliate body and so to understand the effect of this geometry on the formation of metachronal waves, we evaluate the hydrodynamic interactions of cilia near a large spherical body. Using a minimal model, we show that for a chain of cilia around the sphere, the natural periodicity in the geometry leads the system to synchronize. We also report an emergent wavelike behavior when an asymmetry is introduced to the system.

In this paper, the three-dimensional (3D) Rayleigh-Taylor instability (RTI) with low Atwood number ($A_t=0.15$) in a long square duct ($12W\times W\times W$) is studied by using a multiple-relaxation-time lattice Boltzmann (LB) multiphase model. The effect of the Reynolds number on the interfacial dynamics and bubble and spike amplitudes at late time is investigated in detail. The numerical results show that at sufficiently large Reynolds numbers, a sequence of stages in the 3D immiscible RTI can be observed, which includes the linear growth, terminal velocity growth, reacceleration, and chaotic development stages. At late stage, the RTI induces a very complicated topology structure of the interface, and an abundance of dissociative drops are also observed in the system. The bubble and spike velocities at late stage are unstable and their values have exceeded the predictions of the potential flow theory [V. N. Goncharov, Phys. Rev. Lett. 88, 134502 (2002)]. The acceleration of the bubble front is also measured and it is found that the normalized acceleration at late time fluctuates around a constant value of 0.16. When the Reynolds number is reduced to small values, some later stages cannot be reached sequentially. The interface becomes relatively smoothed and the bubble velocity at late time is approximate to a constant value, which coincides with the results of the extended Layzer model [S.-I. Sohn, Phys. Rev. E 80, 055302(R) (2009)] and the modified potential theory [R. Banerjee, L. Mandal, S. Roy, M. Khan, and M. R. Guptae, Phys. Plasmas 18, 022109 (2011)]. In our simulations, the Graphics Processing Unit (GPU) parallel computing is also used to relieve the massive computational cost.

The rate of electric-field-driven transport across ion-selective membranes can exceed the limit predicted by Nernst (the limiting current), and encouraging this “overlimiting” phenomenon can improve efficiency in many electrochemical systems. Overlimiting behavior is the result of electroconvectively induced vortex formation near membrane surfaces, a conclusion supported so far by two-dimensional (2D) theory and numerical simulation, as well as experiments. In this paper we show that the third dimension plays a critical role in overlimiting behavior. In particular, the vortex pattern in shear flow through wider channels is helical rather than planar, a surprising result first observed in three-dimensional (3D) simulation and then verified experimentally. We present a complete experimental and numerical characterization of a device exhibiting this recently discovered 3D electrokinetic instability, and show that the number of parallel helical vortices is a jump-discontinuous function of width, as is the overlimiting current and overlimiting conductance. In addition, we show that overlimiting occurs at lower fields in wider channels, because the associated helical vortices are more readily triggered than the planar vortices associated with narrow channels (effective 2D systems). These unexpected width dependencies arise in realistic electrochemical desalination systems, and have important ramifications for design optimization.

The energy loss of argon ions in a target depends on their velocity and charge density. At the energies studied in this work, it depends mostly on the free and bound electrons in the target. Here the random-phase approximation is used for analyzing free electrons at any degeneracy. For the plasma-bound electrons, an interpolation between approximations for low and high energies is applied. The Brandt-Kitagawa (BK) model is employed to depict the projectile charge space distribution, and the stripping criterion of Kreussler et al. is used to determine its equilibrium charge state $Q_{\text{eq}}$. This latter criterion implies that the equilibrium charge state depends slightly on the electron density and temperature of the plasma. On the other hand, the effective charge $Q_{\text{eff}}$ is obtained as the ratio between the energy loss of the argon ion and that of the proton for the same plasma conditions. This effective charge $Q_{\text{eff}}$ is larger than the equilibrium charge state $Q_{\text{eq}}$ due to the incorporation of the BK charge distribution. Though our charge-state estimations are not exactly the same as the experimental values, our energy loss agrees quite well with the experiments. It is noticed that the energy loss in plasmas is higher than that in the same cold target of about, $\sim 42–62.5\%$ and increases with carbon plasma ionization. This confirms the well-known enhanced plasma stopping. It is also observed that only a small part of this energy loss enhancement is due to an increase of the argon charge state, namely only $\sim 2.2$ and $5.1\%$, for the partially and the fully ionized plasma, respectively. The other contribution is connected with a better energy transfer to the free electrons at plasma state than to the bound electrons at solid state of about, $\sim 38.8–57.4\%$, where higher values correspond to a fully ionized carbon plasma.

The influence of finite relaxation times on Thomson scattering from warm dense plasmas is examined within the framework of the average-atom approximation. Presently most calculations use the collision-free Lindhard dielectric function to evaluate the free-electron contribution to the Thomson cross section. In this work, we use the Mermin dielectric function, which includes relaxation time explicitly. The relaxation time is evaluated by treating the average atom as an impurity in a uniform electron gas and depends critically on the transport cross section. The calculated relaxation rates agree well with values inferred from the Ziman formula for the static conductivity and also with rates inferred from a fit to the frequency-dependent conductivity. Transport cross sections determined by the phase-shift analysis in the average-atom potential are compared with those evaluated in the commonly used Born approximation. The Born approximation converges to the exact cross sections at high energies; however, differences that occur at low energies lead to corresponding differences in relaxation rates. The relative importance of including relaxation time when modeling x-ray Thomson scattering spectra is examined by comparing calculations of the free-electron dynamic structure function for Thomson scattering using Lindhard and Mermin dielectric functions. Applications are given to warm dense Be plasmas, with temperatures ranging from 2 to 32 eV and densities ranging from 2 to 64 g/cc.

We numerically study the unitary time evolution of a nonintegrable model of hard-core bosons with an extensive number of local ${\mathbb{Z}}_2$ symmetries. We find that the expectation values of local observables in the stationary state are described better by the generalized Gibbs ensemble (GGE) than by the canonical ensemble. We also find that the eigenstate thermalization hypothesis fails for the entire spectrum but holds true within each symmetry sector, which justifies the GGE. In contrast, if the model has only one global ${\mathbb{Z}}_2$ symmetry or a size-independent number of local ${\mathbb{Z}}_2$ symmetries, we find that the stationary state is described by the canonical ensemble. Thus, the GGE is necessary to describe the stationary state even in a nonintegrable system if it has an extensive number of local symmetries.

In this article we derive expressions for Casimir-like pressures induced by nonequilibrium concentration fluctuations in liquid mixtures. The results are then applied to liquid mixtures in which the concentration gradient results from a temperature gradient through the Soret effect. A comparison is made between the pressures induced by nonequilibrium concentration fluctuations in liquid mixtures and those induced by nonequilibrium temperature fluctuations in one-component fluids. Some suggestions for experimental verification procedures are also presented.

We study the probability $p\equiv p_{\eta }\left(t\right)$ that two directed polymers in a given random potential $\eta$ and with fixed and nearby endpoints do not cross until time $t$. This probability is itself a random variable (over samples $\eta$), which, as we show, acquires a very broad probability distribution at large time. In particular, the moments of $p$ are found to be dominated by atypical samples where $p$ is of order unity. Building on a formula established by us in a previous work using nested Bethe ansatz and Macdonald process methods, we obtain analytically the leading large time behavior of all moments $\overline{p^m}\simeq {\gamma }_m/t$. From this, we extract the exact tail $\sim \rho \left(p\right)/t$ of the probability distribution of the noncrossing probability at large time. The exact formula is compared to numerical simulations, with excellent agreement.

We present a general phase-space kinetic model for charged-particle transport through combined localized and delocalized states, capable of describing scattering collisions, trapping, detrapping, and losses. The model is described by a generalized Boltzmann equation, for which an analytical solution is found in Fourier-Laplace space. The velocity of the center of mass and the diffusivity about it are determined analytically, together with the flux transport coefficients. Transient negative values of the free particle center-of-mass transport coefficients can be observed due to the trapping to, and detrapping from, localized states. A Chapman-Enskog-type perturbative solution technique is applied, confirming the analytical results and highlighting the emergence of a density gradient representation in the weak-gradient hydrodynamic regime. A generalized diffusion equation with a unique global time operator is shown to arise, reducing to the standard diffusion equation and a Caputo fractional diffusion equation in the normal and dispersive limits. A subordination transformation is used to solve the generalized diffusion equation by mapping from the solution of a corresponding standard diffusion equation.

The response of topological insulators (TIs) to an external weakly classical field can be expressed in terms of Kubo formula, which predicts quantized Hall conductivity of the quantum Hall family. The response of TIs to a single-mode quantized field, however, remains unexplored. In this work, we take the quantum nature of the external field into account and define a Hall conductance to characterize the linear response of a two-band system to the quantized field. The theory is then applied to topological insulators. Comparisons with the traditional Hall conductance are presented and discussed.

Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localized clusters, suggesting a simple mechanism for sympatric speciation. Here we study the role of demographic stochasticity in a model of competing organisms subject to assortative mating. We find that in models with sexual reproduction, noise can also lead to the formation of phenotypic clusters in parameter ranges where deterministic models would lead to a homogeneous distribution. In some cases, noise can have a sizable effect, rendering the deterministic modeling insufficient to understand the phenotypic distribution.