We study the diffusion of complex Wishart matrices and derive a partial differential equation governing the behavior of the associated averaged characteristic polynomial. In the limit of large-size matrices, the inverse Cole-Hopf transform of this polynomial obeys a nonlinear partial differential equation whose solutions exhibit shocks at the evolving edges of the eigenvalue spectrum. In a particular scenario one of those shocks hits the origin that plays the role of an impassable wall. To investigate the universal behavior in the vicinity of this wall, i.e., in the vicinity of a critical point, we derive an integral representation for the averaged characteristic polynomial and study its asymptotic behavior. The result is a Bessoid function.

There is presently considerable interest in accurately simulating the evolution of open systems for which Markovian master equations fail. Examples are systems that are time dependent and/or strongly damped. A number of elegant methods have now been devised to do this, but all use a bath consisting of a continuum of harmonic oscillators. While this bath is clearly appropriate for, e.g., systems coupled to the electromagnetic field, it is not so clear that it is a good model for generic many-body systems. Here we explore a different approach to exactly simulating open systems: using a finite bath chosen to have certain key properties of thermalizing many-body systems. To explore the numerical resources required by this method to approximate an open system coupled to an infinite bath, we simulate a weakly damped system and compare to the evolution given by the relevant Markovian master equation. We obtain the Markovian evolution with reasonable accuracy by using an additional averaging procedure, and elucidate how the typicality of the bath generates the correct thermal steady state via the process of “eigenstate thermalization.”

This study explores the roles of UV-polymerizable silicon-based nanoparticles in polymer-stabilized blue phase (PSBP) liquid crystals. Our analysis reveals that the polymerized polymer leads to widening of the temperature range of the blue phase and stabilization of the reflection wavelength against temperature variations. A polymer morphology study of PSBP reveals the polydomain nature of the blue phase. In practical application, the advantage of the low-surface-energy property of the UV-polymerizable silicon-based nanoparticles leads to a significant reduction in switching voltage from 140 to 40 V.

We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.

Thermal conductivity (κ) of both the ablator materials and deuterium-tritium (DT) fuel plays an important role in understanding and designing inertial confinement fusion (ICF) implosions. The extensively used Spitzer model for thermal conduction in ideal plasmas breaks down for high-density, low-temperature shells that are compressed by shocks and spherical convergence in imploding targets. A variety of thermal-conductivity models have been proposed for ICF hydrodynamic simulations of such coupled and degenerate plasmas. The accuracy of these κ models for DT plasmas has recently been tested against first-principles calculations using the quantum molecular-dynamics (QMD) method; although mainly for high densities (ρ > 100 g/cm${}^3$), large discrepancies in κ have been identified for the peak-compression conditions in ICF. To cover the wide range of density-temperature conditions undergone by ICF imploding fuel shells, we have performed QMD calculations of κ for a variety of deuterium densities of ρ = 1.0 to 673.518 g/cm${}^3$, at temperatures varying from $T$ = 5 × 10${}^3$ K to $T$ = 8 × 10${}^6$ K. The resulting ${\kappa }_{\mathrm{QMD}}$ of deuterium is fitted with a polynomial function of the coupling and degeneracy parameters Γ and θ, which can then be used in hydrodynamic simulation codes. Compared with the “hybrid” Spitzer-Lee-More model currently adopted in our hydrocode lilac, the hydrosimulations using the fitted ${\kappa }_{\mathrm{QMD}}$ have shown up to ∼20% variations in predicting target performance for different ICF implosions on OMEGA and direct-drive–ignition designs for the National Ignition Facility (NIF). The lower the adiabat of an imploding shell, the more variations in predicting target performance using ${\kappa }_{\mathrm{QMD}}$. Moreover, the use of ${\kappa }_{\mathrm{QMD}}$ also modifies the shock conditions and the density-temperature profiles of the imploding shell at early implosion stage, which predominantly affects the final target performance. This is in contrast to the previous speculation that ${\kappa }_{\mathrm{QMD}}$ changes mainly the inside ablation process during the hot-spot formation of an ICF implosion.

A particle diffusing in an asymmetric periodic channel, driven by a sinusoidal force $F\left(t\right)=F_{0}cos\omega t$ (the rocking ratchet) is considered. The asymptotic solution of the generalized Fick–Jacobs equation describing the system is studied in the nonadiabatic regime. The leading term of the rectified current, appearing in the order $\sim F_0^2$, is derived. The method presented enables us to solve the problem analytically for a sawtooth channel and also to look for approximative formulas applicable in a wide range of frequencies $\omega$. Even the simplest approximation qualitatively reproduces the current reversal at higher frequencies as the result of growing phase lag of the rocking density behind the driving force.

The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and atoms are restricted to the sites of a one-dimensional lattice. A path integral formalism is developed within the context of the canonical ensemble in which the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. For the case of a free particle, analytical expressions for the energy, its fluctuations, and the qp-qp correlation function are derived and compared with the Monte Carlo simulations. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp for a periodic interaction potential, forcing the qp to occupy extended states. We consider a striped potential in one dimension, where every other lattice site is occupied by an atom with potential $\epsilon$, and every other lattice site is empty. This potential serves as a stress test for the path integral formalism because of its rapid site-to-site variation. An analytical solution was determined in this case by utilizing Bloch's theorem due to the periodicity of the potential. Comparisons of the potential energy, the total energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the analytical calculations.

We consider the temporal evolution of a zero-energy edge Majorana of a spinless $p$-wave superconducting chain following a sudden change of a parameter of the Hamiltonian. Starting from one of the topological phases that has an edge Majorana, the system is suddenly driven to the other topological phase or to the (topologically) trivial phases and to the quantum critical points (QCPs) separating these phases. The survival probability of the initial edge Majorana as a function of time is studied following the quench. Interestingly when the chain is quenched to the QCP, we find a nearly perfect oscillation of the survival probability, indicating that the Majorana travels back and forth between two ends, with a time period that scales with the system size. We also generalize to the situation when there is a next-nearest-neighbor hopping in a superconducting chain and there results in a pair of edge Majorana at each end of the chain in the topological phase. We show that the frequency of oscillation of the survival probability gets doubled in this case. We also perform an instantaneous quenching of the Hamiltonian (with two Majorana modes at each end of the chain) to an another Hamiltonian which has only one Majorana mode in equilibrium; the MSP shows oscillations as a function of time with a noticeable decay in the amplitude. On the other hand for a quenching which is reverse to the previous one, the MSP decays rapidly and stays close to zero with fluctuations in amplitude.

We present an analytical model of salt- and water-ion transport across an ion-selective interface based on an assumption of local equilibrium of the water-dissociation reaction. The model yields current-voltage characteristics and curves of water-ion current versus salt-ion current, which are in qualitative agreement with experimental results published in the literature. The analytical results are furthermore in agreement with direct numerical simulations. As part of the analysis, we find approximate solutions to the classical problem of pure salt transport across an ion-selective interface. These solutions provide closed-form expressions for the current-voltage characteristics, which include the overlimiting current due to the development of an extended space-charge region. Finally, we discuss how the addition of an acid or a base affects the transport properties of the system and thus provide predictions accessible to further experimental tests of the model.

We present molecular dynamics evidence for the nonanalytic effects of the long-range dispersion forces on the capillary waves fluctuations of a Lennard-Jones liquid surface. The results of the intrinsic sampling method, for the analysis of the instantaneous interfacial shape, are obtained in large systems for several cut-off distances of the potential tail, and they show good agreement with the theoretical prediction by Napiórkowski and Dietrich, based on a density functional analysis. The enhancement of the capillary waves is quantified to be within 1% for a simple liquid near its triple point.

Real networks often exhibit modularity, which is defined as the degree to which a network can be decomposed into several subnetworks. The question of how a modular network arises is still open to discussion. The leading hypothesis is that high modularity evolves under multiple goals, which are decomposable to subproblems, as well as under the evolutionary constraint that selection prefers sparse links in a network. In the present study, we investigate an alternative evolutionary constraint entailing increased robustness to noise. To examine this, we present noise-interfused network models involving an analytically solvable linear system and biologically inspired nonlinear systems. The models demonstrate that it is possible to evolve a modular network under both modularly changing goal orientations and enhancing robustness to noise, thereby reducing sensitivity to noise. By performing theoretical analyses of linear systems, it is shown that the evolutionary constraint enforces the establishment of well-balanced noise sensitivities of multiple noise sources and leads to a modular network underlying a modular structure in goals. Moreover, computer simulations confirm that the presented mechanisms of modular network evolution are robust to variations of nonlinearity in network functions. Our findings suggest a positive role for the presence of noise in network evolution.

Recent theoretical studies show that decoherence process can enhance transport efficiency in quantum systems. This effect is known as environment-assisted quantum transport (ENAQT). The role of ENAQT in optimal quantum transport is well investigated; however, it is less known how robust ENAQT is with respect to variations in the system or its environment characteristic. Toward answering this question, we simulated excitonic energy transfer in Fenna-Matthews-Olson photosynthetic complex. We found that ENAQT is robust with respect to many relevant parameters of environmental interactions and Frenkel-exciton Hamiltonians, including reorganization energy, bath-frequency cutoff, temperature, initial excitations, dissipation rate, trapping rate, disorders, and dipole moments orientations. Our study suggests that the ENAQT phenomenon can be exploited in robust design of highly efficient quantum transport systems.

To model volatile real-world network behavior, we analyze a phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects phase-flipping dynamics, and we find the probability that no more than $q\%$ of nodes and links fail. We derive higher moments of the fractions of active nodes and active links, $f_n\left(t\right)$ and $f_{\ell }\left(t\right)$, and we define two estimators to quantify the level of risk in a network. We find hysteresis in the correlations of $f_n\left(t\right)$ due to failures at the node level, and we derive conditional probabilities for phase-flipping in networks. We apply our model to economic and traffic networks.

We analyze the response of two delay-coupled optoelectronic oscillators. Each oscillator operates under its own delayed feedback. We show that the system can display square-wave periodic solutions that can be synchronized in phase or out of phase depending on the ratio between self- and cross-delay times. Furthermore, we show that multiple periodic synchronized solutions can coexist for the same values of the fixed parameters. As a consequence, it is possible to generate square-wave oscillations with different periods by just changing the initial conditions.

An important component in hybrid atomistic-continuum (HAC) modeling of liquids is the proper termination of the atomistic subdomain (${\Omega }_{\mathrm{A}}$). When the HAC model is based on the Schwarz domain decomposition method, the total number of particles in ${\Omega }_{\mathrm{A}}$ is conserved using specular boundaries in an overlap region, where information is exchanged with the continuum subdomain (${\Omega }_{\mathrm{C}}$). This non-periodic termination of ${\Omega }_{\mathrm{A}}$ fails to account for forces otherwise included in a periodic system, through the minimum image convention. The absence of such forces results in spurious density fluctuations adjacent to the specular boundaries. In this work, we present a new boundary force algorithm that establishes a uniform density profile at non-periodic boundaries of ${\Omega }_{\mathrm{A}}$. We also examine the effects of the non-periodic termination of ${\Omega }_{\mathrm{A}}$ on the liquid properties. The algorithm relies on force measurements carried out over a spatially discretized atomistic subdomain. It is relatively straightforward to implement and can be seamlessly extended to higher dimensions.

The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route ($\mu$ route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the $\mu$ route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the $\mu$ route yields a general better description than the virial, energy, compressibility, and zero-separation routes.

We present two kinds of Bochkov-Kuzovlev work equalities in a two-level system that is described by a quantum Markovian master equation. One is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint. We show that these two equalities are indeed equivalent. Importantly, this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function. We use a numerical model to verify these results.

This paper reports results of a three-dimensional discrete element method modeling investigation of the role of boundary vibration in perturbing stick-slip dynamics in a sheared granular layer. The focus is on the influence of vibration within a range of amplitudes and on the fact that above a threshold early slip will be induced. We study the effects of triggering beyond the vibration interval and their origins. A series of perturbed simulations are performed for 30 large slip events selected from different reference runs, in the absence of vibration. For each of the perturbed simulations, vibration is applied either about the middle of the stick phase or slightly before the onset of a large expected slip event. For both cases, a suppression of energy release is on average observed in the perturbed simulations, within the short term following the vibration application. For cases where vibration is applied in the middle of the stick phase, a significant clock advance of the large slip event occurs. In the long term after vibration, there is a recovery period with higher-energy release and increased activity in the perturbed simulations, which compensates for the temporary suppression observed within the short term.