Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schrödinger picture. We show that a nontrivial damping in the Schrödinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.

The classical surrogate data tests, which are used to differentiate linear noise processes from nonlinear processes, are not suitable for nonstationary time series. In this paper, we propose a surrogate data test that can be applied on both stationary time series as well as nonstationary time series with short-term fluctuations. The method is based on the idea of constructing a network from the time series, employing a generalized symbolic dynamics method introduced in this work, and using any one of the several easily computable network parameters as discriminating statistics. The construction of the network is designed to remove the long-term trends in the data automatically. The network-based test statistics pick up only the short-term variations, unlike the discriminating statistics of the traditional methods, which are influenced by nonstationary trends in the data. The method is tested on several systems generated by linear or nonlinear processes and with deterministic or stochastic trends, and in all cases it is found to be able to differentiate between linear stochastic processes and nonlinear processes quite accurately, especially in cases where the common methods would lead to false rejections of the null hypothesis due to nonstationarity being interpreted as nonlinearity. The method is also found to be robust to the presence of experimental or dynamical noise of a moderate level in an otherwise nonlinear system.

In the context of non-Hermitian photonics, we study the physics of transient growth in coupled waveguide systems that exhibit higher-order exceptional points. We demonstrate the counterintuitive effect of transient growth despite the decaying spectrum, which is a direct consequence of the underlying modal nonorthogonality. Eigenvalue analysis fails to capture the power dynamics and thus we have to rely on methods of nonmodal stability theory, namely singular value decomposition and pseudospectra. The relation between the order of the exceptional point and transient growth is also examined. Our work provides a general methodology that can be applied to any non-Hermitian system that contains complex elements with more loss than gain, and exploits the boundaries of transient amplification in dissipative environments.

We consider a quasi-two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute antiferromagnetic Ising spin system with frustrations. We obtain analytic results for the order-parameter or mean degree of the optimized network using mean-field theories. The cost landscape is analyzed in detail showing complex structures due to frustration as the crossing penalty increases. For the case of strictly no edge crossing is allowed, the mean-field equations lead to a new algorithm that can effectively find the (near) optimal solution even for this strongly frustrated system. All these results are also verified by Monte Carlo simulations and numerical solution of the mean-field equations. Possible applications and relation to the planar triangulation problem is also discussed.

Group synchronization arises when two or more synchronization patterns coexist in a network formed of oscillators of different types, with the systems in each group synchronizing on the same time evolution, but systems in different groups synchronizing on distinct time evolutions. Group synchronization has been observed and characterized when the systems in each group are identical and the couplings between the systems satisfy specific conditions. By relaxing these constraints and allowing them to be satisfied in an approximate rather than exact way, we observe that stable group synchronization may still occur in the presence of small deviations of the parameters of the individual systems and of the couplings from their nominal values. We analyze this case and provide necessary and sufficient conditions for stability through a master stability function approach, which also allows us to quantify the synchronization error. We also investigate the stability of group synchronization in the presence of intragroup connections and for this case extend some of the existing results in the literature. Our analysis points out a broader class of matrices describing intragroup connections for which the stability problem can be reduced in a low-dimensional form.

We numerically study active Brownian particles that can respond to environmental cues through a small set of actions (switching their motility and turning left or right with respect to some direction) which are motivated by recent experiments with colloidal self-propelled Janus particles. We employ reinforcement learning to find optimal mappings between the state of particles and these actions. Specifically, we first consider a predator-prey situation in which prey particles try to avoid a predator. Using as reward the squared distance from the predator, we discuss the merits of three state-action sets and show that turning away from the predator is the most successful strategy. We then remove the predator and employ as collective reward the local concentration of signaling molecules exuded by all particles and show that aligning with the concentration gradient leads to chemotactic collapse into a single cluster. Our results illustrate a promising route to obtain local interaction rules and design collective states in active matter.

The dynamic heterogeneity and the translation-rotation decoupling are the dynamic signatures of glasses and supercooled liquids. Whether and how the dynamic heterogeneity would relate to the local structure of glasses has been a puzzle for decades. In this work we perform molecular dynamics simulations for tracers in both two-dimensional polydisperse colloids (2DPC) and two-dimensional binary colloids (2DBC). In 2DPC glasses, hexatic local structures develop at low enough temperatures and grow quickly along with the dynamic correlation length of the 2DPC, which is well known as the medium-range crystalline order (MRCO). In 2DBC glasses, on the other hand, any explicit local structure has not been reported to grow significantly with the dynamic correlation length at low temperatures. We introduce two different types of tracers into colloidal systems: A diamond tracer that resembles the MRCO of 2DPC glasses and a square tracer that is dissimilar to any local structure of glasses. The translation-rotation decoupling of the diamond tracer in 2DPC glasses is much more significant than that of the square tracer in the same 2DPC glasses. On the other hand, such a tracer shape-dependence of the decoupling is not observed in 2DBC glasses where the local hexatic structure does not develop significantly. We introduce a shape-dependency parameter of the decoupling and find that the shape-dependency parameter grows along with the dynamic correlation length in 2DPC glasses but not in 2DBC glasses. This illustrates that the dynamic heterogeneity and the translation-rotation decoupling of tracers could reveal the local structure that develops in glasses.

This paper deals with a theoretical study of the static magnetization of a composite, consisting of nanodisperse single-domain ferromagnetic particles immobilized in a nonmagnetic medium. This situation is typical for magnetopolymer systems—smart materials, which found applications in high industrial and biomedical applications. It is supposed that the composite was polymerized without an external magnetic field; after curing the particles retain the spatial distribution and orientation of their axes of easy magnetization that they had before the host medium polymerization. Our results demonstrate that, in contrast to ferrofluids with a liquid host medium, a magnetic interparticle interaction provokes a decrease of the macroscopic magnetization of the system.

In a dense gas plasma a short laser pulse propagates in a relativistic self-trapping mode, which enables the effective conversion of laser energy to the accelerated electrons. This regime sustains effective loading which maximizes the total charge of the accelerating electrons, that provides a large amount of betatron radiation. The three-dimensional particle-in-cell simulations demonstrate how such a regime triggers x-ray generation with 0.1–1 MeV photon energies, low divergence, and high brightness. It is shown that a 135-TW laser can be used to produce $3\times {10}^{10}$ photons of $>10$ keV energy and a 1.2-PW laser makes it possible generating about ${10}^{12}$ photons in the same energy range. The laser-to-gamma energy conversion efficiency is up to ${10}^{-4}$ for the high-energy photons, $\sim 100$ keV, while the conversion efficiency to the entire keV-range x rays is estimated to be a few tenths of a percent.

There is a growing interest in the stochastic processes of nonequilibrium systems subject to nonconserved forces, such as the magnetic forces acting on charged particles and the chiral self-propelled force acting on active particles. In this paper, we consider the stationary transport of noninteracting Brownian particles under a constant magnetic field in a position-dependent temperature background. We demonstrate the existence of the Nernst-like stationary density current perpendicular to both the temperature gradient and magnetic field, induced by the intricate coupling between the nonconserved force and the multiplicative noises due to the position-dependent temperature.

A self-repelling two-leg (biped) spider walk is considered where the local stochastic movements are governed by two independent control parameters ${\beta }_d$ and ${\beta }_h$, so that the former controls the distance ($d$) between the legs positions, and the latter controls the statistics of self-crossing of the traversed paths. The probability measure for local movements is supposed to be the one for the “true self-avoiding walk” multiplied by a factor exponentially decaying with $d$. After a transient behavior for short times, a variety of behaviors have been observed for large times depending on the value of ${\beta }_d$ and ${\beta }_h$. Our statistical analysis reveals that the system undergoes a crossover between two (small and large ${\beta }_d$) regimes identified in large times ($t$). In the small ${\beta }_d$ regime, the random walkers (identified by the position of the legs of the spider) remain on average in a fixed nonzero distance in the large time limit, whereas in the second regime (large ${\beta }_d$), the absorbing force between the walkers dominates the other stochastic forces. In the latter regime, $d$ decays in a power-law fashion with the logarithm of time. When the system is mapped to a growth process (represented by a height field which is identified by the number of visits for each point), the roughness and the average height show different behaviors in two regimes, i.e., they show a power law with respect to $t$ in the first regime and $logt$ in the second regime. The fractal dimension of the random walker traces and the winding angle are shown to consistently undergo a similar crossover.

Polymers are frequently deposited on different surfaces, which has attracted the attention of scientists from different viewpoints. In the present approach polymers are represented by rigid rods of length $k$ ($k$-mers), and the substrate takes the form of an $L\times L$ square lattice whose lattice constant matches exactly the interspacing between consecutive elements of the $k$-mer chain. We briefly review the classical description of the nematic transition presented by this system for $k\ge 7$ observing that the high-coverage ($\theta$) transition deserves a more careful analysis from the entropy point of view. We present a possible viewpoint for this analysis that justifies the phase transitions. Moreover, we perform Monte Carlo (MC) simulations in the grand canonical ensemble, supplemented by thermodynamic integration, to first calculate the configurational entropy of the adsorbed phase as a function of the coverage, and then to explore the different phases (and orientational transitions) that appear on the surface with increasing the density of adsorbed $k$-mers. In the limit of $\theta \to 1$ (full coverage) the configurational entropy is obtained for values of $k$ ranging between 2 and 10. MC data are discussed in comparison with recent analytical results [D. Dhar and R. Rajesh, Phys. Rev. E 103, 042130 (2021)]. The comparative study allows us to establish the applicability range of the theoretical predictions. Finally, the structure of the high-coverage phase is characterized in terms of the statistics of $k\times l$ domains (domains of $l$ parallel $k$-mers adsorbed on the surface). A distribution of finite values of $l$ ($l\ll L$) is found with a predominance of $k\times 1$ (single $k$-mers) and $k\times k$ domains. The distribution is the same in each lattice direction, confirming that at high density the adsorbed phase goes to a state with mixed orientations and no orientational preference. An order parameter measuring the number of $k\times k$ domains in the adsorbed layer is introduced.

We investigate heat rectification in a two-qubit system coupled via the Dzyaloshinskii-Moriya (DM) interaction. We derive analytical expressions for heat currents and thermal rectification and provide possible physical mechanisms behind the observed results. We show that the anisotropy of DM interaction in itself is insufficient for heat rectification, and some other form of asymmetry is needed. We employ off-resonant qubits as the source of this asymmetry. We find the regime of parameters for higher rectification factors by examining the analytical expressions of rectification obtained from a global master equation solution. In addition, it is shown that the direction and quality of rectification can be controlled via various system parameters. Furthermore, we compare the influence of different orientations of the DM field anisotropy on the performance of heat rectification. Finally, we investigate the possible interplay between quantum correlations and the performance of the quantum thermal rectifier. We find that asymmetry in the coherences is a fundamental resource for the performance of the quantum thermal rectifier.

A simple numerical model to simulate athermal avalanches is presented. The model is inspired by the “porous collapse” process where the compression of porous materials generates collapse cascades, leading to power law distributed avalanches. The energy $\left(E\right)$, amplitude ($A_{\max }$), and size $\left(S\right)$ exponents are derived by computer simulation in two approximations. Time-dependent “jerk” spectra are calculated in a single avalanche model where each avalanche is simulated separately from other avalanches. The average avalanche profile is parabolic, the scaling between energy and amplitude follows $E\sim A_{max}^2$, and the energy exponent is ε = 1.33. Adding a general noise term in a continuous event model generates infinite avalanche sequences which allow the evaluation of waiting time distributions and pattern formation. We find the validity of the Omori law and the same exponents as in the single avalanche model. We then add spatial correlations by stipulating the ratio $G/N$ between growth processes $G$ (linked to a previous event location) and nucleation processes $N$ (with new, randomly chosen nucleation sites). We found, in good approximation, a power law correlation between the energy exponent ε and the Hausdorff dimension $H_{\mathrm{D}}$ of the resulting collapse pattern $H_{\mathrm{D}}-1\sim {\varepsilon }^{-3}$. The evolving patterns depend strongly on $G/N$ with the distribution of collapse sites equally power law distributed. Its exponent ${\varepsilon }_{\mathrm{topo}}$ would be linked to the dynamical exponent ε if each collapse carried an energy equivalent to the size of the collapse. A complex correlation between $\varepsilon ,{\varepsilon }_{\mathrm{topo}}$, and $H_{\mathrm{D}}$ emerges, depending strongly on the relative occupancy of the collapse sites in the simulation box.

We investigate an asymptotic expansion of the solution of the master equation under the modulation of control parameters. In this case, the nondecaying part of the solution becomes the dynamical steady state expressed as an infinite series using the pseudoinverse of the Liouvillian, whose convergence is not granted in general. We demonstrate that for the relaxation time approximation model, the Borel summation of the infinite series is compatible with the exact solution. By exploiting the series expansion, we obtain the analytic expression of the heat and the activity. In the two-level system coupled to a single bath, under the linear modulation of the energy as a function of time, we demonstrate that the infinite series expression is the asymptotic expansion of the exact solution. The equality of a trade-off relation between the speed of the state transformation and the entropy production [Shiraishi, Funo, and Saito, Phys. Rev. Lett. 121, 070601 (2018)] holds in the lowest order of the frequency of the energy modulation in the two-level system. To obtain this result, the heat emission and absorption at edges (the initial and end times) or the differences of the Shannon entropy between the instantaneous steady state and the dynamical steady state at edges are essential: If we ignore these effects, the trade-off relation can be violated.

The paper is devoted to the dynamics of dissipative gap solitons in the periodically corrugated optical waveguides whose spectrum of linear excitations contains a mode that can be referred to as a quasi-bound state in the continuum. These systems can support a large variety of stable bright and dark dissipative solitons that can interact with each other and with the inhomogeneities of the pump. One of the focus points of this work is the influence of slow variations of the pump on the behavior of the solitons. It is shown that for the fixed sets of parameters the effect of pump inhomogeneities on the solitons is not the same for the solitons of different kinds. The second main goal of the paper is systematic study of the interaction between the solitons of the same or different kinds. It is demonstrated that various scenarios of intersoliton interactions can occur: The solitons can repulse each other or get attracted. In the latter case, the solitons can annihilate, fuse in a single soliton, or form a new bound state depending on the kinds of the interacting solitons and on the system parameters.

We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, and the dynamics is governed by equations that usually describe food search of the paradigmatic Physarum polycephalum. In this work we assume that the two paths undergo damping whose relative strength is periodically modulated in time, and we analyze the dynamics in the presence of stochastic forces simulating Gaussian noise. We identify different responses depending on the modulation frequency and on the noise amplitude. At frequencies smaller than the mean dissipation rate, the system tends to switch to the path which minimizes dissipation. Synchronous switching occurs at an optimal noise amplitude which depends on the modulation frequency. This behavior disappears at larger frequencies, where the dynamics can be described by the time-averaged equations. Here we find metastable patterns that exhibit the features of noise-induced resonances.

We investigate the topological excitations of half-quantum vortices (HQVs) with higher topological quantum numbers in a homogeneous spinor exciton-polariton condensate pumped by a laser beam and an additional coherent light carrying orbital angular momentum. The spin texture and integrated topological charge can be controlled through the pump. Among these textures, the polaritonic half-skyrmions (or polaritonic merons) can be created with a suitable excitation condition. Moreover, when the pump polarization is in favor of the vortex component of the HQV, there is an inversion of circular polarization (spin flipping) from the center of the HQV towards the edge. The radial flipping position can be manipulated by the pump polarization or power. Finally, we demonstrate that the HQVs can stably exist from the linear stability analysis.

This paper introduces the notion of comodularity, to cocluster observations of bipartite networks into co-communities. The task of coclustering is to group together nodes of one type with nodes of another type, according to the interactions that are the most similar. The measure of comodularity is introduced to assess the strength of co-communities, as well as to arrange the representation of nodes and clusters for visualization, and to define an objective function for optimization. We demonstrate the usefulness of our proposed methodology on simulated data, and with examples from genomics and consumer-product reviews.

The challenges presented by the COVID-19 epidemic have created a renewed interest in the development of new methods to combat infectious diseases, and it has shown the importance of preparedness for possible future diseases. A prominent property of the SARS-CoV-2 transmission is the significant fraction of asymptomatic transmission. This may influence the effectiveness of the standard contact tracing procedure for quarantining potentially infected individuals. However, the effects of asymptomatic transmission on the epidemic threshold of epidemic spreading on networks have rarely been studied explicitly. Here we study the critical percolation transition for an arbitrary disease with a nonzero asymptomatic rate in a simple epidemic network model in the presence of a recursive contact tracing algorithm for instant quarantining. We find that, above a certain fraction of asymptomatic transmission, standard contact tracing loses its ability to suppress spreading below the epidemic threshold. However, we also find that recursive contact tracing opens a possibility to contain epidemics with a large fraction of asymptomatic or presymptomatic transmission. In particular, we calculate the required fraction of network nodes participating in the contact tracing for networks with arbitrary degree distributions and for varying recursion depths and discuss the influence of recursion depth and asymptomatic rate on the epidemic percolation phase transition. We anticipate recursive contact tracing to provide a basis for digital, app-based contact tracing tools that extend the efficiency of contact tracing to diseases with a large fraction of asymptomatic transmission.