We investigate the extent to which the probabilistic properties of chaotic scattering systems with dissipation can be understood from the properties of the dissipation-free system. For large energies, a fully chaotic scattering leads to an exponential decay of the survival probability $P\left(t\right)\sim e^{-\kappa t}$, with an escape rate $\kappa$ that decreases with energy. Dissipation leads to the appearance of different finite-time regimes in $P\left(t\right)$. We show how these different regimes can be understood for small dissipations and long times from the (effective) escape rate $\kappa$ (including the nonhyperbolic regime) of the conservative system, until the energy reaches a critical value at which no escape is possible. More generally, we argue that for small dissipation and long times the surviving trajectories in the dissipative system are distributed according to the conditionally invariant measure of the conservative system at the corresponding energy. Quantitative predictions of our general theory are compared with numerical simulations in the Hénon-Heiles model.

A simple model of water, called the rose model, is used in this work. The rose model is a very simple model that can provide insight into the anomalous properties of water. In the rose water model, the molecules are represented as two-dimensional Lennard-Jones disks with potentials for orientation-dependent pairwise interactions mimicking formations of hydrogen bonds. We have recently applied a Wertheim integral equation theory (IET) and a thermodynamic perturbation theory (TPT) to the rose model in bulk. These analytical theories offer the advantage of being computationally less intensive than computer simulations by orders of magnitudes. Here we have applied the TPT to study the transfer of a nonpolar solute into rose water, the so-called hydrophobic effect. Similarly as in our previous work for bulk water, we have found that the theory reproduces the computer simulation results quite well at higher temperatures, while the theories predict the qualitative trends at low temperatures.

Krylov complexity is an important dynamical quantity with relevance to the study of operator growth and quantum chaos and has recently been much studied for various time-independent systems. We initiate the study of K complexity in time-dependent (driven) quantum systems. For periodic time-dependent (Floquet) systems, we develop a natural method for doing the Krylov construction and then define (state and operator) K complexity for such systems. Focusing on kicked systems, in particular the quantum kicked rotor on a torus, we provide a detailed numerical study of the time dependence of Arnoldi coefficients as well as of the K complexity with the system coupling constant interpolating between the weak and strong coupling regimes. We also study the growth of the Krylov subspace dimension as a function of the system coupling constant.

Understanding how local traffic congestion spreads in urban traffic networks is fundamental to solving congestion problems in cities. In this work, by analyzing the high-resolution data of traffic velocity in Seoul, we empirically investigate the spreading patterns and cluster formation of traffic congestion in a real-world urban traffic network. To do this, we propose a congestion identification method suitable for various types of interacting traffic flows in urban traffic networks. Our method reveals that congestion spreading in Seoul may be characterized by a treelike structure during the morning rush hour but a more persistent loop structure during the evening rush hour. Our findings suggest that diffusion and stacking processes of local congestion play a major role in the formation of urban traffic congestion.

In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance matrices, without knowledge of the true covariance matrix. In this study, we demonstrate that this minimization problem is equivalent to minimizing the loss of information between the true population covariance and the rotational invariant estimator for normal multivariate variables. However, for Student's $t$ distributions, the minimal Frobenius norm does not necessarily minimize the information loss in finite-sized matrices. Nevertheless, such deviations vanish in the asymptotic regime of large matrices, which might extend the applicability of random matrix theory results to Student's $t$ distributions. These distributions are characterized by heavy tails and are frequently encountered in real-world applications such as finance, turbulence, or nuclear physics. Therefore, our work establishes a connection between statistical random matrix theory and estimation theory in physics, which is predominantly based on information theory.

We have studied in detail the $M\text{−}p$ balanced spin-glass model, especially the case $p=4$. These types of model have relevance to structural glasses. The models possess two kinds of broken replica states; those with one-step replica symmetry breaking (1RSB) and those with full replica symmetry breaking (FRSB). To determine which arises requires studying the Landau expansion to quintic order. There are nine quintic-order coefficients, and five quartic-order coefficients, whose values we determine for this model. We show that it is only for $2\le M<2.4714\cdots$ that the transition at mean-field level is to a state with FRSB, while for larger $M$ values there is either a continuous transition to a state with 1RSB (when $M\le 3$) or a discontinuous transition for $M>3$. The Gardner transition from a 1RSB state at low temperatures to a state with FRSB also requires the Landau expansion to be taken to quintic order. Our result for the form of FRSB in the Gardner phase is similar to that found when $2\le M<2.4714\cdots$, but differs from that given in the early paper of Gross et al. [Phys. Rev. Lett. 55, 304 (1985)]. Finally we discuss the effects of fluctuations on our mean-field solutions using the scheme of Höller and Read [Phys. Rev. E 101, 042114 (2020)] and argue that such fluctuations will remove both the continuous 1RSB transition and discontinuous 1RSB transitions when $8>d\ge 6$ leaving just the FRSB continuous transition. We suggest values for $M$ and $p$ which might be used in simulations to confirm whether fluctuation corrections do indeed remove the 1RSB transitions.

A thermal diode or rectifier is a system that transmits heat or energy in one direction better than in the opposite direction. We investigate the influence of the distribution of energy among wave numbers on the diode effect for the junction of two dissimilar harmonic chains. An analytical expression for the diode coefficient, characterizing the difference between heat fluxes through the junction in two directions, is derived. It is shown that the diode coefficient depends on the distribution of energy among wave numbers. For an equilibrium energy distribution, the diode effect is absent, while for non-equilibrium energy distributions the diode effect is observed even though the system is harmonic. We show that the diode effect can be maximized by varying the energy distribution and relative position of spectra of the two harmonic chains. Conditions are formulated under which the system acts as an ideal thermal rectifier, i.e., transmits heat only in one direction. The results obtained are important for understanding the heat transfer in heterogeneous low-dimensional nanomaterials.

We are exploring in experiments the aggregation process in a shaken granular mixture of glass and magnetized steel beads, filled in a horizontal vessel, after the shaking amplitude is suddenly decreased. Then the magnetized beads form a transient network that coarsens in time into compact clusters, resembling a viscoelastic phase separation [Tanaka, J. Phys.: Condens. Matter 12, R207 (2000)], where attached beads represent the slow phase. Here we investigate how a homogeneous magnetic field oriented in vertical direction impedes the emergence and growth of the networks. With increasing field amplitude this phase is replaced by a fluctuating arrangement of repelling, isolated steel beads. The experimental results are compared with those of computer simulations. Coarse-grained molecular dynamics confirms the impact of an applied magnetic field on the structural transitions and allows us to investigate long-time regimes and magnetic response not yet accessible in the experiment. It turns out that an applied magnetic field has different impacts, depending on it strength. It can be used either to slow down the dynamics of the structural transitions without changing the type of the resulting phases and only affecting the amount and sizes of clusters, or to fully impede the formation of network-like and compact aggregates of steel beads.

Since the characteristic timescales of the various transport processes inside the discharge plasma span several orders of magnitude, it can be regarded as a typical fast-slow system. Interestingly, in this work, a special kind of complex oscillatory dynamics composed of a series of large-amplitude relaxation oscillations and small-amplitude near-harmonic oscillations, namely, mixed-mode oscillations (MMOs), was observed. By using the ballast resistance as the control parameter, a period-adding bifurcation sequence of the MMOs, i.e., from $L^s$ to $L^{s+1}$, was obtained in a low-pressure DC glow discharge system. Meanwhile, a series of intermittently chaotic regions caused by inverse saddle-node bifurcation was embedded between the two adjacent periodic windows. The formation mechanism of MMOs was analyzed, and the results indicated that the competition between electron production and electron loss plays an important role. Meanwhile, the nonlinear time series analysis technique was used to study the dynamic behavior quantitatively. The attractor in the reconstructed phase space indicated the existence of the homoclinic orbits of type ${\mathrm{\Gamma }}^{-}$. In addition, by calculating the largest Lyapunov exponent (LLE), the chaotic nature of these states was confirmed and quantitatively characterized. With the decrease in the ballast resistance, the return map of the chaotic state gradually changed from the nearly one-dimensional single-peak structure to the multibranch structure, which indicates that the dissipation of the system decreased. By further calculating the correlation dimension, it was shown that the complexity of the strange attractors increased for higher-order chaotic states.

We present measurements of the temporal decay rate of one-dimensional (1D), linear Langmuir waves excited by an ultrashort laser pulse. Langmuir waves with relative amplitudes of approximately $6\%$ were driven by $1.7\mathrm{J}$, $50\mathrm{fs}$ laser pulses in hydrogen and deuterium plasmas of density $n_{e0}=8.4\times {10}^{17}{\mathrm{cm}}^{-3}$. The wakefield lifetimes were measured to be ${\tau }_{\mathrm{wf}}^{{\mathrm{H}}_2}=(9\pm 2)$ ps and ${\tau }_{\mathrm{wf}}^{{\mathrm{D}}_2}=(16\pm 8)$ ps, respectively, for hydrogen and deuterium. The experimental results were found to be in good agreement with 2D particle-in-cell simulations. In addition to being of fundamental interest, these results are particularly relevant to the development of laser wakefield accelerators and wakefield acceleration schemes using multiple pulses, such as multipulse laser wakefield accelerators.

We present improved first-principle fermionic path integral Monte Carlo (PIMC) simulation results for a dense partially ionized hydrogen (deuterium) plasma, for temperatures in the range $15000\mathrm{K}\le T\le 400000\mathrm{K}$ and densities $7\times {10}^{-7}\mathrm{g}/{\mathrm{cm}}^3\le {\rho }_H\le 0.085\mathrm{g}/{\mathrm{cm}}^3$ ($1.4\times {10}^{-6}\mathrm{g}/{\mathrm{cm}}^3\le {\rho }_D\le 0.17\mathrm{g}/{\mathrm{cm}}^3$), corresponding to $100\ge r_s\ge 2$, where $r_s=\overline{r}/a_B$ is the ratio of the mean interparticle distance to the Bohr radius. These simulations are based on the fermionic propagator PIMC (FP-PIMC) approach in the grand canonical ensemble [Filinov et al., Contrib. Plasma Phys. 61, e202100112 (2021)] and fully account for correlation and quantum degeneracy and spin effects. For the application to hydrogen and deuterium, we develop a combination of the fourth-order factorization and the pair product ansatz for the density matrix. Moreover, we avoid the fixed node approximation that may lead to uncontrolled errors in restricted PIMC (RPIMC). Our results allow us to critically reevaluate the accuracy of the RPIMC simulations for hydrogen by Hu et al. [Phys. Rev. B 84, 224109 (2011)] and of various chemical models. The deviations are generally found to be small, but for the lowest temperature, $T=15640$ K they reach several percent. We present detailed tables with our first principles results for the pressure and energy isotherms. We expect our updated results will serve as a valuable benchmark for comparison with other methods.

Causal analysis plays a significant role in physics, chemistry, and biology. Dynamics of complex (bio)molecular and nanosystems, from the microscopic to the macroscopic scale, are characterized by time-dependent vectors such as positions, forces, momenta, angular momenta, or torques. Identification and analysis of causal relationships between these time-dependent signals is an important problem in the multidimensional time-series analysis and is of great practical importance in describing the properties of such dynamical systems, and to understanding their functionality. For linear stochastic systems characterized by multidimensional scalar signals, Granger proposed a simple procedure to detect causal relationships, called Granger causality. In this study we extended this formalism to vector signals representing physical vector quantities. For this purpose, we used quaternion algebra, where vector signals are treated as time-dependent quaternions. The developed analytical model is based on the autoregressive formalism. This formalism (Q-MVAR) and its numerical implementation were validated using two simple dynamic models: a rigid body model represented by a benzenelike molecular fragment, interacting with a short-range harmonic potential with a wall, as well as a system of three model atomic balls moving inside a soft spherical surface and interacting with long range electrostatic forces. Although the motivation to these studies was the analysis of classical motions in complex (bio)molecular systems, described with a mechanical model and based on molecular dynamics (MD) simulations, in particular coarse-grained ones, it should be noted that the developed extended formalism can be applied to any system composed of many rigid elements that interact with arbitrary potentials and are characterized by complex internal motions. A description of the detailed procedure for calculating causality measures is provided in the Appendices of the Supplemental Material. This formalism and the prototype of its numerical implementation can be further developed and applied in many different fields of physical, natural, and engineering sciences.

We present exact results for the fluctuations in the number of particles crossing the origin up to time $t$ in a collection of noninteracting run and tumble particles in one dimension. In contrast to passive systems, such active particles are endowed with two inherent degrees of freedom, positions and velocities, which can be used to construct density and magnetization fields. We introduce generalized disorder averages associated with both these fields and perform annealed and quenched averages over various initial conditions. We show that the variance ${\sigma }^2$ of the current in annealed versus quenched magnetization situations exhibits a surprising difference at short times, ${\sigma }^2\sim t$ vs ${\sigma }^2\sim t^2$, respectively, with a $\sqrt{t}$ behavior emerging at large times. Our analytical results demonstrate that in the strictly quenched scenario, where both the density and magnetization fields are initially frozen, the fluctuations in the current are strongly suppressed. Importantly, these anomalous fluctuations cannot be obtained solely by freezing the density field.

Substances with a complex electronic structure exhibit non-Drude optical properties that are challenging to interpret experimentally and theoretically. In our recent paper [Phys. Rev. E 105, 035307 (2022)], we offered a computational method based on the continuous Kubo-Greenwood formula, which expresses dynamic conductivity as an integral over the electron spectrum. In this Letter, we propose a methodology to analyze the complex conductivity using liquid Zr as an example to explain its nontrivial behavior. To achieve this, we apply the continuous Kubo-Greenwood formula and extend it to include the imaginary part of the complex conductivity into the analysis. Our method is suitable for a wide range of substances, providing an opportunity to explain optical properties from ab initio calculations of any difficulty.

In this work we analyze an Otto-type cycle operating with a working substance composed of a quantum harmonic oscillator (QHO). Unlike other studies in which the work extraction is done by varying the frequency of the QHO and letting it thermalize with a squeezed reservoir, here we submit the QHO to a parametric pumping controlled by the squeezing parameter and let it thermalize with a thermal reservoir. We then investigate the role of the squeezing parameter in our Otto-type engine powered by parametric pumping and show that it is possible to reach the Carnot limit by arbitrarily increasing the squeezing parameter. Notably, for certain squeezing parameters $r$, e.g., $r=0.4$, the quasistatic Otto limit can be reached even at nonzero power. We also investigated the role of entropy production in the efficiency behavior during the unitary strokes, showing that positive (negative) changes in entropy production correspond to increases (decreases) in engine efficiency, as expected. Furthermore, we show that under thermal reservoirs a work extraction process that is more efficient than the Carnot engine is impossible, regardless of the quantum resource introduced via the Hamiltonian of the system.

We point out that a classical analog of the Sachdev-Ye-Kitaev (SYK) model, a solvable model of quantum many-body chaos, was studied long ago in the turbulence literature. Motivated by the Navier-Stokes equation in the turbulent regime and the nonlinear Schrödinger equation describing plasma turbulence, in which there is mixing between many different modes, the random coupling model has a Gaussian-random coupling between any four of a large number $N$ of modes. The model was solved in the 1960s, before the introduction of large-$N$ path-integral techniques, using a method referred to as the direct interaction approximation. We use the path integral to derive the effective action for the model. The large-$N$ saddle gives an integral equation for the two-point function, which is very similar to the corresponding equation in the SYK model. The connection between the SYK model and the random coupling model may, on the one hand, provide new physical contexts in which to realize the SYK model and, on the other hand, suggest new models of turbulence and techniques for studying them.

In our previous study [N. Tsutsumi, K. Nakai, and Y. Saiki, Chaos 32, 091101 (2022)] we proposed a method of constructing a system of ordinary differential equations of chaotic behavior only from observable deterministic time series, which we will call the radial-function-based regression (RfR) method. The RfR method employs a regression using Gaussian radial basis functions together with polynomial terms to facilitate the robust modeling of chaotic behavior. In this paper, we apply the RfR method to several example time series of high- or infinite-dimensional deterministic systems, and we construct a system of relatively low-dimensional ordinary differential equations with a large number of terms. The examples include time series generated from a partial differential equation, a delay differential equation, a turbulence model, and intermittent dynamics. The case when the observation includes noise is also tested. We have effectively constructed a system of differential equations for each of these examples, which is assessed from the point of view of time series forecast, reconstruction of invariant sets, and invariant densities. We find that in some of the models, an appropriate trajectory is realized on the chaotic saddle and is identified by the stagger-and-step method.

Traffic congestion is a major problem in megacities which increases vehicle emissions and degrades ambient air quality. Various models have been developed to address the universal features of traffic jams. These models range from microscopic car-following models to macroscopic collective dynamic models. Here, we study the macrostructure of congested traffic influenced by the complex geometry of the commute. Our main focus is on the dynamics of traffic patterns in Paris and Los Angeles, each with distinct urban structures. We analyze the complexity of the giant traffic clusters based on a percolation framework during rush hours in the mornings, evenings, and holidays. We uncover that the universality described by several critical exponents of traffic patterns is highly correlated with the geometry of commute and the underlying urban structure. Our findings might have broad implications for developing a greener, healthier, and more sustainable future city.

Pancreatic beta cells are coupled excitable oscillators that synchronize their activity via different communication pathways. Their oscillatory activity manifests itself on multiple timescales and consists of bursting electrical activity, subsequent oscillations in the intracellular ${\mathrm{Ca}}^{2+}$, as well as oscillations in metabolism and exocytosis. The coordination of the intricate activity on the multicellular level plays a key role in the regulation of physiological pulsatile insulin secretion and is incompletely understood. In this paper, we investigate theoretically the principles that give rise to the synchronized activity of beta cell populations by building up a phenomenological multicellular model that incorporates the basic features of beta cell dynamics. Specifically, the model is composed of coupled slow and fast oscillatory units that reflect metabolic processes and electrical activity, respectively. Using a realistic description of the intercellular interactions, we study how the combination of electrical and metabolic coupling generates collective rhythmicity and shapes functional beta cell networks. It turns out that while electrical coupling solely can synchronize the responses, the addition of metabolic interactions further enhances coordination, the spatial range of interactions increases the number of connections in the functional beta cell networks, and ensures a better consistency with experimental findings. Moreover, our computational results provide additional insights into the relationship between beta cell heterogeneity, their activity profiles, and functional connectivity, supplementing thereby recent experimental results on endocrine networks.

When a solution of interpenetrating and entangled long flexible polymer chains is cooled to low enough temperatures, the chains crystallize into thin lamellae of nanoscopic thickness and microscopic lateral dimensions. Depending on the nature of the solvent and growth conditions, the lamellae exhibit several sectors that have differing growth kinetics and melting temperatures. Remarkably, these lamellae can spontaneously form tentlike morphology. The experimentally well-documented phenomenology of lamellar sectorization and tent formation has so far eluded a fundamental understanding of their origins. We present a theoretical model to explain this longstanding challenge and derive conditions for the relative stabilities of planar, sectored, and tent morphologies for polymer lamellae in terms of their elastic constants and interfacial tensions. While the present model offers an explanation of the origin of the spontaneous formation of sectored tentlike morphology as well as sectored planar morphology, in contrast to planar unsectored morphology, predictions are made for morphology transformations based on the materials properties of the polymeric lamellae.