A model based on optical Bloch equations is developed to describe the interaction of femtosecond laser pulses with dielectric solids, accounting for optical-cycle-resolved electron dynamics. It includes the main physical processes at play: photoionization, impact ionization, direct and collisional laser heating, and recombination. By using an electron band structure, this approach also accounts for material optical properties as nonlinear polarization response. Various studies are performed, shedding light on the contribution of various processes to the full electron dynamics depending on laser intensity and wavelength. In particular, the standard influence of the impact ionization process is retrieved.

We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable dynamical observable, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform. The general transformations of the dynamics that we consider go beyond time-reversal or spatial isometries, and an implication is the existence of FRs for observables irrespective of their behavior under time reversal, for example for time-symmetric observables rather than currents. We further show how to deduce in the long-time limit these FRs from the symmetry properties of the generator of the dynamics. We illustrate our results with four examples that highlight the novel features of our work.

We consider a percolation process in which $k$ points separated by a distance proportional the system size $L$ simultaneously connect together ($k>1$), or a single point at the center of a system connects to the boundary ($k=1$), through adjacent connected points of a single cluster. These processes yield new thresholds ${\overline{p}}_{ck}$ defined as the average value of $p$ at which the desired connections first occur. These thresholds not sharp, as the distribution of values of $p_{ck}$ for individual samples remains broad in the limit of $L\to \infty$. We study ${\overline{p}}_{ck}$ for bond percolation on the square lattice and find that ${\overline{p}}_{ck}$ are above the normal percolation threshold $p_c=1/2$ and represent specific supercritical states. The ${\overline{p}}_{ck}$ can be related to integrals over powers of the function $P_{\infty }\left(p\right)$ equal to the probability a point is connected to the infinite cluster; we find numerically from both direct simulations and from measurements of $P_{\infty }\left(p\right)$ on $L\times L$ systems that for $L\to \infty , {\overline{p}}_{c1}=0.51755\left(5\right), {\overline{p}}_{c2}=0.53219\left(5\right), {\overline{p}}_{c3}=0.54456\left(5\right)$, and ${\overline{p}}_{c4}=0.55527\left(5\right)$. The percolation thresholds ${\overline{p}}_{ck}$ remain the same, even when the $k$ points are randomly selected within the lattice. We show that the finite-size corrections scale as $L^{-1/{\nu }_k}$ where ${\nu }_k=\nu /(k\beta +1)$, with $\beta =5/36$ and $\nu =4/3$ being the ordinary percolation critical exponents, so that ${\nu }_1=48/41, {\nu }_2=24/23, {\nu }_3=16/17, {\nu }_4=6/7$, etc. We also study three-point correlations in the system and show how for $p>p_c$, the correlation ratio goes to 1 (no net correlation) as $L\to \infty$, while at $p_c$ it reaches the known value of $1.022$.

A method of windowed spatiotemporal spectral filtering is proposed to segregate different nonlinear wave components and to calculate the surface of free waves. The dynamic kurtosis (i.e., produced by the free wave component) is shown able to contribute essentially to the abnormally large values of the surface displacement kurtosis, according to the direct numerical simulations of realistic sea waves. In this situation the free wave stochastic dynamics is strongly non-Gaussian, and the kinetic equation for sea surface waves fails. Traces of coherent wave patterns are found in the Fourier transform of the directional irregular sea waves; they may form “jets” in the Fourier domain which strongly violate the classic dispersion relation.

The correlation diagrams of vibrational energy levels considering the Planck constant as a variable parameter have proven as a very useful tool to study vibrational molecular states, and more specifically in relation to the quantum manifestations of chaos in such dynamical systems. In this paper, we consider the highly nonlinear K-CN molecule, showing how the regular classical structures, i.e., Kolmogorov-Arnold-Moser tori, existing in the mixed classical phase space appear in the quantum levels correlation diagram as emerging diabatic states, something that remains hidden when only the actual value of the Planck constant is considered. Additionally, a quantum transition from order to chaos is unveiled with the aid of these correlation diagrams, where it appears as a frontier of scarred functions.

Cellular behaviors such as migration, division, and differentiation rely on precise timing, and yet the molecular events that govern these behaviors are highly stochastic. We investigate regulatory strategies that decrease the timing noise of molecular events. Autoregulatory feedback increases noise. Yet we find that in the presence of regulation by a second species, autoregulatory feedback decreases noise. To explain this finding, we develop a method to calculate the optimal regulation function that minimizes the timing noise. The method reveals that the combination of feedback and regulation minimizes noise by maximizing the number of molecular events that must happen in sequence before a threshold is crossed. We compute the optimal timing precision for all two-node networks with regulation and feedback, derive a generic lower bound on timing noise, and discuss our results in the context of neuroblast migration during Caenorhabditis elegans development.

Newton's third law—the action-reaction symmetry—can be violated for effective interbody forces in open and nonequilibrium systems that are ubiquitous in areas as diverse as complex plasmas, colloidal suspensions, active and living soft matter, and social behavior. While studying monolayer complex plasma (confined charged particles in an ionized gas) with nonreciprocal interactions mediated by plasma flows, in silico we found that an interplay between melting and thermal activation drastically transforms the collective dynamics: the order-disorder transition modifies the system's thermal steady state so that the crystal tends to melt, whereas the fluid tends to freeze, jumping chaotically between the two states. We identified this collective chaotic behavior as strange attractors formed in a monolayer complex plasma and link the strange attractor behavior to the specifics of interparticle interactions.

It is well established that ensembles of globally coupled stochastic oscillators may exhibit a nonequilibrium phase transition to synchronization in the thermodynamic limit (infinite number of elements). In fact, since the early work of Kuramoto, mean-field theory has been used to analyze this transition. In contrast, work that directly deals with finite arrays is relatively scarce in the context of synchronization. And yet it is worth noting that finite-number effects should be seriously taken into account since, in general, the limits $N\to \infty$ (where $N$ is the number of units) and $t\to \infty$ (where $t$ is time) do not commute. Mean-field theory implements the particular choice first $N\to \infty$ and then $t\to \infty$. Here we analyze an ensemble of three-state coupled stochastic units, which has been widely studied in the thermodynamic limit. We formally address the finite-$N$ problem by deducing a Fokker-Planck equation that describes the system. We compute the steady-state solution of this Fokker-Planck equation (that is, finite $N$ but $t\to \infty$). We use this steady state to analyze the synchronic properties of the system in the framework of the different order parameters that have been proposed in the literature to study nonequilibrium transitions.

We investigate eigenstate thermalization from the point of view of vanishing particle and heat currents between a few-body fermionic Hamiltonian prepared in one of its eigenstates and an external, weakly coupled Fermi-Dirac gas. The latter acts as a thermometric probe, with its temperature and chemical potential set so that there is neither particle nor heat current between the two subsystems. We argue that the probe temperature can be attributed to the few-fermion eigenstate in the sense that (i) it varies smoothly with energy from eigenstate to eigenstate, (ii) it is equal to the temperature obtained from a thermodynamic relation in a wide energy range, (iii) it is independent of details of the coupling between the two systems in a finite parameter range, (iv) it satisfies the transitivity condition underlying the zeroth law of thermodynamics, and (v) it is consistent with Carnot's theorem. For the spinless fermion model considered here, these conditions are essentially independent of the interaction strength. When the latter is weak, however, orbital occupancies in the few-fermion system differ from the Fermi-Dirac distribution so that partial currents from or to the probe will eventually change its state. We find that (vi) above a certain critical interaction strength, orbital occupancies become close to the Fermi-Dirac distribution, leading to a true equilibrium between the few-fermion system and the probe. In that case, the coupling between the Fermi-Dirac gas and few-fermion system does not modify the state of the latter, which justifies our approach a posteriori. From these results, we conjecture that for few-body systems with sufficiently strong interaction, the eigenstate thermalization hypothesis is complemented by ensemble equivalence: individual many-body eigenstates define a microcanonical ensemble that is equivalent to a canonical ensemble with grand canonical orbital occupancies.

Critical thinking and skepticism are fundamental mechanisms that one may use to prevent the spreading of rumors, fake news, and misinformation. We consider a simple model in which agents without previous contact with the rumor, being skeptically oriented, may convince spreaders to stop their activity or, once exposed to the rumor, decide not to propagate it as a consequence, for example, of fact checking. We extend a previous, mean-field analysis of the combined effect of these two mechanisms, active and passive skepticism, to include spatial correlations. This can be done either analytically, through the pair approximation, or simulating an agent-based version on diverse networks. Our results show that while in mean field there is no coexistence between spreaders and susceptibles (although, depending on the parameters, there may be bistability depending on the initial conditions), when spatial correlations are included, because of the protective effect of the isolation provided by removed agents, coexistence is possible.

Punishment has been considered as an effective mechanism for promoting and sustaining cooperation. In most existing models, punishment always comes as a third strategy alongside cooperation and defection, and it is commonly assumed to be executed based on individual decision rules rather than collective decision rules. Differently from previous works, we employ a democratic procedure by which cooperators cast votes independently and simultaneously for whether to impose punishment on defectors, and we establish a relationship between the cooperators' willingness to punish defectors (WTPD) and whether the punishment is inflicted on defectors. The results illustrate that the population can evolve to full cooperation under consensual punishment. It is noteworthy that, compared with autonomous punishment, whether consensual punishment is more in favor of cooperation crucially depends on the minimum number of votes required for punishment execution as well as the cooperators' WTPD. Our findings highlight the importance of collective decision making in the evolution of cooperation and may provide a mathematical framework for explaining the prevalence of democracy in modern societies.

We perform the state-of-the-art tensor network simulations directly in the thermodynamic limit to clarify the critical properties of the $q$-state clock model on the square lattice. We determine accurately the two phase transition temperatures through the singularity of the classical analog of the entanglement entropy, and provide extensive numerical evidences to show that both transitions are of the Berezinskii-Kosterlitz-Thouless (BKT) type for $q\ge 5$ and that the low-energy physics of this model is well described by the ${\mathbb{Z}}_q$-deformed sine-Gordon theory. We also determine the characteristic conformal parameters, especially the compactification radius, that govern the critical properties of the intermediate BKT phase.

We study lattice gas systems on the honeycomb lattice where particles exclude neighboring sites up to order $k$ ($k=1,...,5$) from being occupied by another particle. Monte Carlo simulations were used to obtain phase diagrams and characterize phase transitions as the system orders at high packing fractions. For systems with first-neighbors exclusion (1NN), we confirm previous results suggesting a continuous transition in the two-dimensional Ising universality class. Exclusion up to second neighbors (2NN) lead the system to a two-step melting process where, first, a high-density columnar phase undergoes a first-order phase transition with nonstandard scaling to a solidlike phase with short-range ordered domains and, then, to fluidlike configurations with no sign of a second phase transition. 3NN exclusion, surprisingly, shows no phase transition to an ordered phase as density is increased, staying disordered even to packing fractions up to 0.98. The 4NN model undergoes a continuous phase transition with critical exponents close to the three-state Potts model. The 5NN system undergoes two first-order phase transitions, both with nonstandard scaling. We, also, propose a conjecture concerning the possibility of more than one phase transition for systems with exclusion regions further than 5NN based on geometrical aspects of symmetries.

Progressive quenching (PQ) is the stochastic process in which the system's degrees of freedom are sequentially fixed. While such a process does not satisfy the local detailed balance, it has been found that the some physical observable of a complete spin network exhibits the martingale property. We studied the system's response to the perturbation given at intermediate stages of the PQ. The response at the final stage reveals the persistent memory, and we show that this persistence is a direct consequence of the martingale process behind it. Not only the mean response, the shape of the probability distribution at the stage of perturbation is also memorized. Using the hidden martingale process we can predict the final bimodal distribution from the early-stage unimodal distribution in the regime where the unfrozen spins are paramagnetic. We propose a viewpoint that the martingale property is a stochastic conservation law which is supported by some stochastic invariance.

The lack of thermodynamic consistency is a well-recognized problem in the single-component pseudopotential lattice Boltzmann models which prevents them from replicating accurate liquid and vapor phase densities; i.e., current models remain unable to exactly match coexisting density values predicted by the associated thermodynamic model. Most of the previous efforts had attempted to solve this problem by introducing tuning parameters, whose determination required empirical trial and error until acceptable thermodynamic consistency was achieved. In this study, we show that the problem can be alternatively solved by properly designing customized equations of state (EOSs) that replace any cubic EOS of choice during the computation of effective mass used in Shan-Chen forces. A two-parameter cubic-shaped customized EOS is introduced. Contrary to previous efforts, customization parameters in the new EOS are nonempirical and are rather derived from solving the integral mechanical stability equation, which neglects the need for any type of tuning for the attainment of rigorous thermodynamic consistency. The proposed approach reduces the errors of the coexisting densities and saturated pressure in the simulation to a maximum of $0.01\%$ within the liquid-vapor density ratio range from $O\left(1\right)$ to $O\left({10}^4\right)$, which had not been achieved in any of the previous tuning-based efforts. A straightforward way for achieving the desired surface tension via the customized EOS is also provided.

Quantifying how distinguishable two stochastic processes are is at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and ease of use. In this article, we suggest a set of requirements for a well-behaved measure of process distinguishability. Moreover, we propose a family of measures, called divergence rates, that satisfy all of these requirements. Focusing on a particular member of this family—the coemission divergence rate—we show that it can be computed efficiently, behaves qualitatively similar to other commonly used measures in their regimes of applicability, and remains well behaved in scenarios where other measures break down.

Anomalous diffusion is simulated in this paper by studying the transport of discrete solitons in a lattice with evolving disorder. We find a Richardson-type diffusion for the small solitons and a regime of transient diffusion for larger solitons within the ensemble-averaged description. As a comparison, the time-averaged observables present a ballistic scaling for both cases. However, distribution of these observables changes remarkably with the soliton size. Our results suggest violation of ergodicity for the solitons' diffusive processes, which are expected to shed light on further understanding of the discreteness-disorder-nonlinearity interaction.

We use the Hénon-Heiles system as a paradigmatic model for chaotic scattering to study the Lorentz factor effects on its transient chaotic dynamics. In particular, we focus on how time dilation occurs within the scattering region by measuring the time with a clock attached to the particle. We observe that the several events of time dilation that the particle undergoes exhibit sensitivity to the initial conditions. However, the structure of the singularities appearing in the escape time function remains invariant under coordinate transformations. This occurs because the singularities are closely related to the chaotic saddle. We then demonstrate using a Cantor-like set approach that the fractal dimension of the escape time function is relativistic invariant. In order to verify this result, we compute by means of the uncertainty dimension algorithm the fractal dimensions of the escape time functions as measured with an inertial frame and a frame comoving with the particle. We conclude that, from a mathematical point of view, chaotic transient phenomena are equally predictable in any reference frame and that transient chaos is coordinate invariant.