We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we calculate the bi-invariant cost associated with these time-dependent Hamiltonians by suitably regularizing their norms and obtain analytical expressions of the costs for several well-known time-dependent quantum mechanical systems. In particular, we show that an equivalence exists between the total costs of obtaining an operator through time evolution generated by a unit mass harmonic oscillator whose frequency depends on time, and a harmonic oscillator whose both mass and frequency are functions of time. These results are illustrated with several examples, including a specific smooth quench protocol where the comparison of time variation of the cost with other information theoretic quantities, such as the Shannon entropy, is discussed.

Existing experiments demonstrated that constant light has either enhancing or diminishing effects on the behavioral rhythms of mammals, sparking our intense interest in the underlying mechanisms of this paradoxical phenomenon. The influence of constant light on behavioral rhythms involves the regulation of collective neuronal behavior. The robustness of behavioral rhythms stems from the synchronization of neurons. In mammals, the synchronization among neurons is regulated by the suprachiasmatic nucleus (SCN) located in the hypothalamus. Neurons within the SCN exhibit significant heterogeneity. The intrinsic frequency and coupling strength are two fundamental characteristics determining the internal dynamics of the SCN. In this study, the Poincaré model was employed to investigate the impact of constant light on SCN neuronal dynamics. We found that constant light can modulate neuronal synchronization, a phenomenon tightly linked to the critical threshold value of coupling strength among the neurons. Specifically, under weak coupling, constant light enhances neuronal synchronization. Under strong coupling, constant light weakens synchronization among oscillators. Furthermore, higher light intensity results in lengthened periods and reduced amplitudes. Our findings elucidate important underlying mechanisms by which constant light either enhances or diminishes mammalian behavioral rhythms, and provide a new perspective for understanding the complex regulation network of circadian rhythms.

Interactions between organisms are mediated by an intricate network of physico-chemical substances and other organisms. Understanding the dynamics of mediators and how they shape the population spatial distribution is key to predict ecological outcomes and how they would be transformed by changes in environmental constraints. However, due to the inherent complexity involved, this task is often unfeasible, from the empirical and theoretical perspectives. In this paper, we make progress in addressing this central issue, creating a bridge that provides a two-way connection between the features of the ensemble of underlying mediators and the wrinkles in the population density induced by a landscape defect (or spatial perturbation). The bridge is constructed by applying the Feynman-Vernon decomposition, which disentangles the influences among the focal population and the mediators in a compact way. This is achieved through an interaction kernel, which effectively incorporates the mediators' degrees of freedom, explaining the emergence of nonlocal influence between individuals, an ad hoc assumption in modeling population dynamics. Concrete examples are worked out and reveal the complexity behind a possible top-down inference procedure.

The effects of nonuniformities in axonal connectivity on natural modes of brain activity are explored to determine their contributions to modal eigenvalues, structure, and communication and to clarify the limits of validity of widely used uniform-connectivity approximations. Preferred channels of communication are demonstrated that are supported by natural modes of mean connectivity and resulting activity. The effects of axonal tracts on these modes are calculated using perturbation methods, and it is found that modes and their spectra are only moderately perturbed by even the largest white matter tracts. However, perturbations of activity are greatly magnified when modes are near-critical and realistic connectivity and gain perturbations can then enable rapid responses to stimuli on the observed timescales of evoked responses. It is thus argued that dynamic mode-mode communication channels complement ones based on white matter tracts and that both rely on near-criticality to have their observed effects.

Starting from the reported experimental evidence that the residence time of contacts between the ends of biopolymers is length dependent, we investigate the kinetics of contact breaking in simple polymer models from a theoretical point of view. We solved Kramers equation first for an ideal chain and then for a polymer with attracting ends, and compared the predictions with the results of molecular dynamics simulations. We found that the mean residence time always shows a power-law dependence on the length of the polymer with exponent $-1$, although it is significantly smaller when obtained from the analysis of a single trajectory than when calculated from independent initial conformations. Only when the interaction is strong ($\gg kT$) and the interaction range is small (of the order of the distance between consecutive monomers) does the residence time converge to that of the Arrhenius equation, independent of the length. We are able to provide expressions of the mean residence time for cases when the exact definition of contact is not available a priori, expressions that can be useful in typical cases of microscopy experiments.

Hydrodynamics of surfactant monolayers are governed by surface tension, surface shear viscosity, surface dilatational viscosity, and surface diffusivity. While the first two have been studied comprehensively with consistent results, surface dilatational viscosity is plagued with anomalies, including apparent negative values. Here, full-field interfacial velocity measurements together with the Navier-Stokes equations reveal that a source of these anomalies is the use of equilibrium surface diffusivity for systems far from equilibrium. Specifically, surface diffisivity was found to be more than seven orders of magnitude (ten million times) larger in a nonsolenoidal interfacial flow field. Micron-sized phase domains in the monolayer are the likely culprit for the enhanced diffusivity.

Dynamical trapping occurs when the duration of time spent in specific regions of phase space increases, often associated with stickiness around invariant islands during manifold crossings. This paper introduces the Hurst exponent as a tool to characterize the dynamics of a typical quasiintegrable Hamiltonian system with coexisting regular and chaotic regions. Beyond detecting chaotic orbits and sticky regions, applying a finite-time analysis reveals a multimodal distribution of the finite-time Hurst exponent, where each mode corresponds to motion around islands of different hierarchical levels. The advantage of the Hurst exponent method over other standard techniques lies in its ability to quickly indicate chaotic dynamical structures. It effectively distinguishes between quasiperiodic and chaotic orbits temporarily trapped in sticky domains using very short trajectories. Additionally, since it operates based on time series data, it facilitates the exploration of trapping effects in dynamic systems that lack well-defined laws, a common scenario in natural dynamics.

Wave dynamics in disordered open media is an intriguing topic and has lately attracted a lot of attention in non-Hermitian physics, especially in photonics. In fact, spatial distributions of gain and loss elements are physically possible in the context of integrated photonic waveguide arrays. In these type of lattices, counterintuitive quantized jumps along the propagation direction appear in the strong disorder limit (where all eigenstates are localized), and they have also been recently experimentally observed. We systematically study the non-Hermitian quasiperiodic Aubry-André-Harper model with on-site gain and loss distribution, with an emphasis on the spectral sensitivity based on pseudospectra analysis. Moreover, diffraction dynamics and the quantized jumps as well as the effect of saturable nonlinearity are investigated in detail. In this paper, we reveal the intricate relation between the nonlinearity and non-hermiticity.

In this study, we explore transfer entropy (TE) as a tool to explore the evolution of population contact patterns in epidemic processes. Initially, we apply TE to a classical age-stratified SIR model and find that the inferred patterns align with the interaction structure of the population, as defined by the age-mixing matrix. Applying this methodology to the COVID-19 pandemic data from Spain, we illustrate how TE can capture temporal changes in individual behavior. Furthermore, we demonstrate that incorporating the inherent dynamics of the epidemic process allows us to create a coarse-grained representation of the time series, providing richer information than raw data. We argue that this macro-level perspective is enhanced by the effectiveness of causal analysis across different scales. Our findings underscore the potential of informational approaches to retrospectively track behavioral adaptations during a pandemic, offering valuable insights for tailoring strategies to control disease spread. This paper paves the way for future research into using such methods for model-free estimation of contact patterns during pandemics.

We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second dispersion, we calculate the conditional probability density functional in the leading and next-to-leading order in the dimensionless second dispersion parameter associated with the input signal bandwidth. Taking into account the specific filtering of the output signal by the output signal receiver, we calculate the mutual information in the leading and next-to-leading order in the dispersion parameter and at large signal-to-noise ratio ($\mathrm{SNR}$). Further, we find the explicit analytical expression for the mutual information in the case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal. We explain the behavior of the mutual information as a function of the average input signal power and the input signal bandwidth in connection with the frequency broadening in the presence of small dispersion.

We study large fluctuations of the current in a Dyson gas, a one-dimensional system of particles interacting through a logarithmic potential and subjected to random noise. We adapt the macroscopic fluctuation theory to the Dyson gas and derive two coupled partial differential equations describing the evolution of the density and momentum. These equations are nonlinear and nonlocal, and the "boundary" conditions are mixed: some at the initial and others at the final time. If the initial condition can fluctuate (annealed setting), this boundary-value problem is tractable. We compute the cumulant generating function encoding all the cumulants of the current.

We consider the critical behavior of two-dimensional Potts models in the presence of a bond disorder in which the correlation decays as a power law. In some recent work the thermal sector of this theory was investigated by a renormalization group computation based on perturbed conformal field theory. Here we apply the same approach to study instead the magnetic sector. In particular, we compute the leading corrections to the Potts spin scaling dimension. Our results include as a special case the long-range disorder Ising model. We compare our prediction to Monte Carlo simulations. Finally, by studying the magnetization scaling function, we show a clear numerical evidence of a cross-over between the long-range and the short-range class of universality.

We present a comprehensive numerical study of dynamic phase transitions in the two-dimensional kinetic Ising model under a nonantisymmetric time-dependent magnetic field including a sinusoidal term and a second harmonic component. We demonstrate that the expected antisymmetric property and the scaling behavior of the order parameter are maintained using the recently proposed generalized conjugate field approach. Via a detailed finite-size scaling analysis we compute, for zero-bias field, the set of critical exponents suggesting that the Ising universality class is conserved, even in the absence of half-wave antisymmetry in the time-dependent magnetic field. Our results verify up-to-date experimental observations and provide a deeper understanding of nonequilibrium phase transitions, establishing a broader framework for exploring symmetry-breaking phenomena in driven magnetic systems.

We explore the critical properties of the recently discovered finite-time dynamical phase transition in the nonequilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the relaxation dynamics and it occurs at a sharp critical time. While previous works have focused either on mean-field interactions or on investigating the critical time, we analyze the critical fluctuations at the phase transition in the nearest-neighbor Ising model on a square lattice using Monte Carlo simulations. By means of a finite-size scaling analysis, we extract the critical exponents for the transition. In two spatial dimensions, we find that the exponents are consistent with those of the two-dimensional Ising universality class when the system is initially in the vicinity of the critical point. For initial temperatures below the critical one, however, the critical exponents differ from the Ising-exponents, indicating a distinct dynamical critical phenomenon.

Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a theoretical framework still remains to be developed to understand species-level dynamical heterogeneity within a given community, hampering real-world ecosystems' theoretical assessment and management. Here, we consider empirical plant-pollinator mutualistic networks, additionally including all-to-all intragroup competition, where species abundance evolves under a Lotka-Volterra-type equation. Setting the strengths of competition and mutualism to be uniform, we investigate how individual species persist or go extinct under varying these interaction strengths. By taking a dynamical systems approach, we meticulously study how increments in these interactions create particular sequences of extinctions and find the interaction strengths threshold values in which multistability arises. Hence, we are able to elucidate interaction strength regimes where, depending on the initial abundances of the species, different extinction scenarios arise within an ecological network.

We present analytical and numerical investigations of the size and shape evolution of localized disturbances during their propagation in elastic media (furthermore, we refer to this process as energy dispersion). We consider two models of media: the continuum, described by the multidimensional wave equation, and the simple scalar harmonic lattice. The presented research is based on the energy dynamics approach. We describe the evolution of the disturbance by the concept of the energy ellipsoid, which characterizes the eigenvectors and eigenvalues of the second moment of the energy distribution. The wave packet is considered as an example of a localized disturbance. For this case, the time evolution of the energy ellipsoid is obtained. It is shown that the velocities and directions of the energy dispersion are determined by the second derivative of the dispersion relation with respect to the wave vector. The analytical results are numerically confirmed for the case of a square lattice. The obtained results demonstrate that both the propagation and the dispersion of the wave packet energy can be described analytically in the framework of the energy dynamics.

The interaction between a thin foil target and a circularly polarized laser light injected along an external magnetic field is investigated numerically by particle-in-cell simulations. A standing wave appears at the front surface of the target, overlapping the injected and partially reflected waves. Hot electrons are efficiently generated at the standing wave due to the relativistic two-wave resonant acceleration if the magnetic field amplitude of the standing wave is larger than the ambient field. A bifurcation occurs in the gyration motion of electrons, allowing all electrons with nonrelativistic velocities to acquire relativistic energy through the cyclotron resonance. The optimal conditions for the highest energy and the most significant fraction of hot electrons are derived precisely through a simple analysis of test-particle trajectories in the standing wave. Since the number of hot electrons increases drastically by many orders of magnitude compared to the conventional unmagnetized cases, this acceleration could be a great advantage in laser-driven ion acceleration and its applications.

There has been of significant interest lately in the study of electromagnetic (EM) waves interacting with magnetized plasmas. The variety of resonances and the existence of several pass and stop bands in the dispersion curve for different orientations of the magnetic field offer new mechanisms of EM wave energy absorption [1–3]. However, earlier studies have investigated only special cases of magnetized plasma geometry [e.g., RL mode $\left(\vec{k}\right||{\vec{B}}_{\mathrm{ext}}$) or $(\vec{k}\perp {\vec{B}}_{\mathrm{ext}})$ X,O-mode configuration]. In these specific cases, EM waves encounter specific resonances [e.g., for $(\theta =0)$ cyclotron resonances, and for $(\theta =\pi /2)$, hybrid resonances]. A general case of EM wave propagation is at an oblique angle with respect to the externally applied magnetic field ${\vec{B}}_{\mathrm{ext}}$ considered here. Furthermore, the magnetic field is chosen to be inhomogeneous such that the EM wave pulse encounters a resonance layer within the plasma medium. A 2D particle-in-cell (PIC) simulation using the OSIRIS 4.0 platform has been carried out for these studies. A significant enhancement in absorption leading to almost complete absorption of laser energy by the plasma has been observed. A detailed study characterizing the role of the external magnetic field profile, EM wave intensity, etc., has also been carried out.

Rogue waves, presented in numerous fields of science, are attracting significant attention. We study the excitation of electromagnetic rogue waves in magnetized plasmas caused by the thermal electron anisotropic loss cone distribution. The Krylov-Bogoliubov-Mitropolsky method is used to derive the nonlinear Schrödinger equation (NLSE) from collisionless magnetohydrodynamics equations satisfied by electrons. By solving numerically the one-dimensional NLSE, the rogue waves can be excited owing to their association with modulational instability. We can obtain the initial magnetic field conditions necessary for the excitation of electromagnetic rogue waves from the plane wave solution satisfied by the vector potential. Meanwhile, we apply a 2.5D fully kinetic particle-in-cell (PIC) method to simulate the excitation of electromagnetic rogue waves in magnetized plasmas. The PIC simulation results show that the excitation of electromagnetic rogue waves is primarily caused by the instability of the transverse perturbation components.