The particle-in-cell (PIC) and Monte Carlo collisions (MCC) methods are workhorses of many numerical simulations of physical systems. Recently, it was pointed out that, while the two methods can be exactly—or nearly—energy-conserving independently, combining the two leads to anomalous numerical heating. This paper reviews the standard explicit PIC-MCC algorithm, elucidates the origins of the anomalous numerical heating, and explains how to couple the two methods such that the anomalous numerical heating is avoided.

The role of long-range temporal correlations in kinetic roughening processes is significant, potentially influencing surface morphologies and dynamic scaling properties. This type of correlation, acting as a nonlocal interaction during growth processes, disrupts the self-affine fractal structure by causing the emergence of nontrivial global properties from individual local interactions. In this work, two typical discrete growth models, including random deposition and ballistic deposition, are investigated numerically in the presence of long-range temporal correlations. Two quantitative measurement methods, the Hellinger distance and the novelty detection, are used independently to determine whether emergence occurs. Our simulation results indicate that, above a critical threshold of temporal correlation exponent, the systems exhibit emergence behavior, consistent with the existence of nontrivial scaling properties and surface morphologies when long-range temporal correlations are presented.

We propose a stable charging scheme for a quantum battery in which the stable energy transfer of a noninteracting quantum charger-battery is induced by a common photonic band gap (PBG). By manipulating the transition frequency of the quantum battery to form multiple bound states, it is found that the capability of stable charging can be obtained without direct interaction between the quantum battery and the quantum charger. Among them, the formation of two bound states results in a lossless Rabi-like oscillatory behavior of the energy exchange. The formation of three bound states leads to a continuous collapse-revival process based on the oscillation of the stored energy. Particularly, the formation of three bound states also significantly enhances the energy extraction capability of the quantum battery. In addition, the stable charging scheme proposed in this paper can be further optimized from the perspective of environmental engineering. The expansion of the forbidden band gap width of the PBG environment not only enlarges the regulatory region for the formation of multiple bound states but also improves energy storage and extraction work.

We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schrödinger equation. The quantum system is initialized with local random uncorrelated Gaussian amplitude and phase fluctuations. In analogy with classical diffusion, the persistence probability is defined as the probability that the local (amplitude or phase) fluctuations have not changed sign up to time $t$. Our results show that the persistence probability in quantum diffusion exhibits exponential-like tails. More specifically, in $d=1$ the persistence probability decays in a stretched exponential fashion, while in $d=2$ and $d=3$ as an exponential. We also provide some insights by analyzing the two-point spatial and temporal correlation functions in the limit of small fluctuations. In particular, in the long-time asymptotic limit, the temporal correlation functions for both local amplitude and phase fluctuations become time-homogeneous. Hence, the zero-crossing events correspond to those governed by a stationary Gaussian process, with an autocorrelation-function power-law tail decaying sufficiently fast to imply an exponential-like tail of the persistence probabilities.

Usually, the impact of structural disorder on the magnetic phase transition in the 3D Ising model is analyzed within the framework of quenched dilution by a nonmagnetic component, where some lattice sites are occupied by Ising spins, while others are nonmagnetic. This kind of quenched dilution, according to the Harris criterion, leads to a change in the critical exponents that govern the asymptotics in the vicinity of the phase transition point. However, the inherent reason for the emergence of a new, random Ising model universality class is not the presence of a nonmagnetic component, but the disorder in structure of spin arrangement. To demonstrate this fact, in this paper we set up extensive Monte Carlo simulations of a random mixture of two Ising-like magnets that differ in spin length $s$ and concentration $c$. In doing so, we analyze the effect of structural disorder per se without appealing to the presence of a nonmagnetic component. We support our numerical simulations with renormalization group calculations. Our results demonstrate the emergence of the 3D randomly diluted Ising model universality class in a random mixture of two Ising magnets. While the asymptotic critical exponents coincide with those known for the site-diluted 3D Ising model, the effective critical behavior is triggered by parameters $s$ and $c$. The impact of their interplay is a subject of detailed analysis.

We present a fluctuating hydrodynamic description of an active lattice gas model with excluded volume interactions that exhibits motility-induced phase separation under appropriate conditions. For quasi-one-dimension and higher, stability analysis of the noiseless hydrodynamics gives quantitative bounds on the phase boundary of the motility-induced phase separation in terms of spinodal and binodal. Inclusion of the multiplicative noise in the fluctuating hydrodynamics describes the exponentially decaying two-point correlations in the stationary-state homogeneous phase. Our hydrodynamic description and theoretical predictions based on it are in excellent agreement with our Monte Carlo simulations and pseudospectral iteration of the hydrodynamics equations. Our construction of hydrodynamics for this model is not suitable in strictly one dimension with single-file constraints, and we argue that this breakdown is associated with microphase separation.

We introduce a spin-1 version of the random energy model with a crystal field. The crystal field controls the density of 0 spins in the system. We solve the model in the microcanonincal ensemble. The model has a spin-glass transition at a finite temperature for all strengths of the crystal field. By introducing the magnetic field we also obtain the de Almeida–Thouless line for the model. The spin-glass transition persists in the presence of an external field. We also find that the magnetization shows nonmonotonic behavior for high positive crystal field strengths. The zero magnetic field specific heat and magnetic susceptibility also exhibit a cusp beyond a threshold value of the crystal field.

The kinetics of biological motors such as kinesin or dynein is notably influenced by a viscoelastic intracellular environment. The characteristic relaxation time of the cytosol is not separable from the colloidal timescale and therefore their dynamics is inherently non-Markovian. In this paper, we consider a variant of a Brownian motor model, namely, a Brownian ratchet immersed in a correlated thermal bath, and we analyze how memory influences its dynamics. In particular, we demonstrate the memory-induced current reversal effect and explain this phenomenon by applying the effective mass approximation as well as uncovering the memory-induced dynamical localization of the motor trajectories in the phase space. Our results reveal new aspects of the role of memory in microscopic systems out of thermal equilibrium.

Detection of phase transitions is a critical task in statistical physics, traditionally pursued through analytic methods and direct numerical simulations. Recently, machine-learning techniques have emerged as promising tools in this context, with a particular focus on supervised and unsupervised learning methods, along with nonlearning approaches. In this paper, we study the performance of unsupervised learning in detecting phase transitions in the $J_1\text{−}{J}_2$ Ising model on the square lattice. The model is chosen due to its simplicity and complexity, thus providing an understanding of the application of machine-learning techniques in both straightforward and challenging scenarios. We propose a simple method based on a direct comparison of configurations. The reconstruction error, defined as the mean-squared distance between two configurations, is used to determine the critical temperatures. The results from the comparison of configurations are contrasted with those of the configurations generated by variational autoencoders. Our findings highlight that for certain systems a simpler method can yield results comparable to more complex neural networks. This paper contributes to the broader understanding of machine-learning applications in statistical physics and introduces an efficient approach to the detection of phase transitions using machine determination techniques.

Pattern dynamics on curved surfaces are ubiquitous. Although the effect of surface topography on pattern dynamics has gained much interest, there is a limited understanding of the roles of surface geometry and topology in pattern dynamics. Recently, we reported that a static pattern on a flat plane can become a propagating pattern on a curved surface [Phys. Rev. Lett. 128, 224101 (2022)]. By examining reaction-diffusion equations on axisymmetric surfaces, certain conditions for the onset of pattern propagation were determined. However, this analysis was limited by the assumption that the pattern propagates at a constant speed. Here, we investigate the pattern propagation driven by surface curvature using weakly nonlinear analysis, which enables a more comprehensive approach to the aforementioned problem. The analysis reveals consistent conditions of the pattern propagation similar to our previous results, and further predicts that rich dynamics other than pattern propagation, such as periodic and chaotic behaviors, can arise depending on the surface geometry. This study provides a perspective on the relationship between surfaces and pattern dynamics and a basis for controlling pattern dynamics on surfaces.

Methods of local topology are introduced to the field of protein physics. This is done by interpreting the folding and unfolding processes of a globular protein in terms of conformational bifurcations that alter the local topology of the proteins $\mathrm{C}\alpha$ backbone. The mathematical formulation extends Arnold's perestroikas to piecewise linear chains using the discrete Frenet frame formalism. In the low-temperature folded phase, the backbone geometry generalizes the concept of a Peano curve, with its modular building blocks modeled by soliton solutions of a discretized nonlinear Schrödinger equation. The onset of thermal unfolding begins when perestroikas change the flattening and branch points that determine the centers of solitons. When temperature increases, the perestroikas cascade, which leads to a progressive disintegration of the modular structures. The folding and unfolding processes are quantitatively characterized by a correlation function that describes the evolution of perestroikas under temperature changes. The approach provides a comprehensive framework for understanding the Physics of protein folding and unfolding transitions, contributing to the broader field of protein structure and dynamics.

Synchronization of mobile oscillators occurs in numerous contexts, including physical, chemical, biological, and engineered systems. In vertebrate embryonic development, a segmental body structure is generated by a population of mobile oscillators. Cells in this population produce autonomous gene expression rhythms and interact with their neighbors through local signaling. These cells form an extended tissue where frequency and cell mobility gradients coexist. Gene expression kinematic waves travel through this tissue and pattern the segment boundaries. It has been shown that oscillator mobility promotes global synchronization. However, in vertebrate segment formation, mobility may also introduce local fluctuations in kinematic waves and impair segment boundaries. Here, we derive a general framework for mobile oscillators that relates local mobility fluctuations to synchronization dynamics and pattern robustness. We formulate a statistical description of mobile phase oscillators in terms of probability density. We obtain and solve diffusion equations for the average phase and variance, revealing the relationship between local fluctuations and global synchronization in a homogeneous population of oscillators. Analysis of the probability density for large mobility identifies a mean-field onset, where locally coupled oscillators start behaving as if each oscillator was coupled with all the others. We extend the statistical description to inhomogeneous systems to address the gradients present in the vertebrate segmenting tissue. The theory relates pattern stability to mobility, coupling, and pattern wavelength. The general approach of the statistical description may be applied to mobile oscillators in other contexts, as well as to other patterning systems where mobility is present.

We propose a framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional approaches relying on identifying all short, fundamental unstable periodic orbits to compute ergodic averages via cycle expansion are computationally prohibitive for high-dimensional fluid systems. Our framework stems from the observation in Lasagna [D. Lasagna, Phys. Rev. E 102, 052220 (2020)] that a single unstable periodic orbit with a period sufficiently long to span a large fraction of the attractor captures the statistical properties of chaotic trajectories. Given the difficulty of identifying unstable periodic orbits for high-dimensional fluid systems, approximate trajectories residing in a low-dimensional subspace are instead constructed using resolvent modes, which inherently capture the temporal periodicity of unstable periodic orbits. The amplitude coefficients of these modes are adjusted iteratively with gradient-based optimization to minimize the violation of the projected governing equations, producing trajectories that approximate, rather than exactly solve, the system dynamics. An attempt at utilizing this framework on a chaotic system is made here on the Lorenz 1963 equations, where resolvent analysis enables an exact dimensionality reduction from three to two dimensions. Key observables averaged over these trajectories produced by the approach as well as probability distributions and spectra rapidly converge to values obtained from long chaotic simulations, even with a limited number of iterations. This indicates that exact solutions may not be necessary to approximate the system's statistical behavior, as the trajectories obtained from partial optimization provide a sufficient “sketch” of the attractor in state space.

We describe the generation of plasma filaments for application in plasma-based particle accelerators. The complete characterization of a plasma filament generated by a low-energy self-guided femtosecond laser pulse is studied experimentally and theoretically in a low-pressure nitrogen gas environment. For this purpose, we adopted a spectroscopic methodology to measure the plasma density and electron temperature. In addition to this, we also employed a side-imaging technique to retrieve the plasma column sizes (length and diameter). The measurements show the stable generation of a $\approx 4\text{−}\mathrm{cm}$-long plasma filament with $\approx 300\mu \mathrm{m}$ diameter. The peak plasma density and temperature are $n_e\approx {10}^{16}{\mathrm{cm}}^{-3}$ and $T_e\approx 1.3\mathrm{eV}$, respectively, with a decay time of approximately 8 ns. We show that the experimental results are in agreement with numerical simulations in terms of filament size and density decay time.

We demonstrate an ion acceleration scheme capable of simultaneously focusing and accelerating a multispecies ion beam with monoenergetic spectra to a few micron radius. The focal length and ion mean energy can be independently controlled: the former by using a different front-surface shape and the latter by tuning the laser-plasma parameters. We interpret the results using simple models and validate the results using first-principles simulations. The scheme is applicable to different laser transverse profiles and multi-ion species targets, and limiting factors for the ion focusing are delineated. The generated ion beam exhibits high charge, low emittance, and high-energy flux and is of interest for various applications, including inertial confinement fusion, high-flux neutron generation, and biomedical applications.

Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a mechanism of pattern propagation in which a static pattern on a flat plane becomes a propagating pattern on a curved surface [Phys. Rev. Lett. 128, 224101 (2022)]. Here, we address whether surface curvature can drive more complex pattern dynamics beyond propagation. By employing a combination of weakly nonlinear analysis and numerical simulation, we theoretically determine the condition for the emergence of pattern dynamics on curved surfaces and show that oscillatory and chaotic pattern dynamics can emerge by controlling the surface shapes. These findings highlight a role of surface topography in pattern formation and dynamics.

The microscopic understanding of the dramatic increase in viscosity of liquids when cooled toward the glass transition is a major unresolved issue in condensed matter physics. Here, we use machine learning methods to accelerate molecular dynamics simulations with first-principles accuracy for the glass-former toluene. We show that the increase in viscosity is intimately linked to the increasing number of dynamically correlated molecules $N^{*}$. While certain hallmark features of glassy dynamics, like physical aging, are linked to $N^{*}$ as well, others, like relaxation stretching, are not.

In this paper we explore the significance of nonextensive terms in Massieu functions. Finite-size effects are in many cases dominated by a term proportional to the surface area. Nevertheless, in numerical simulations of finite systems with periodic boundary conditions, the nonextensive term can become the dominant correction to Massieu functions. This paper presents a general approach linking these nonextensive terms to thermodynamic fluctuations, demonstrating that equations of state inherently encode this information. Numerical simulations corroborate our results. The examples used are hard sphere and hard disk fluids and a one-dimensional spin lattice, emphasizing the applicability of the results across different classes of systems.

In this paper, we show that classical lattices can be classified into two universality classes for thermalization, based solely on the properties of their eigenmodes. This discovery is a consequence of our systematic multiwave quasiresonance analysis, a tool developed to this end. Lattices with extended modes belong to one class that can thermalize within a finite time, even when the nonlinearity strength is very weak, provided the system size is sufficiently large. In contrast, lattices with purely localized modes fall into another class. For these systems, the scaling behavior of thermalization time shifts stepwise from low-order to progressively higher-order quasiresonances as nonlinear strength decreases, implying that thermalization may become unattainable within a reasonable time for sufficiently weak nonlinearity strength. Furthermore, we show that the real-space energy diffusion behavior of the two classes is qualitatively different as well.