Diffusion-limited processes (DLP) are found in various physical, biological, and engineering systems, yet their quantification within complex spatial domains remains a challenge. In this study, we develop one-dimensional nonperiodic and periodic pair-correlation functions (PCF) to assess the spatial patterns of DLP within a cylindrical domain. By refining previous PCF formulations, we introduce an efficient binning-based approach that significantly reduces computational costs, making the method feasible for large-scale simulations. Our analysis provides a comprehensive examination of PCF variability, distinguishing between global deviations from complete spatial randomness state and sampling-induced variation. An off-lattice agent-based model is implemented, successfully reproducing self-organized patterns reminiscent of classical DLP studies and aligning with fractal-like aggregation behaviors. We demonstrate the utility of periodic PCFs in capturing key spatial correlations in DLP, particularly in azimuthal and Cartesian projections, while highlighting the conditions under which nonperiodic PCFs remain preferable. Our findings underscore the potential of PCFs as robust summary statistics for complex spatial models, with applications ranging from microbial colony formation and blood clotting dynamics to image analysis and classification algorithms.

We present two symplectic integrators for stochastic spin systems, based on the classical implicit midpoint method. The spin systems are identified with Lie-Poisson systems in matrix algebras, after which the numerical methods are derived from structure-preserving Lie-Poisson integrators for isospectral stochastic matrix flows. The integrators are thus geometric methods, require no auxiliary variables, and are suited for general Hamiltonians and a large class of stochastic forcing functions. Conservation properties and convergence rates are shown for several single-spin and multispin systems.

We systematically investigate the performance of many-body quantum batteries (QBs) with open boundary conditions (OBCs) and periodic boundary conditions (PBCs). Specifically, we apply a general approach to study the effects of interactions and boundary conditions on ergotropy and power in the Ising-, XXX-, XXZ-, and XYZ-type QBs. We find that the Ising and XYZ models can serve as viable candidates for illustrating the superiority of the collective charging proposal. For these two types of QBs, the interactions between the cells play an important role in the enhancement of ergotropy and power. Moreover, the boundary conditions significantly influence the performance of the QBs. For a smaller QB system, the QB with PBCs outperforms the QB with OBCs. Finally, we show the scaling relationships of the maximum power for the QBs and find that the superiority of collective charging for the Ising- and XYZ-type QBs with appropriate boundary conditions can be maintained in infinite QB systems.

We present a compelling observation of ballistic thermal transport in a nonintegrable classical many-body system, substantiated by extending a system with alternating long-range (LR) inverse couplings proposed in a recent study [Yoshimura et al., Phys. Rev. E 105, 024140 (2022)] from its close-to-linear regime to the fully nonlinear regime. Through this extension, we identify all characteristic hallmarks of ballistic thermal transport, including the ballistic scaling of equilibrium dynamical correlations, size-independent energy current, and flat bulk temperature profile. These features persist for large system sizes (long times), indicating the validity of such ballistic transport in the thermodynamic limit. The underlying mechanism is related to the presence of specific moving energy excitations that seem to be induced by a complex combination of alternating LR inverse couplings and nonlinearity, which enables the regularity in transport within this fully chaotic nonintegrable system. We also discuss the potential connection of these moving energy excitations to traveling discrete breathers.

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough $p$ such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any $p$ step.

We study the large-scale dynamics of event-chain Monte Carlo (ECMC) algorithms in one dimension and their relation to the true self-avoiding walk. In particular, we study the influence of stress and different forms of interaction on the equilibration and sampling properties of algorithms that satisfy global balance but not local balance. We conclude that a broad class of interaction potentials, corresponding to different physical systems, display identical large-scale dynamics.

The added mass effect is the contribution to a Brownian particle's effective mass arising from the hydrodynamic flow its motion induces. For a spherical particle in an incompressible fluid, the added mass is half the fluid's displaced mass, but in a compressible fluid its value depends on a competition between timescales. Here we illustrate this behavior with a solvable model of two harmonically coupled Brownian particles of mass $m$, one representing the sphere and the other representing the immediately surrounding fluid. The measured distribution of the Brownian particle's velocity, $P\left(\overline{v}\right)$, follows a Maxwell-Boltzmann distribution with an effective mass $m^{*}$. Solving analytically for $m^{*}$, we find that its value is determined by three relevant timescales: the momentum relaxation time, $t_p$; the harmonic oscillation period, $\tau$; and the velocity measurement time resolution, $\mathrm{\Delta }t$. In limiting cases of large timescale separations, $m^{*}$ reduces to $m$ or $2m$. The model exhibits similar behavior when generalized to the case of unequal masses.

Physical and chemical factors limit the maximum amount of energy that a living cell can expend per unit time. As the cell ages, its capacity to produce energy gradually decreases, ultimately vanishing when it reaches its natural life limit. The present analysis shows that the maximum energy-spending capacity of a cell, referred to as the cell's power capacity, depends on the overall solute concentration of the cytosol when the cell is in its rest state. An effective age is then introduced that is proportional to the cell's power capacity rather than time, as does chronological age. Being related to the cell's power, the effective age provides an indicator of the cell's vitality, irrespective of its chronological age. Old cells can be energetically young if their effective age is low. In contrast, a chronologically young cell with a high effective age is nearing the end of its life due to a lack of power capacity. This paper shows how the cell's effective age can be determined experimentally and how it can be used to know the state of health of the cells in an organ or to assess the efficacy of treatments aimed at rejuvenating or demising a cell. Finally, the experimental data available today to support the present study are discussed.

Controlling the behavior of impacting droplets continues to remain a challenge. We demonstrate a simple method of inclining a plane superhydrophobic surface with a sudden wettability change in the form of a superhydrophilic spot to control the droplet impact dynamics. We find that, depending on the operating conditions, the impacting drops can exhibit two distinct regimes: no-splitting and jetting. We characterize the transition between the regimes in terms of the ratio of the Weber number to the Bond number, the spot diameter, and the surface inclination angle using experiments and predict the transition using a scaled theoretical model. We study the jet angle and diameter of the ejected droplets using experiments and scaled theoretical models in terms of an energy ratio comprising relevant energies of the system. In addition to the advances in the physics of drop impact, uniquely, our study may find relevance in practical applications that require delivery of an ejected droplet of a particular size at a desired orientation onto a target substrate.

The hypersphere model is a simple one-parameter model of the potential-energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in ${\mathbb{R}}^{3N}$, in which $N$ is the number of particles. We study random walks within overlapping hyperspheres above the percolation threshold in 12 to 45 dimensions, utilizing an algorithm for on-the-fly placement of the hyperspheres in conjunction with the kinetic Monte Carlo method. We find behavior typical of viscous liquids; decreasing the hypersphere density (corresponding to decreasing the temperature) leads to a slowing down of the dynamics by many orders of magnitude. The shape of the mean-square displacement as a function of time is found to be similar to that of the Kob-Andersen binary Lennard-Jones mixture and the random barrier model, which predicts well the frequency-dependent fluidity of nine glass-forming liquids of different chemistry [Bierwirth et al., Phys. Rev. Lett. 119, 248001 (2017)].

We investigate the effect of stochastic restart/resetting on discrete-time quantum walks concerning its impact on the meantime to absorption in the walk on the one-dimensional lattice terminated by a pair of totally absorbing sites. The two distinguished sites also play the role of an apparatus that detects the moment of time when a quantum walk reaches these boundaries. Our results reveal a notable difference between the quantum walk and its classical counterpart. Specifically, we focus on instances of classical random walks in which stochastic resetting fails to reduce the meantime to absorption. Conversely, we show that stochastic resetting can be utilized to effectively diminish the meantime to absorption in the quantum version of this walk. We relate the observed difference between quantum and classical cases to the fact that restarting the quantum state not only changes position distribution but inevitably changes complementary quasimomentum distribution.

The goal of thermodynamic optimal control theory is to find protocols to change the state of a system from an initial to a desired final distribution, within a finite time, with the least possible expenditure of work. The optimal protocol is closely linked to the intrinsic dynamics of the system at hand. The fact that these dynamics can vary widely from system to system has made a general solution elusive. Recent years have seen great progress by recasting the question in terms of a quantity called total activity, i.e., the average number of jumps between states of the system over the course of the operation, rather than the time that the operation is allowed to take. This perspective has allowed for general expressions for the minimal work as a function of the total activity, and the minimal total activity required for a given work. The expression for minimal total activity can be recast as an apparent minimal operation time or speed limit, determined by the average activity rate and work done. A maximal activity rate can be justified by appealing to physical restrictions on the underlying transition rates, but it is unclear whether protocols optimized under a constrained activity actually require the lowest work input for a given operation time under these restrictions. In the context of bit reset, we show that directly minimizing work for a given operation time under constraints on the rates leads to protocols that require significantly less work to perform the operation than the activity-constrained protocol of the same duration. We show how the resulting protocols for both optimization schemes differ. One reason for the difference between both optimization schemes is the fact that the activity rate is not constant over the course of the protocol: it depends on both the transition rates and the distribution of the bit, both of which change over the course of the copy operation. In the limit of long protocol duration, we find an expression for the difference between the resulting minimal work for both optimization schemes, for a general class of dynamics. The time-constrained approach always outperforms the activity-constrained approach for a given constrained duration, and the difference in work can be arbitrarily large, depending on the boundary conditions and dynamics of the system under consideration.

According to thermodynamics, the efficiency of a heat engine is upper bounded by Carnot efficiency. For macroscopic systems, the Carnot efficiency is, however, achieved only for reversible processes. And, considerable attention has been paid to provide general evaluation of the efficiency at a finite speed. Recently, several upper bounds of the efficiency have been derived in the context of the trade-off among the efficiency, power, and other quantities such as the fluctuation of power. Here, we show general lower and upper bounds of the efficiency from the thermodynamic uncertainty relations for the entropy production and for the heat transfers. The lower bound is characterized by the ratio between the fluctuation of the irreversible entropy production and mean output work. The upper bound of the efficiency is described by a generalized precision of the heat transfers among the working substance, and hot and cold reservoirs. Fix the quantities except for the variance, the lower bound increases with a decrease in fluctuation, while the upper bound rises with an increase in fluctuation. We explicitly derive necessary and sufficient conditions of both the lower and upper bounds in a unified manner. Hence, our result provides an operating principle of the heat engine.

We study the problem of a run-and-tumble particle in a harmonic trap, with a finite run-and-tumble time, by direct integration of the equation of motion. An exact one-dimensional steady state distribution is obtained. Diagram laws and a programmable Volterra difference equation are derived to calculate any order of moments in any dimension, both for the steady state as well as the time Laplace transform for the intermediate states. We finally infer the complete distribution from the moments by considering a Gaussian quadrature for the corresponding measure and from the scaling law of higher order moments.

Superscars are quantum eigenstates that are localized in an extended region of a family of parallel periodic orbits. They are prevalent in pseudointegrable systems. Here we consider a pseudo-integrable right-triangular quantum billiard with an acute angle $\pi /5$ as an example. In the configuration space, we identify and explain a fringe structure of superscar eigenstates originating from a correlation between the two quantum numbers imposed by the sign change rule of the wave function during unfolding. In the wave-vector space, we unveil unique characteristics of the peaks for superscar states, and in return, exploit these features to determine the family of periodic orbits and the corresponding quantum numbers without ambiguity. We also find that the eigenstates can be superpositions not only of superscar modes corresponding to different families of periodic orbits, but also of superscar modes corresponding to the same family but with different sets of quantum numbers, which poses a challenge for conventional approaches in identifying the superscar modes but can be addressed properly by our analysis. These results are also applicable to superscar states in other pseudointegrable systems.

Understanding photon-count dynamics is crucial for applications such as quantum random number generators and quantum key distributions, where random and memoryless photon-count arrival processes are essential for performance and security. We investigated the fluctuation dynamics of aggregated photon-count time series for two distinct light sources: a 780-nm laser diode and a spontaneous parametric down-conversion source, using detrended fluctuation analysis (DFA) and the index of dispersion for intervals (IDI). Despite the degradation of photon statistics to Poissonian due to optical losses and detector inefficiencies, our analysis reveals significant long-range dependence at large timescales. The DFA scaling exponents $\overline{\alpha }>0.75$ and IDI values $c_k^2>1$ at high mean photon count and large aggregation timescales indicate photon-count fluctuations deviated from Poisson model. Our findings underscore the necessity of models beyond Poisson statistics to accurately describe the photon-count dynamics over extended timescales.

Current-carrying steady states of interacting spin chains exhibit rich structures generated through an interplay of constraints from the Hamiltonian dynamics and those induced by the current. The $XXZ$ spin chain when coupled to maximally polarizing Lindblad terms (with opposite signs on either end) admits an exact solution for the steady state in a matrix product state (MPS) form. We use this exact solution to study the correlations and distributions of local spin observables in the nonequilibrium steady state. We present exact expressions for spin correlators, entropy per site, and scaled cumulant generating functions (SCGF) for distributions of local observables in the $XX$ limit (Ising anisotropy $\mathrm{\Delta }=0$). Further, we use the exact MPS solution in the $\mathrm{\Delta }>0$ regime to calculate numerically exact entropy, correlations, as well as full distributions of spin observables in large systems. In systems where $\mathrm{\Delta }$ is a cosine of rational multiple of $\pi$, we can numerically exactly estimate the large system limit of the SCGF and the large deviation/rate functions of local-$z$ magnetization. For these, we show that the deviations of the SCGF, calculated in finite systems, from the asymptotic large system size limit decay exponentially with system size; however, the decay rate is a discontinuous function of $\mathrm{\Delta }$. The $x$ magnetization density shows a double peak structure at $\mathrm{\Delta }\lesssim 1$, suggesting short-range ferromagnetic ordering in the $x$ direction similar to what was reported for the ground state of the $XXZ$ chain.