We study a one dimensional gas of $N$ noninteracting diffusing particles in a harmonic trap, whose stiffness switches between two values ${\mu }_1$ and ${\mu }_2$ with constant rates $r_1$ and $r_2$, respectively. Despite the absence of direct interaction between the particles, we show that strong correlations between them emerge in the stationary state at long times, induced purely by the dynamics itself. We compute exactly the joint distribution of the positions of the particles in the stationary state, which allows us to compute several physical observables analytically. In particular, we show that the extreme value statistics (EVS), i.e., the distribution of the position of the rightmost particle, has a nontrivial shape in the large $N$ limit. The scaling function characterizing this EVS has a finite support with a tunable shape (by varying the parameters). Remarkably, this scaling function turns out to be universal. First, it also describes the distribution of the position of the $k\mathrm{th}$ rightmost particle in a $1d$ trap. Moreover, the distribution of the position of the particle farthest from the center of the harmonic trap in $d$ dimensions is also described by the same scaling function for all $d\ge 1$. Numerical simulations are in excellent agreement with our analytical predictions.

We discuss exchange scenario thermodynamic uncertainty relations for the work done on a two-qubit entangled nonequilibrium steady state obtained by coupling the two qubits and putting each of them in weak contact with a thermal bath. In this way we investigate the use of entangled nonequilibrium steady states as end points of thermodynamic cycles. In this framework we prove analytically that for a paradigmatic unitary it is possible to construct an exchange scenario thermodynamic uncertainty relation. However, despite holding in many cases, we also show that such a relation ceases to be valid when considering other suitable unitary quenches. Furthermore, this paradigmatic example allows us to shed light on the role of the entanglement between the two qubits for precise work absorption. By considering the projection of the entangled steady state onto the set of separable states, we provide examples where such projection implies an increase of the relative uncertainty, showing the usefulness of entanglement.

This article analyzes and compares two general techniques of rare event simulation for generating paths of Markov processes over fixed time horizons: exponential tilting and stochastic bridge. These two methods allow us to accurately compute the probability that a Markov process ends within a rare region which is unlikely to be attained. Exponential tilting is a general technique for obtaining an alternative or tilted sampling probability measure, under which the Markov process becomes likely to hit the rare region at terminal time. The stochastic bridge technique involves conditioning paths towards two endpoints: the terminal point and the initial one. The terminal point is generated from some appropriately chosen probability distribution that covers well the rare region. We show that both methods belong to the class of importance sampling procedures by providing a common mathematical framework of these two conceptually different methods of sampling rare trajectories. We also conduct a numerical comparison of these two methods, revealing distinct areas of application for each Monte Carlo method, where they exhibit superior efficiency. Detailed simulation algorithms are provided.

It is well known that the classic Fermi-Pasta-Ulam-Tsingou (FPUT) study of a chain of nonlinear oscillators is closely related to a number of completely integrable systems, including the Toda lattice. Here, we present a method that captures the departure of nonintegrable FPUT dynamics from those of a nearby integrable Toda lattice. Using initial long-wave data, we find that the former depart rather sharply from the latter near the predicted shock time of an asymptotic partial differential equation approximation, at which point energy cascades into higher lattice modes. Our method provides an appropriate frame of reference for one to distinguish the short-term dynamics of the two systems, whose macroscopic trajectories diverge noticeably only on a much longer timescale, when the FPUT dynamics thermalize.

While classical in many theoretical settings—and in particular in statistical physics-inspired works—the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we redeem this line of work in the case of generalized linear classification, also known as the perceptron model, with random labels. We argue that there is a large universality class of high-dimensional input data for which we obtain the same minimum training loss as for Gaussian data with corresponding data covariance. In the limit of vanishing regularization, we further demonstrate that the training loss is independent of the data covariance. On the theoretical side, we prove this universality for an arbitrary mixture of homogeneous Gaussian clouds. Empirically, we show that the universality holds also for a broad range of real data sets.

Animals and some robots locomote by interacting with the environment through cyclic shape changes, or gaits. Many animals make significant use of passive dynamics with flexible tails or pendulum action to reduce the effort required to execute these gaits. Although geometric tools have been developed to study optimal passive gaits for swimmers in drag-dominated physics regimes, they have not yet been used to study larger-scale swimmers whose physics are dominated by inertial effects. In this paper, we leverage previous work in the geometric mechanics field to examine passive-elastic inertial swimmers and show that geometric mechanics can be used to rapidly determine many classes of optimal gaits for such systems. We also discuss how considering swimmer metabolic costs in addition to the mechanical costs of driving actuation is useful for discussing swimmer efficiency. In particular, we focus on two models of active-passive swimming inertial systems: the perfect-fluid three-link swimmer, and a swimmer with a passively flexible tail.

During the ultraintense laser interaction with solids (overdense plasmas), the competition between two possible quantum electrodynamics (QED) mechanisms responsible for $e^{\pm }$ pair production, i.e., linear and nonlinear Breit-Wheeler (BW) processes, remains to be studied. Here, we have implemented the linear BW process via a Monte Carlo algorithm into the QED particle-in-cell (PIC) code yunic, enabling us to self-consistently investigate both pair production mechanisms in the plasma environment. By a series of two-dimensional QED-PIC simulations, the transition from the linear to the nonlinear BW process is observed with the increase of laser intensities in the typical configuration of a linearly polarized laser interaction with solid targets. A critical normalized laser amplitude about $a_0\sim 400–500$ is found under a large range of preplasma scale lengths, below which the linear BW process dominates over the nonlinear BW process. This work provides a practicable technique to model linear QED processes via integrated QED-PIC simulations. Moreover, it calls for more attention to be paid to linear BW pair production in near future 10-PW-class laser-solid interactions.

In this paper, the underlying problem with the color-gradient (CG) method in handling density-contrast fluids is explored. It is shown that the CG method is not fluid invariant. Based on nondimensionalizing the CG method, a phase-field interface-capturing model is proposed which tackles the difficulty of handling density-contrast fluids. The proposed formulation is developed for incompressible, immiscible two-fluid flows without phase-change phenomena, and a solver based on the lattice Boltzmann method is proposed. Coupled with an available robust hydrodynamic solver, a binary fluid flow package that handles fluid flows with high density and viscosity contrasts is presented. The macroscopic and lattice Boltzmann equivalents of the formulation, which make the physical interpretation of it easier, are presented. In contrast to existing color-gradient models where the interface-capturing equations are coupled with the hydrodynamic ones and include the surface tension forces, the proposed formulation is in the same spirit as the other phase-field models such as the Cahn-Hilliard and the Allen-Cahn equations and is solely employed to capture the interface advected due to a flow velocity. As such, similarly to other phase-field models, a so-called mobility parameter comes into play. In contrast, the mobility is not related to the density field but a constant coefficient. This leads to a formulation that avoids individual speed of sound for the different fluids. On the lattice Boltzmann solver side, two separate distribution functions are adopted to solve the formulation, and another one is employed to solve the Navier-Stokes equations, yielding a total of three equations. Two series of numerical tests are conducted to validate the accuracy and stability of the model, where we compare simulated results with available analytical and numerical solutions, and good agreement is observed. In the first set the interfacial evolution equations are assessed, while in the second set the hydrodynamic effects are taken into account.

The universality of avalanches characterizing the inelastic response of disordered materials has the potential to bridge the gap from micro to macroscale. In this study, we explore the statistics and the scaling behavior of avalanches occurring during the fracture process in silica glass using molecular mechanics. We introduce a robust method for capturing and quantifying these avalanches, allowing us to perform rigorous statistical analyses, revealing universal power laws associated with critical phenomena. The influence of an initial crack is explored, observing deviations from mean-field predictions while maintaining the property of criticality. However, the avalanche exponents in the unnotched samples are predicted correctly by the mean-field depinning model. Furthermore, we investigate the strain-dependent probability density function, its cutoff function, and the interrelation between the critical exponents. Finally, we unveil distinct scaling behavior for small and large avalanches of the crack growth, shedding light on the underlying fracture mechanisms in silica glass.

We present a comprehensive study on extracting conformal field theory data using tensor network methods, especially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the classical two-dimensional Ising model near the critical temperature. Utilizing two different methods, we extract operator scaling dimensions and operator product expansion coefficients by introducing defects on the lattice and by employing the fixed-point tensor. We also explore the effects of pointlike defects in the lattice on the coarse-graining process. We find that there is a correspondence between coarse-grained defect tensors and conformal states obtained from the lTRG fixed-point equation. We also analyze the capabilities and limitations of our proposed coarse-graining scheme for tensor networks with pointlike defects, including graph-independent local truncation (GILT) and higher-order tensor renormalization group (HOTRG). Our results provide a better understanding of the capacity and limitations of the tensor renormalization group scheme in coarse-graining defect tensors, and we show that GILT+HOTRG can be used to give accurate two- and four-point functions under specific conditions. We also find that employing the minimal canonical form further improves the stability of the RG flow.

We present analytical and numerical solutions of the Lippmann-Schwinger equation for the scattered wave functions generated by confocal parabolic billiards and parabolic segments with various $\delta$-type potential-strength functions. The analytical expressions are expressed as summations of products of parabolic cylinder functions $D_m$. We numerically investigate the resonances and tunneling in the confocal parabolic billiards by employing an accurate boundary wall method that provides a complete inside-outside picture. The criterion for discretizing the parabolic sides of the billiard is explained in detail. We discuss the phenomenon of transparency at certain eigenenergies.

Graphs have become widely used to represent and study social, biological, and technological systems. Statistical methods to analyze empirical graphs were proposed based on the graph's spectral density. However, their running time is cubic in the number of vertices, precluding direct application to large instances. Thus, efficient algorithms to calculate the spectral density become necessary. For sparse graphs, the cavity method can efficiently approximate the spectral density of locally treelike undirected and directed graphs. However, it does not apply to most empirical graphs because they have heterogeneous structures. Thus, we propose methods for undirected and directed graphs with heterogeneous structures using a new vertex's neighborhood definition and the cavity approach. Our methods' time and space complexities are $O\left(\right|E\left|h_{max}^{3}t\right)$ and $O\left(\right|E\left|h_{max}^{2}t\right)$, respectively, where $\left|E\right|$ is the number of edges, $h_{max}$ is the size of the largest local neighborhood of a vertex, and $t$ is the number of iterations required for convergence. We demonstrate the practical efficacy by estimating the spectral density of simulated and real-world undirected and directed graphs.

In the age of technology, individuals accelerate their biased gathering of information, which in turn leads to a population becoming extreme and more polarized. Here we study a partial-differential-equation model for opinion dynamics that exhibits collective behavior subject to nonlocal interactions. We developed an interaction kernel function to represent biased information gathering. Through a linear stability analysis, we show that biased populations can still form opinionated groups. However, a population that is too heavily biased can no longer come to a consensus, that is, the initial homogeneous mixed state becomes stable. Numerical simulations with biased information gathering show the ability for groups to collectively drift towards one end of the opinion space. This means that a small bias in each individual will collectively lead to groups of individuals becoming extreme together. The characteristic time scale for a group's existence is captured from numerical experiments using the temporal correlation function. Supplementing this, we included a measure of how different each population is after regular time intervals using a form of the Manhattan and Euclidean distance metrics. We conclude by exploring how wall boundary conditions induce pattern formation initially on the most extreme sides of the domain.

We derive unexpected first-passage properties for nearest-neighbor hopping on finite intervals with disordered hopping rates, including (a) a highly variable spatial dependence of the first-passage time, (b) huge disparities in first-passage times for different realizations of hopping rates, (c) significant discrepancies between the first moment and the square root of the second moment of the first-passage time, and (d) bimodal first-passage time distributions. Our approach relies on the backward equation, in conjunction with probability generating functions, to obtain all moments, as well as the distribution of first-passage times. Our approach is simpler than previous approaches based on the forward equation, in which computing the $m\mathrm{th}$ moment of the first-passage time requires all preceding moments.

Quenched disorder in semiconductors induces localized electronic states at the band edge, which manifest as an exponential tail in the density of states. For large impurity densities, this tail takes a universal Lifshitz form that is characterized by short-ranged potential fluctuations. We provide both analytical expressions and numerical values for the Lifshitz tail of a parabolic conduction band including its exact fluctuation prefactor. Our analysis is based on a replica field integral approach, where the leading exponential scaling of the tail is determined by an instanton profile and fluctuations around the instanton determine the subleading preexponential factor. This factor contains the determinant of a fluctuation operator, and we avoid a full computation of its spectrum by using a Gel'fand-Yaglom formalism, which provides a concise general derivation of fluctuation corrections in disorder problems. We provide a revised result for the disorder band tail in two dimensions.

The Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including a symmetry-permitted nonlocal nonlinear term of active origin that is of the same order as the one included in the KPZ equation. Including this term, the 2D active KPZ equation is stable in some parameter regimes, in which the interface conformation fluctuations exhibit sublogarithmic or superlogarithmic roughness, with nonuniversal exponents, giving positional generalized quasi-long-ranged order. For other parameter choices, the model is unstable, suggesting a perturbatively inaccessible algebraically rough interface or positional short-ranged order. Our model should serve as a paradigmatic nonlocal growth equation.

The phenomenon of percolation is one of the core topics in statistical mechanics. It allows one to study the phase transition known in real physical systems only in a purely geometrical way. In this paper, we determine thresholds $p_c$ for random-site percolation in triangular and honeycomb lattices for all available neighborhoods containing sites from the sixth coordination zone. The results obtained (together with the percolation thresholds gathered from the literature also for other complex neighborhoods and also for a square lattice) show the power-law dependence $p_c\propto {(\zeta /K)}^{-\gamma }$ with $\gamma =0.526\left(11\right)$, 0.5439(63), and 0.5932(47), for a honeycomb, square, and triangular lattice, respectively, and $p_c\propto {\zeta }^{-\gamma }$ with $\gamma =0.5546\left(67\right)$ independently on the underlying lattice. The index $\zeta ={\sum }_i{z}_i{r}_i$ stands for an average coordination number weighted by distance, that is, depending on the coordination zone number $i$, the neighborhood coordination number $z_i$, and the distance $r_i$ to sites in the $i\mathrm{th}$ coordination zone from the central site. The number $K$ indicates lattice connectivity, that is, $K=3$, 4, and 6 for the honeycomb, square, and triangular lattice, respectively.

Cooling of systems to sub-Kelvin temperatures is usually done using either a cold bath of particles or spontaneous photon scattering from a laser field; in either case, cooling is driven by interaction with a well-ordered cold (i.e., low-entropy) system. However, there have recently been several schemes proposed for “cooling by heating,” in which raising the temperature of some mode drives the cooling of the desired system faster. We discuss how to cool a trapped ion to its motional ground state using unfiltered sunlight at $5800\mathrm{K}$ to drive the cooling. We show how to treat the statistics of thermal light in a single-mode fiber for delivery to the ion and show experimentally how the blackbody spectrum is strongly modified by being embedded in quasi-one-dimension. Quantitative estimates for the achievable cooling rate with our measured fiber-coupled low-dimensional sunlight show promise for demonstrating this implementation of cooling by heating.

While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered by failures of links and overloads in networks with a spatial characteristic link length $\zeta$. Our results indicate that this abrupt transition has features and critical exponents similar to those of interdependent networks, suggesting that both systems are in the same universality class. For weakly embedded systems (i.e., $\zeta$ of the order of the system size $L$) we observe a mixed-order transition, where the order parameter collapses following a long critical plateau. On the other hand, strongly embedded systems (i.e., $\zeta \ll L$) exhibit a pure first-order transition, involving nucleation and the growth of damage. The system's critical behavior in both limits is similar to that observed in interdependent networks.

We generalize the Bush-Mosteller learning, the Roth-Erev learning, and the social learning to include mistakes, such that the nonlinear replicator-mutator equation with either additive or multiplicative mutation is generated in an asymptotic limit. Subsequently, we exhaustively investigate the ubiquitous rock-paper-scissors game for some analytically tractable motifs of mutation pattern for which the replicator-mutator flow is seen to exhibit rich dynamics that include limit cycles and chaotic orbits. The main result of this paper is that in both symmetric and asymmetric game interactions, mistakes can sometimes help the players learn; in fact, mistakes can even control chaos to lead to rational Nash-equilibrium outcomes. Furthermore, we report a hitherto-unknown Hamiltonian structure of the replicator-mutator equation.