The stick-slip phenomenon widely exists in contact mechanics, from the macroscale to the nanoscale. During cholesteric-nematic unwinding by external fields, there is controversy regarding the role of planar surface anchoring, which may induce discontinuous stick-slip behaviors despite the well-known continuous transitions observed in past experiments. Here we observe three regimes, namely, constrained, stick-slip, and sliding-slip, under mechanical winding with different anchoring conditions, and measure the corresponding forces by the surface force balance. These behaviors result from a balance of cholesteric elastic torque and surface torque, reminiscent of the slip morphology on frictional substrates [T. G. Sano et al., Phys. Rev. Lett. 118, 178001 (2017)], and provide evidence of dynamics in static rotational friction.

In this paper, we report the results of a centroid molecular dynamics (CMD) study of the canonical velocity autocorrelation functions (VACFs) in liquid $\mathrm{Ne}\text{−}{\mathrm{D}}_2$ mixtures at a temperature of $T=30\mathrm{K}$ and in the full ${\mathrm{D}}_2$-concentration range ($0\%\le x_{{\mathrm{D}}_2}\le 100\%$). This binary system was selected because of its moderate, although sizable, quantum effects which, as far as its equilibrium properties are concerned, are fully described by the path integral Monte Carlo (PIMC) simulations that have been also implemented. A comprehensive test of the VACF spectral moments carried out using three physical quantities (namely, mean kinetic energy, Einstein frequency, and mean-squared force) obtained from PIMC was performed revealing the potentialities, as well as the limitations, of the CMD approach to the single-particle dynamics in these low-$T$ liquid mixtures. Additional physical information was extracted from the canonical VACFs by fitting their spectra via two distinct methods: the Levesque-Verlet model (LV, very flexible but highly heuristic) and the itinerant oscillator model (IO, based on the physical ground of a single particle rattling inside a short-lived diffusing pseudocage). Both provided good fits of the CMD outputs, with LV being always more adequate than IO in the case of the Ne VACFs, while, as for the ${\mathrm{D}}_2$ VACFs, the LV superiority is evident only at high $x_{{\mathrm{D}}_2}$ values. However, a peculiar and systematic effect was found after analyzing the IO-fitted parameters: the estimated pseudocage masses turned out to be at least one order of magnitude lower than the corresponding values inferred from the PIMC simulations. This outcome concerns both the Ne and the ${\mathrm{D}}_2$ rattling molecule and, as we also discovered, had already been observed (but promptly forgotten) in purely classical simulations of liquid Ar. The possible physical origins of this finding have been finally discussed in some detail, also in connection with the result of the more recent exponential expansion theory (EET), which manages to shed more light on the concept of single particles rattling inside short-lived pseudocages, ultimately demonstrating its untenability.

The random diffusivity, initially proposed to explain Brownian yet non-Gaussian diffusion, has garnered significant attention due to its capacity not only for elucidating the internal physical mechanism of non-Gaussian diffusion, but also for establishing an analytical framework to characterize particle motion in complex environments. In this paper, based on the correlation function $\mathcal{C}(t_1,t_2)=\langle D\left(t_1\right)D\left(t_2\right)\rangle$ of random diffusivity $D\left(t\right)$, we quantitatively propose a general criterion of determining the ergodic property of the Langevin equation with the arbitrary random diffusivity $D\left(t\right)$. Due to the critical role of correlation function $\mathcal{C}(t_1,t_2)$, we derive the criterion for the two cases with stationary diffusivity or nonstationary diffusivity, respectively. By utilizing the quantitative criterion, we can directly judge the ergodic properties of the random diffusivity model based on the correlation function $\mathcal{C}(t_1,t_2)$ of random diffusivity $D\left(t\right)$. Several typical diffusivities, including the common square of the Brownian motion and of the (fractional) Ornstein-Uhlenbeck process, are found to contribute to different ergodic properties, which validates our proposed criterion built on the correlation function $\mathcal{C}(t_1,t_2)$.

Recent pioneering experiments on non-Markovian dynamics done, e.g., for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still awaiting discovery. It is related to the fact that typically for simplification the Markovian approximation is employed and as a consequence the memory is neglected. Therefore, methods allowing to study memory effects are extremely valuable. We demonstrate that a non-Markovian system described by the Generalized Langevin Equation (GLE) for a Brownian particle of mass $M$ can be approximated by the memoryless Langevin equation in which the memory effects are correctly reproduced solely via the effective mass $M^{*}$ of the Brownian particle which is determined only by the form of the memory kernel. Our work lays the foundation for an impactful approach which allows one to readily study memory-related corrections to Markovian dynamics.

Entropy plays a crucial role in both physics and information science, encompassing classical and quantum domains. In this paper, we present the quantum neural entropy estimator (QNEE), an approach that combines classical neural network (NN) with variational quantum circuits to estimate the von Neumann and Rényi entropies of a quantum state. QNEE provides accurate estimates of entropy while also yielding the eigenvalues and eigenstates of the input density matrix. Leveraging the capabilities of classical NN, QNEE can classify different phases of quantum systems that accompany the changes of entanglement entropy. Our numerical simulation demonstrates the effectiveness of QNEE by applying it to the 1D XXZ Heisenberg model. In particular, QNEE exhibits high sensitivity in estimating entanglement entropy near the phase transition point. We expect that QNEE will serve as a valuable tool for quantum entropy estimation and phase classification.

Whether the strong coupling to thermal baths can improve the performance of quantum thermal machines remains an open issue under active debate. Here we revisit quantum thermal machines operating with the quasistatic Carnot cycle and aim to unveil the role of strong coupling in maximum efficiency. Our analysis builds upon definitions of excess work and heat derived from an exact formulation of the first law of thermodynamics for the working substance, which captures the non-Gibbsian thermal equilibrium state that emerges at strong couplings during quasistatic isothermal processes. These excess definitions differ from conventional ones by an energetic cost for maintaining the non-Gibbsian characteristics. With this distinction, we point out that one can introduce two different yet thermodynamically allowed definitions for efficiency of both the heat engine and refrigerator modes. We dub them excess and hybrid definitions, which differ in the way of defining the gain for the thermal machines at strong couplings by either just analyzing the energetics of the working substance or instead evaluating the performance from an external system upon which the thermal machine acts, respectively. We analytically demonstrate that the excess definition predicts that the Carnot limit remains the upper bound for both operation modes at strong couplings, whereas the hybrid one reveals that strong coupling can suppress the maximum efficiency rendering the Carnot limit unattainable. These seemingly incompatible predictions thus indicate that it is imperative to first gauge the definition for efficiency before elucidating the exact role of strong coupling, thereby shedding light on the ongoing investigation on strong-coupling quantum thermal machines.

Work extraction in quantum finite systems is an important issue in quantum thermodynamics. The optimal work extracted is called ergotropy, and it is achieved by maximizing the average work extracted over all the unitary cycles. However, an agent that is non-neutral to risk is affected by fluctuations and should extract work by following the expected utility hypothesis. Thus, we investigate the optimal work extraction performed by a risk non-neutral agent by maximizing the average utility function over all the unitary cycles. We mainly focus on initial states that are incoherent with respect to the energy basis, achieving a probability distribution of work. In this case we show how the optimal work extraction will be performed with an incoherent unitary transformation, namely a permutation of the energy basis, which depends on the risk aversion of the agent. We give several examples, in particular also the work extraction from an ensemble of quantum batteries is examined. Furthermore, we also investigate how work extraction is affected by the presence of initial quantum coherence in the energy basis by considering a quasiprobability distribution of work.

We investigate analytically the distribution tails of the area $A$ and perimeter $L$ of a convex hull for different types of planar random walks. For $N$ noninteracting Brownian motions of duration $T$ we find that the large-$L$ and -$A$ tails behave as $\mathcal{P}\left(L\right)\sim e^{-b_N{L}^2/DT}$ and $\mathcal{P}\left(A\right)\sim e^{-c_{N}A/DT}$, while the small-$L$ and -$A$ tails behave as $\mathcal{P}\left(L\right)\sim e^{-d_{N}DT/L^2}$ and $\mathcal{P}\left(A\right)\sim e^{-e_{N}DT/A}$, where $D$ is the diffusion coefficient. We calculated all of the coefficients ($b_N,c_N,d_N,e_N$) exactly. Strikingly, we find that $b_N$ and $c_N$ are independent of $N$ for $N\ge 3$ and $N\ge 4$, respectively. We find that the large-$L$ ($A$) tails are dominated by a single, most probable realization that attains the desired $L$ ($A$). The left tails are dominated by the survival probability of the particles inside a circle of appropriate size. For active particles and at long times, we find that large-$L$ and -$A$ tails are given by $\mathcal{P}\left(L\right)\sim e^{-T{\mathrm{\Psi }}_N^{\text{per}}(L/T)}$ and $\mathcal{P}\left(A\right)\sim e^{-T{\mathrm{\Psi }}_N^{\text{area}}(\sqrt{A}/T)}$, respectively. We calculate the rate functions ${\mathrm{\Psi }}_N$ exactly and find that they exhibit multiple singularities. We interpret these as DPTs of first order. We extended several of these results to dimensions $d>2$. Our analytic predictions display excellent agreement with existing results that were obtained from extensive numerical simulations.

Confined active particles constitute simple, yet realistic, examples of systems that converge into a nonequilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a given distribution $g\left(t\right)$ of waiting times between tumbling events whose mean value is equal to $\tau$. Unless $g\left(t\right)$ is an exponential distribution (corresponding to a constant tumbling rate), the process is non-Markovian, which makes the analysis of the model particularly challenging. We use an analytical framework involving effective position-dependent tumbling rates to develop a numerical method that yields the full steady-state distribution (SSD) of the particle's position. The method is very efficient and requires modest computing resources, including in the large-deviation and/or small-$\tau$ regime, where the SSD can be related to the the large-deviation function, $s\left(x\right)$, via the scaling relation $P_{\mathrm{st}}\left(x\right)\sim e^{-s\left(x\right)/\tau }$.

This article confronts the formidable task of exploring chaos within hidden attractors in nonlinear three-dimensional autonomous systems, highlighting the lack of established analytical and numerical methodologies for such investigations. As the basin of attraction does not touch the unstable manifold, there are no straightforward numerical processes to detect those attractors and one has to implement special numerical and analytical strategies. In this article we present an alternative approach that allows us to predict the basin of attraction associated with hidden attractors, overcoming the existing limitations. The method discussed here is based on the Kosambi-Cartan-Chern theory which enables us to conduct a comprehensive theoretical analysis by means of evaluating geometric invariants and instability exponents, thereby delineating the regions encompassing chaotic and periodic zones. Our analytical predictions are thoroughly validated by numerical results.

Humans are exposed to sequences of events in the environment, and the interevent transition probabilities in these sequences can be modeled as a graph or network. Many real-world networks are organized hierarchically and while much is known about how humans learn basic transition graph topology, whether and to what degree humans can learn hierarchical structures in such graphs remains unknown. We probe the mental estimates of transition probabilities via the surprisal effect phenomenon: humans react more slowly to less expected transitions. Using mean-field predictions and numerical simulations, we show that surprisal effects are stronger for finer-level than coarser-level hierarchical transitions, and that surprisal effects at coarser levels are difficult to detect for limited learning times or in small samples. Using a serial response experiment with human participants ($n=100$), we replicate our predictions by detecting a surprisal effect at the finer level of the hierarchy but not at the coarser level of the hierarchy. We then evaluate the presence of a trade-off in learning, whereby humans who learned the finer level of the hierarchy better also tended to learn the coarser level worse, and vice versa. This study elucidates the processes by which humans learn sequential events in hierarchical contexts. More broadly, our work charts a road map for future investigation of the neural underpinnings and behavioral manifestations of graph learning.

Electronic excitation and ionization in oxygen-argon mixtures are analyzed using a three-temperature electronic state-resolved model and evaluated using recent experimental data from reflected shock experiments. A detailed description of the model formulation and parameter selection is provided. Excellent agreement is obtained between model predictions and experimental measurements of ${\mathrm{O}}_2$ number density during dissociation in mixtures of 2%–5% ${\mathrm{O}}_2$ dilute in argon. Next, electron number density measurements are leveraged to infer a rate constant for the heavy particle impact excitation of argon, facilitating improved modeling of net ionization and a clearer understanding of the electronic excitation kinetics of oxygen. The electronic state-resolved model is then assessed using measured data for three electronic states of atomic oxygen. The model successfully reproduces the multistage behavior observed in the measured time histories and yields new insights into the multistage behavior that revises previous interpretations. For several experiments, the modeling choices involved in the calculation of escape factors significantly influence the predicted time histories. A global sensitivity analysis considering nearly 300 parameters is then conducted to identify which model parameters most sensitively influence the predicted excited state populations. Excitation of the measured states from the metastable levels and collisional excitation between the three measured states are important across all conditions. The excited state populations demonstrate complex sensitivities involving a large number of collisional and radiative processes, highlighting the importance of adopting a detailed modeling approach when interpreting excited state measurements.

Auto-ejection of liquid is an important process in engineering applications, and is also very complicated since it involves interface moving, deforming, and jet breaking up. In this work, a theoretical velocity of meniscus at nozzle exit is first derived, which can be used to analyze the critical condition for auto-ejection of liquid. Then a consistent and conservative axisymmetric lattice Boltzmann (LB) method is proposed to study the auto-ejection process of liquid jet from a nozzle. We test the LB model by conducting some simulations, and find that the numerical results agree well with the theoretical and experimental data. We further consider the effects of contraction ratio, length ratio, contact angle, and nozzle structure on the auto-ejection, and observe some distinct phenomena during the ejection process, including the deformation of meniscus, capillary necking, and droplet pinch off. Finally, the results reported in the present work may play an instructive role on the design of droplet ejectors and the understanding of jetting dynamics in microgravity environment.

In this Letter, we introduce an inline model for stimulated Raman scattering (SRS), which runs on our radiation hydrodynamics code troll. This model accounts for nonlinear kinetic effects and for the SRS feedback on the plasma hydrodynamics. We dubbed it PIEM because it is a fully “PredIctivE Model,” because no free parameter is to be adjusted a posteriori in order to match the experimental results. PIEM predictions are compared against experimental measurements performed at the Ligne d'Intégration Laser. From these comparisons, we discuss the PIEM ability to correctly catch the impact of nonlinear kinetic effects on SRS.

Using mode-coupling theory, the conditions for all allowed dynamical universality classes for the conserved modes in one-dimensional driven systems are presented in closed form as a function of the stationary currents and their derivatives. With an eye on the search for the golden ratio universality class, the existence of some families of microscopic models is ruled out a priori by using an Onsager-type macroscopic current symmetry. In particular, if the currents are symmetric or antisymmetric under the interchange of the conserved densities, then at equal mean densities the golden modes can only appear in the antisymmetric case and if the conserved quantities are correlated, but not in the symmetric case where at equal densities one mode is always diffusive and the second may be either Kardar-Parisi-Zhang (KPZ), modified KPZ, 3/2-Lévy, or also diffusive. We also show that the predictions of mode-coupling theory for a noisy chain of harmonic oscillators are exact.

We study the equilibrium thermodynamics of quantum hard spheres in the infinite-dimensional limit, determining the boundary between liquid and glass phases in the temperature-density plane by means of the Franz-Parisi potential. We find that as the temperature decreases from high values, the effective radius of the spheres is enhanced by a multiple of the thermal de Broglie wavelength, thus increasing the effective filling fraction and decreasing the critical density for the glass phase. Numerical calculations show that the critical density continues to decrease monotonically as the temperature decreases further, suggesting that the system will form a glass at sufficiently low temperatures for any density. The methods used in this paper can be extended to more general potentials, and also to other transitions such as the Kauzman/Replica Symmetry Breaking (RSB) transition, the Gardner transition, and potentially even jamming.

The intermittent dynamics of driven interfaces through disordered media and its subsequent depinning for large enough driving force is a common feature for a myriad of diverse systems, starting from mode-I fracture, vortex lines in superconductors, and magnetic domain walls to invading fluid in a porous medium, to name a few. In this work, we outline a framework that can give a precursory signal of the imminent depinning transition by monitoring the variations in sizes or the inequality of the intermittent responses of a system that are seen prior to the depinning point. In particular, we use measures traditionally used to quantify economic inequality, i.e., the Gini index and the Kolkata index, for the case of the unequal responses of precritical systems. The crossing point of these two indices serves as a precursor to imminent depinning. Given a scale-free size distribution of the responses, we calculate the expressions for these indices, evaluate their crossing points, and give a recipe for forecasting depinning transitions. We apply this method to the Edwards-Wilkinson, Kardar-Parisi-Zhang, and fiber bundle model interface with variable interaction strengths and quenched disorder. The results are applicable for any interface dynamics undergoing a depinning transition. The results also explain previously observed near-universal values of Gini and Kolkata indices in self-organized critical systems.

The quantum dynamical activity constitutes a thermodynamic cost in trade-off relations such as the quantum speed limit and the quantum thermodynamic uncertainty relation. However, calculating the quantum dynamical activity has been a challenge. In this paper, we present the exact solution for the quantum dynamical activity by deploying the continuous matrix product state method. Moreover, using the derived exact solution, we determine the upper bound of the dynamical activity, which comprises the standard deviation of the system Hamiltonian and jump operators. We confirm the exact solution and the upper bound by performing numerical simulations.

In this paper we study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the Hénon-Heiles Hamiltonian, we numerically study the topology of different kind of exit basins and compare it with the case of low velocities in which the Newtonian version of the system is valid. Specifically, we numerically study the escapes in the phase space, in the energy plane, and in the $\beta$ plane, which richly characterize the dynamics of the system. In all cases, fractal structures are present, and the escaping dynamics is characterized. In every case a scaling law is numerically obtained in which the percentage of the trapped trajectories as a function of the relativistic parameter $\beta$ and the energy is obtained. Our work could be useful in the context of charged particles which eventually can be trapped in the magnetosphere, where the analysis of these structures can be relevant.

A statistical-mechanical study of the effect of constraint relaxation on the minimum vertex cover problem in Erdős-Rényi random graphs is presented. Using a penalty-method formulation for constraint relaxation, typical properties of solutions, including infeasible solutions that violate the constraints, are analyzed by means of the replica method and cavity method. The problem involves a competition between reducing the number of vertices to be covered and satisfying the edge constraints. The analysis under the replica-symmetric (RS) ansatz clarifies that the competition leads to degeneracies in the vertex and edge states, which determine the quantitative properties of the system, such as the cover and penalty ratios. A precise analysis of these effects improves the accuracy of RS approximation for the minimum cover ratio in the replica symmetry-breaking (RSB) region. Furthermore, the analysis based on the RS cavity method indicates that the RS/RSB boundary of the ground states with respect to the mean degree of the graphs is expanded, and the critical temperature is lowered by constraint relaxation.