This paper discusses analytical and numerical results for nonharmonic, undamped, single-well, stochastic oscillators driven by additive noises. It focuses on average kinetic, potential, and total energies together with the corresponding distributions under random drivings, involving Gaussian white, Ornstein-Uhlenbeck, and Markovian dichotomous noises. It demonstrates that insensitivity of the average total energy to the single-well potential type, $V\left(x\right)\propto x^{2n}$, under Gaussian white noise does not extend to other noise types. Nevertheless, in the long-time limit ($t\to \infty$), the average energies grow as power law with exponents dependent on the steepness of the potential $n$. Another special limit corresponds to $n\to \infty$, i.e., to the infinite rectangular potential well, when the average total energy grows as a power law with the same exponent for all considered noise types.

We explore how the expectation values $\langle \psi \left|A\right|\psi \rangle$ of a largely arbitrary observable $A$ are distributed when normalized vectors $|\psi \rangle$ are randomly sampled from a high-dimensional Hilbert space. Our analytical results predict that the distribution exhibits a very narrow peak of approximately Gaussian shape, while the tails significantly deviate from a Gaussian behavior. In the important special case that the eigenvalues of $A$ satisfy Wigner's semicircle law, the expectation-value distribution for asymptotically large dimensions is explicitly obtained in terms of a large deviation function, which exhibits two symmetric nonanalyticities akin to critical points in thermodynamics.

This paper analyzes the forces on a cylindrical straight rod penetrated into a granular bed in the partially fluidized state. As gas flow is blown from the bed bottom, the resistance force decreases linearly with increasing gas flow velocity. After the bed is fluidized, the resistance force is close to zero. When the bed is under the action of vibration, the average resistance force ($F_{b,\mathrm{ave}}$) linearly decreases with increasing vibration acceleration but is barely influenced by the vibration frequency. The bed cannot be completely liquefied under vibration only, and $F_{b,\mathrm{ave}}$ constantly exists with increasing vibration acceleration. Based on the equivalent effects of gas flow and vibration, the calculation formula of the resistance force in the partially fluidized bed is established as $F_{b,\mathrm{ave}}/F_{b,0}=1-u/u_{\mathrm{MF}}-0.748\mathrm{\Gamma }$, and the minimum vibration liquid velocity is estimated as $u_{\mathrm{ML}}/u_{\mathrm{MF}}=1-0.748\mathrm{\Gamma }$.

In thermal glasses at temperatures sufficiently lower than the glass transition, the constituent particles are trapped in their cages for a sufficiently long time such that their time-averaged positions can be determined before diffusion and structural relaxation takes place. The effective forces are those that hold these average positions in place. In numerical simulations the effective forces ${\mathit{F}}_{ij}$ between any pair of particles can be measured as a time average of the bare forces ${\mathit{f}}_{ij}({\mathit{r}}_{ij}\left(t\right))$. In general, even if the bare forces come from two-body interactions, thermal dynamics dress the effective forces to contain many-body interactions. Here, we develop the effective theory for systems with generic interactions, where the effective forces are derivable from an effective potential and in turn they give rise to an effective Hessian whose eigenvalues are all positive when the system is stable. In this Rapid Communication, we offer analytic expressions for the effective theory, and demonstrate the usefulness and the predictive power of the approach.

Single-molecule experiments have found near-perfect thermodynamic efficiency in the rotary motor ${\mathrm{F}}_1$-ATP synthase. To help elucidate the principles underlying nonequilibrium energetic efficiency in such stochastic machines, we investigate driving protocols that minimize dissipation near equilibrium in a simple model rotary mechanochemical motor, as determined by a generalized friction coefficient. Our simple model has a periodic friction coefficient that peaks near system energy barriers. This implies a minimum-dissipation protocol that proceeds rapidly when the system is overwhelmingly in a single macrostate but slows significantly near energy barriers, thereby harnessing thermal fluctuations to kick the system over energy barriers with minimal work input. This model also manifests a phenomenon not seen in otherwise similar nonperiodic systems: Sufficiently fast protocols can effectively lap the system. While this leads to a trade-off between accuracy of driving and energetic cost, we find that our designed protocols outperform naive protocols.

Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.

We investigate the effects of resetting mechanisms on random processes that follow the telegrapher's equation instead of the usual diffusion equation. We thus study the consequences of a finite speed of signal propagation, the landmark of telegraphic processes. Likewise diffusion processes where signal propagation is instantaneous, we show that in telegraphic processes, where signal propagation is not instantaneous, random resettings also stabilize the random walk around the resetting position and optimize the mean first-arrival time. We also obtain the exact evolution equations for the probability density of the combined process and study the limiting cases.

The critical properties of the one-dimensional spin-$1/2$ transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility was used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction $J_2$, we calculated the fidelity susceptibility as a function of the transverse field $B_x$ and the longitudinal field $B_z$. The phase diagram in the ($B_x,B_z$)-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For $B_x<1$, we observed an antiferromagnetic phase for small values of $B_z$ and a paramagnetic phase for large values of $B_z$. For $B_x>1$ and low $B_z$, we found a disordered phase that undergoes a second-order phase transition to a paramagnetic phase for large values of $B_z$.

The emergence of rigidity upon changes of temperature, density, or applied stresses in disordered assemblies of particles is of interest in a wide range of soft matter, from glass formers, gels, foams, and granular matter. Shear jamming of frictional grains presents an interesting special case wherein the application of shear stress leads to rigidity rather than its loss. The formation of self-organized structures that resist shear deformation offers an appealing geometric picture of shear jamming, which nevertheless is incompletely developed, and not well integrated with ideas concerning rigidity in frictionless systems. Exploiting the observation that athermally sheared sphere assemblies develop structural features necessary for shear jamming even in the absence of friction [H. A. Vinutha and S. Sastry, Nature Physics 12, 578 (2016)], we analyze conditions for jamming in such assemblies computationally. Solving force and torque balance conditions for their contact geometry, we show, and validate with frictional simulations, that the mean contact number $Z$ equals $D+1$ (for spatial dimension $D=2,3$) at jamming for both finite and infinite friction, above the “random loose packing” limit density, at variance with previous analyses of frictional jamming. We show that the shear jamming threshold satisfies the marginal stability condition recently proposed for jamming in frictionless systems. Along lines explored in studying covalent glasses, we perform rigidity percolation analysis for $D=2$ and find that rigidity percolation precedes shear jamming, which, however, coincides with the percolation of over-constrained regions, leading to the identification of a regime analogous to the intermediate phase observed in covalent glasses. Together, these results provide a geometric description of shear jamming that relate closely with analyses of jamming, rigidity, and the glass transition in frictionless systems, and thus help develop a unified description of jamming phenomenology in diverse disordered matter.

Polygonal desiccation crack patterns are commonly observed in natural systems. Despite their quotidian nature, it is unclear whether similar crack patterns which span orders of magnitude in length scales share the same underlying physics. In thin films, the characteristic length of polygonal cracks is known to monotonically increase with the film thickness; however, existing theories that consider the mechanical, thermodynamic, hydrodynamic, and statistical properties of cracking often lead to contradictory predictions. Here we experimentally investigate polygonal cracks in drying suspensions of micron-sized particles by varying film thickness, boundary adhesion, packing fraction, and solvent. Although polygonal cracks were observed in most systems above a critical film thickness, in cornstarch-water mixtures, multiscale crack patterns were observed due to two distinct desiccation mechanisms. Large-scale, primary polygons initially form due to capillary-induced film shrinkage, whereas small-scale, secondary polygons appear later due to the deswelling of the hygroscopic particles. In addition, we find that the characteristic area of the polygonal cracks, $A_p$, obeys a universal power law, $A_p=\alpha h^{4/3}$, where $h$ is the film thickness. By quantitatively linking $\alpha$ with the material properties during crack formation, we provide a robust framework for understanding multiscale polygonal crack patterns from microscopic to geologic scales.

A spinning ball moving through air experiences a net lift due to the “Magnus effect” resulting from the pressure difference across its two sides. In this work, with the help of numerical simulations, we present a similar phenomenon on a circular intruder undergoing both translational and rotational motion in a two-dimensional granular medium. The direction of this “Magnus” lift in a granular medium, irrespective of its area fraction, is opposite to the general direction in viscous fluids in the range of velocities studied. We relate this effect to the switching in the direction of tangential forces, uneven shearing of the force chains, and uneven distribution in the number of contacts across the rotating intruder. Moreover, this is observed for area fractions $\mathrm{\Phi }$ as low as 0.35 to as high as 0.82, which lies just below the jamming point. Distribution of the contact force around the intruder surface is also studied with respect to the nondimensionalized rotation speed of the intruder. A saturation in the lift to drag ratio is achieved at very high rotation speed, and the ratio is seen to be weakly dependent on the area fraction of the granular medium. The change in local flow fields of velocity, area fraction, and granular temperature around the intruder for several spin ratios is also discussed. The downstream wake of the intruder also deflects in the opposite direction when compared to the case in viscous fluids.

Acoustic nonreciprocity has been shown to enable a plethora of effects analogous to phenomena seen in quantum physics and electromagnetics, such as immunity from backscattering and unidirectional band gaps, which could lead to the design of direction-dependent acoustic devices. One way to break reciprocity is by spatiotemporally modulating material properties, which breaks parity and time-reversal symmetries. In this paper, we present a model for a medium in which a slow nonlinear deformation modulates the effective material properties for small overlaid disturbances (often referred to as “small-on-large” propagation). The medium is modeled as a discrete spring-mass chain that undergoes large deformation via prescribed displacements of certain points in the unit cell. A multiple-scale perturbation analysis shows that, for sufficiently slow modulations, the small-scale waves can be described by a linear monatomic chain with time- and space-dependent on-site stiffness. The modulation depth can be tuned by changing the geometric and stiffness parameters of the unit cell. The accuracy of the small-on-large approximation is demonstrated using direct numerical simulations.

We study boundary conditions applied to the macroscopic dynamics of Newtonian liquids from the view of microscopic particle systems. We assume the existence of microscopic boundary conditions that are uniquely determined from a microscopic description of the fluid and the wall. By using molecular dynamical simulations, we examine a possible form of the microscopic boundary conditions. In the macroscopic limit, we may introduce a scaled velocity field by ignoring the higher-order terms in the velocity field that is calculated from the microscopic boundary condition and standard fluid mechanics. We define macroscopic boundary conditions as the boundary conditions that are imposed on the scaled velocity field. The macroscopic boundary conditions contain a few phenomenological parameters for an amount of slip, which are related to a functional form of the given microscopic boundary condition. By considering two macroscopic limits of the nonequilibrium steady state, we propose two different frameworks for determining macroscopic boundary conditions.

The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum-classical variational approaches. This methodology can be applied to a variety of optimization problems, but its practical performance is not well studied yet. This paper moves some steps in the direction of characterizing the practical performance of the methodology, in the context of finding solutions to classical combinatorial optimization problems. Our study is based on numerical results obtained applying several classical nonlinear optimization algorithms to Hamiltonians for six combinatorial optimization problems; the experiments are conducted via noise-free classical simulation of the quantum circuits implemented in Qiskit. We empirically verify that: (1) finding the ground state is harder for Hamiltonians with many Pauli terms; (2) classical global optimization methods are more successful than local methods due to their ability of avoiding the numerous local optima; (3) there does not seem to be a clear advantage in introducing entanglement in the variational form.

Linear response theory (LRT) is one of the main approaches to the dynamics of quantum many-body systems. However, this approach has limitations and requires, e.g., that the initial state is (i) mixed and (ii) close to equilibrium. In this paper, we discuss these limitations and study the nonequilibrium dynamics for a certain class of properly prepared initial states. Specifically, we consider thermal states of the quantum system in the presence of an additional static force which, however, become nonequilibrium states when this static force is eventually removed. While for weak forces the relaxation dynamics is well captured by LRT, much less is known in the case of strong forces, i.e., initial states far away from equilibrium. Summarizing our main results, we unveil that, for high temperatures, the nonequilibrium dynamics of so-called binary operators is always generated by an equilibrium correlation function. In particular, this statement holds true for states in the far-from-equilibrium limit, i.e., outside the linear response regime. In addition, we confirm our analytical results by numerically studying the dynamics of local fermionic occupation numbers and local energy densities in the spin-$1/2$ Heisenberg chain. Remarkably, these simulations also provide evidence that our results qualitatively apply in a more general setting, e.g., in the anisotropic XXZ model where the local energy is a non-binary operator, as well as for a wider range of temperature. Furthermore, exploiting the concept of quantum typicality, all of our findings are not restricted to mixed states, but are valid for pure initial states as well.

We address the question of the relevance of thermalization and scrambling to the increase of correlations in the quench dynamics of an isolated system with a finite number of interacting bosons. Specifically, we study how, in the process of thermalization, the correlations between occupation numbers increase in time, resulting in the emergence of the Bose-Einstein distribution. Despite the exponential increase of the number of principal components of the wave function, we show, both analytically and numerically, that the two-point correlation function before saturation increases quadratically in time according to perturbation theory. In contrast, we find that the out-of-time-order correlator increases algebraically and not exponentially in time after the perturbative regime and before the saturation. Our results can be confirmed experimentally in traps with interacting bosons and they may be relevant to the problem of black hole scrambling.

The phase transition and critical properties for the ${\mathrm{RP}}^2$ model in two dimensions is investigated by means of the nonequilibrium relaxation method (NER) together with the dynamical scaling analysis. The relaxation of nematic order from the all-aligned state is observed by Monte Carlo simulations. The comparison of types of the asymptotic form of the relaxation time around the transition point is considered by the dynamical scaling analysis, which clearly discriminates the Kosterlitz-Thouless (KT)-type transition from the second-order one. Using the relaxation of fluctuation, the static critical exponent $\eta$ and the dynamical one $z$, which are only the intrinsic exponents for the KT transition, are estimated at and below the KT transition temperature. The result shows similar behaviors with those observed in the KT phase for the ferromagnetic $\mathit{XY}$ model in two dimensions, which has been recognized as a typical KT system, and reveals the confirmation of the present KT transition.

This paper presents a Monte Carlo study of percolation in a distorted square lattice, in which the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable parameter $\alpha$ to create a distorted empty lattice. In this model, two occupied neighboring sites are considered to be connected to each other in order to belong to the same cluster, if the distance between them is less than or equal to a certain value, called connection threshold $d$. While spanning becomes difficult in distorted lattices as is manifested by the increment of the percolation threshold $p_c$ with $\alpha$, an increased connection threshold $d$ makes it easier for the system to percolate. The scaling behavior of the order parameter studied through relevant critical exponents, and the fractal dimension $d_f$ of the percolating cluster at $p_c$ suggest that this new type of percolation may belong to the same universality class as ordinary percolation. This model can be very useful in various realistic applications since it is almost impossible to find a natural system that is perfectly ordered.

We consider the dynamics of a microswimmer and show that they can be approximated by active Brownian motion. The swimmer is modeled by coupled overdamped Langevin equations with periodic driving. We compare the energy dissipation of the real swimmer to that of the active Brownian motion model, finding that the latter can massively underestimate the complete dissipation. This discrepancy is related to the inability to infer the full dissipation from partial observation of the complete system. We introduce an efficiency that measures how much of the dissipated energy is spent on forward propulsion.

The low- and high-amplitude oscillations in the system of three nonlinear coupled pendula (trimer) are analyzed beyond the quasilinear approximation. The considered oscillations are fundamental for many models of the energy exchange processes in physical, mechanical, and biological systems, in particular, for the torsional vibrations of flexible polymers or DNA's double strands. We obtained the conditions of the basic stationary solutions' stability. These solutions correspond to the nonlinear normal modes (NNMs), the instability of which leads to the appearance of localized NNMs (stationary energy localization). Using an asymptotic procedure, we reduce the dimension of the system's phase space that allows us to analyze the energy exchange between pendula in the slow timescale and to reveal periodic interparticle energy exchange and nonstationary energy localization. It has been shown recently that essentially nonstationary resonance processes of this type are adequately described in terms of the limiting phase trajectories (LPTs) corresponding to beatings between the oscillators or coherence domains in the slow timescale. Moreover, it turns out that criteria of the transition to the stationary and nonstationary energy localization can be formulated as the bifurcation conditions for NNMs and LPTs, respectively. The trimer under consideration is a nonintegrable system, and therefore its equations of motion is only after dimensions reduction can be analyzed by the Poincare sections method. Finally, we aim to study the highly nonstationary regimes, which correspond to beatinglike periodic or quasiperiodic recurrent energy exchange between the pendula.