We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact diagonalization. We thus characterize the deviations from ensemble equivalence at finite sizes. We describe multiple ways to compute the microcanonical entropy and present numerical results for the entropy and temperature computed in these various ways. We show that using an energy window whose width has a particular energy dependence results in a temperature with minimal deviations from the canonical temperature.

During coarsening, small structures disappear, leaving behind only large ones. Here we study the spectral energy transfers in Model A, where the order parameter $\varphi$ evolves via nonconserved dynamics. We show that the nonlinear interactions dissipate fluctuations and facilitate energy transfers among the Fourier modes so that only $\varphi (k=0)$, where $k$ is the wave number, survives at the end and approaches the asymptotic value $+1$ or $-1$. We contrast the coarsening evolution for the initial conditions with $\langle \varphi (x,t=0)\rangle =0$ and with uniformly positive or negative $\varphi (x,t=0)$.

In a wide variety of natural systems, closely related microbial strains coexist stably, resulting in high levels of fine-scale biodiversity. However, the mechanisms that stabilize this coexistence are not fully understood. Spatial heterogeneity is one common stabilizing mechanism, but the rate at which organisms disperse throughout the heterogeneous environment may strongly impact the stabilizing effect that heterogeneity can provide. An intriguing example is the gut microbiome, where active mechanisms affect the movement of microbes and potentially maintain diversity. We investigate how biodiversity is affected by migration rate using a simple evolutionary model with heterogeneous selection pressure. We find that the biodiversity-migration rate relationship is shaped by multiple phase transitions, including a reentrant phase transition to coexistence. At each transition, an ecotype goes extinct and dynamics exhibit critical slowing down (CSD). CSD is encoded in the statistics of fluctuations due to demographic noise—this may provide an experimental means for detecting and altering impending extinction.

Granular materials are critical to many natural and industrial processes, yet the chaotic flow behavior makes granular dynamics difficult to understand, model, and control, causing difficulties for natural disaster mitigation as well as scale-up and optimization of industrial devices. Hydrodynamic instabilities in externally excited grains often resemble those in fluids, but have different underlying mechanisms, and these instabilities provide a pathway to understand geological flow patterns and control granular flows in industry. Granular particles subject to vibration have been shown to exhibit Faraday waves analogous to those in fluids; however, waves can only form at high vibration strengths and in shallow layers. Here, we demonstrate that combined gas flow and vibration induces granular waves without these limitations to enable structured, controllable granular flows at larger scale with lower energy consumption for potential industrial processes. Continuum simulations reveal that drag force under gas flow creates more coordinated particle motions to allow waves in taller layers as seen in liquids, bridging the gap between waves produced in conventional fluids and granular particles subject to vibration alone.

A theoretical investigation of weak-anchoring effects in a thin two-dimensional pinned static ridge of nematic liquid crystal resting on a flat solid substrate in an atmosphere of passive gas is performed. Specifically, we solve a reduced version of the general system of governing equations recently derived by Cousins et al. [Proc. R. Soc. A 478, 20210849 (2022)] valid for a symmetric thin ridge under the one-constant approximation of the Frank-Oseen bulk elastic energy with pinned contact lines to determine the shape of the ridge and the behavior of the director within it. Numerical investigations covering a wide range of parameter values indicate that the energetically preferred solutions can be classified in terms of the Jenkins-Barratt-Barbero-Barberi critical thickness into five qualitatively different types of solution. In particular, the theoretical results suggest that anchoring breaking occurs close to the contact lines. The theoretical predictions are supported by the results of physical experiments for a ridge of the nematic $4^{\prime }$-pentyl-4-biphenylcarbonitrile (5CB). In particular, these experiments show that the homeotropic anchoring at the gas-nematic interface is broken close to the contact lines by the stronger rubbed planar anchoring at the nematic-substrate interface. A comparison between the experimental values of and the theoretical predictions for the effective refractive index of the ridge gives a first estimate of the anchoring strength of an interface between air and 5CB to be $(9.80\pm 1.12)\times {10}^{-6}{\mathrm{N}\mathrm{m}}^{-1}$ at a temperature of $(22\pm 1.5){}^{\circ }\mathrm{C}$.

In a quantum system, different energy eigenstates have different properties or features, allowing us to define a classifier to divide them into different groups. We find that the ratio of each type of energy eigenstate in an energy shell $[E_c-\mathrm{\Delta }E/2,E_c+\mathrm{\Delta }E/2]$ is invariant with changing width $\mathrm{\Delta }E$ or Planck constant $\hslash$ as long as the number of eigenstates in the shell is statistically large enough. We give an argument that such self-similarity in energy eigenstates is a general feature for all quantum systems, which is further illustrated numerically with various quantum systems, including circular billiard, double top model, kicked rotor, and Heisenberg XXZ model.

We study the $J_1\text{−}{J}_2$ Ising model on the square lattice using the random local field approximation (RLFA) and Monte Carlo (MC) simulations for various values of the ratio $p=J_2/\left|J_1\right|$ with antiferromagnetic coupling $J_2$, ensuring spin frustration. RLFA predicts metastable states with zero order parameter (polarization) at low temperature for $p\in (0,1)$. This is supported by our MC simulations, in which the system relaxes into metastable states with not only zero, but also with arbitrary polarization, depending on its initial value, external field, and temperature. We support our findings by calculating the energy barriers of these states at the level of individual spin flips relevant to the MC calculation. We discuss experimental conditions and compounds appropriate for experimental verification of our predictions.

To understand how competition affects the diversity of information, we study the social contagion model introduced by Halvorsen-Pedersen-Sneppen (HPS) [G. S. Halvorsen, B. N. Pedersen, and K. Sneppen, Phys. Rev. E 103, 022303 (2021)] on one-dimensional (1D) and two-dimensional (2D) static networks. By mapping the information value to the height of the interface, we find that the width $W(N,t)$ does not satisfy the well-known Family-Vicsek finite-size scaling ansatz. From the numerical simulations, we find that the dynamic exponent $z$ should be modified for the HPS model. For 1D static networks, the numerical results show that the information landscape is always rough with an anomalously large growth exponent, $\beta$. Based on the analytic derivation of $W(N,t)$, we show that the constant small number of influencers created for unit time and the recruitment of new followers are two processes responsible for the anomalous values of $\beta$ and $z$. Furthermore, we also find that the information landscape on 2D static networks undergoes a roughening transition, and the metastable state emerges only in the vicinity of the transition threshold.

Traveling waves of electrical activity are ubiquitous in biological neuronal networks. Traveling waves in the brain are associated with sensory processing, phase coding, and sleep. The neuron and network parameters that determine traveling waves' evolution are the synaptic space constant, synaptic conductance, membrane time constant, and synaptic decay time constant. We used an abstract neuron model in a one-dimensional network to investigate the propagation characteristics of traveling wave activity. We formulate a set of evolution equations based on the network connectivity parameters. Using a combination of numerical and analytical approaches, we show that these traveling waves are stable to a series of perturbations with biological relevance.

We study a stochastic version of the Wilson-Cowan model of neural dynamics, where the response function of neurons grows faster than linearly above the threshold. The model shows a region of parameters where two attractive fixed points of the dynamics exist simultaneously. One fixed point is characterized by lower activity and scale-free critical behavior, while the second fixed point corresponds to a higher (supercritical) persistent activity, with small fluctuations around a mean value. When the number of neurons is not too large, the system can switch between these two different states with a probability depending on the parameters of the network. Along with alternation of states, the model displays a bimodal distribution of the avalanches of activity, with a power-law behavior corresponding to the critical state, and a bump of very large avalanches due to the high-activity supercritical state. The bistability is due to the presence of a first-order (discontinuous) transition in the phase diagram, and the observed critical behavior is connected with the line where the low-activity state becomes unstable (spinodal line).

We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and mesoscale elastoplastic models (EPM) for amorphous solids sheared in the athermal quasistatic limit. We show that the spatial correlations in plastic activity exhibit a short length scale that grows as $t^{3/4}$ in MD and ballistically in EPM, which is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similarities in spatial correlations explain why simple EPMs accurately capture the size distribution of avalanches observed in MD, though the temporal profiles and dynamical critical exponents are quite different.

We study the evolution of electrostatic plasma waves, using the relativistic Vlasov equation extended by the Landau-Lifshitz radiation reaction, accounting for the back-reaction due to the emission of single particle Larmor radiation. In particular, the Langmuir wave damping is calculated as a function of wave number, initial temperature, and initial electric field amplitude. Moreover, the background distribution function loses energy in the process, and we calculate the cooling rate as a function of initial temperature and initial wave amplitude. Finally, we investigate how the relative magnitude of wave damping and background cooling varies with the initial parameters. In particular, it is found that the relative contribution to the energy loss associated with background cooling decreases slowly with the initial wave amplitude.

$J$-driven dynamic nuclear polarization (JDNP) was recently proposed for enhancing the sensitivity of solution-state nuclear magnetic resonance (NMR), while bypassing the limitations faced by conventional (Overhauser) DNP at magnetic fields of interest in analytical applications. Like Overhauser DNP, JDNP also requires saturating the electronic polarization using high-frequency microwaves known to have poor penetration and associated heating effects in most liquids. The present microwave-free JDNP (MF-JDNP) proposal seeks to enhance solution NMR's sensitivity by shuttling the sample between higher and lower magnetic fields, with one of these fields providing an electron Larmor frequency that matches the interelectron exchange coupling $J_{\mathrm{ex}}$. If spins cross this so-called JDNP condition sufficiently fast, we predict that a sizable nuclear polarization will be created without microwave irradiation. This MF-JDNP proposal requires radicals whose singlet–triplet self-relaxation rates are dominated by dipolar hyperfine relaxation, and shuttling times that can compete with these electron relaxation processes. This paper discusses the theory behind the MF-JDNP, as well as proposals for radicals and conditions that could enable this new approach to NMR sensitivity enhancement.

We present the analysis of the slowing down exhibited by stochastic dynamics of a ring-exchange model on a square lattice, by means of numerical simulations. We find the preservation of coarse-grained memory of initial state of density-wave types for unexpectedly long times. This behavior is inconsistent with the prediction from a low frequency continuum theory developed by assuming a mean-field solution. Through a detailed analysis of correlation functions of the dynamically active regions, we exhibit an unconventional transient long ranged structure formation in a direction which is featureless for the initial condition, and argue that its slow melting plays a crucial role in the slowing-down mechanism. We expect our results to be relevant also for the dynamics of quantum ring-exchange dynamics of hard-core bosons and more generally for dipole moment conserving models.

We investigate heat current magnification (CM) due to asymmetry in the number of spins in two-branched classical as well as quantum spin systems that are kept between two heat baths at different temperatures. We study the classical Ising-like spin models using Q2R and Creutz cellular automaton dynamics. We show that just the difference in the number of spins is not enough and some other source of asymmetry like unequal spin-spin interaction strengths in the upper and lower branches is required for heat CM. We also provide a suitable physical motivation for CM along with ways to control and manipulate it. We then extend this study to a quantum system with modified Heisenberg XXZ interaction and preserved magnetization. Interestingly, in this case, just the asymmetry in the number of spins in the branches is enough to achieve heat CM. We observe that the onset of CM is accompanied by a dip in the total heat current flowing through the system. We then discuss how the observed CM characteristics can be attributed to the intersection of nondegenerate energy levels, population inversion, and atypical magnetization trends as a function of the asymmetry parameter in the Heisenberg XXZ Hamiltonian. Finally we use the concept of ergotropy to support our findings.

Recently membrane filters have gained in significance due to the need to provide protection against airborne pollution. A question of importance, and some controversy, is the efficiency of filters for small nanoparticles with diameters below 100 nm as these are considered particularly dangerous due to possible penetration into the lungs. The efficiency is measured by the number of particles blocked by the pore structure after passing though the filter. To study the penetration into pores by nanoparticles suspended in a fluid, a stochastic transport theory based on an atomistic model is used to calculate particle density and flow within the pores, resulting pressure gradient, and filter efficiency. The importance of pore size relative to particle diameter and of the parameters of the pore wall interactions are investigated. The theory is applied to aerosols in fibrous filters and found to reproduce common trends in measurements. As particles enter the initially empty pores on relaxation to the steady state the small penetration measured at the onset of filtration increases faster in time the smaller the nanoparticle diameter. Control of pollution by filtration is achieved by strong repulsion of pore walls for particle diameters greater than twice the effective pore width. For smaller nanoparticles the steady-state efficiency decreases as the pore wall interactions weaken. Effective efficiency is increased when the suspended nanoparticles inside the pores combine into clusters of sizes greater than the filter channel width.

A mechanism responsible for the generic features of the mean squared displacement and the decay of the orientational autocorrelator of a molecule in a glass forming liquid is poorly understood, where such a mechanism would be critical for creating the theory of glass transition. A discrete random walk model is proposed where, instead of a straight line, a walk is along a tortuous path consisting of blocks of switchback ramps. Subdiffusive regime, short-term dynamic heterogeneity, and existence of the α- and β-relaxation processes emerge naturally from the model. The model suggests that slowing of the rate of relaxation may be due to an increase in the number of the switchback ramps per block rather than due to growth of an energy barrier as typically assumed.

It is established that charged particles crossing the interference field of two colliding electromagnetic (EM) waves can behave chaotically, leading to a stochastic heating of the particle distribution. A fine understanding of the stochastic heating process is crucial to the optimization of many physical applications requiring a high EM energy deposition to these charged particles. Predicting key stochastic heating features (particle distribution, chaos threshold) is usually achieved using a heavy Hamiltonian formalism required to model particle dynamics in chaotic regimes. Here, we explore an alternative and more intuitive path, which makes it possible to reduce the equations of motion of particles to rather simple and well-known physical systems such as Kapitza and gravity pendulums. Starting from these simple systems, we first show how to estimate chaos thresholds by deriving a model of the stretching and folding dynamics of the pendulum bob in phase space. Based on this first model, we then derive a random walk model for particle dynamics above the chaos threshold, which can predict major features of stochastic heating for any EM polarization and angle ${\theta }_i$.

One of the key issues in problems related to quantum information theory is concerned with the distinguishability of quantum states. In this context, Bures distance serves as one of the foremost choices among various distance measures. It also relates to fidelity, which is another quantity of immense importance in quantum information theory. In this work we derive exact results for the average fidelity and variance of the squared Bures distance between a fixed density matrix and a random density matrix and also between two independent random density matrices. These results go beyond the recently obtained results for the mean root fidelity and mean of the squared Bures distance. The availability of both mean and variance also enables us to provide a gamma-distribution-based approximation for the probability density of the squared Bures distance. The analytical results are corroborated using Monte Carlo simulations. Furthermore, we compare our analytical results with the mean and variance of the squared Bures distance between reduced density matrices generated using coupled kicked tops and a correlated spin chain system in a random magnetic field. In both cases, we find good agreement.

In this work, we give a characterization of the reservoir computer (RC) by the network structure, especially the probability distribution of random coupling constants. First, based on the path integral method, we clarify the universal behavior of the random network dynamics in the thermodynamic limit, which depends only on the asymptotic behavior of the second cumulant generating functions of the network coupling constants. This result enables us to classify the random networks into several universality classes, according to the distribution function of coupling constants chosen for the networks. Interestingly, it is revealed that such a classification has a close relationship with the distribution of eigenvalues of the random coupling matrix. We also comment on the relation between our theory and some practical choices of random connectivity in the RC. Subsequently, we investigate the relationship between the RC's computational power and the network parameters for several universality classes. We perform several numerical simulations to evaluate the phase diagrams of the steady reservoir states, common-signal-induced synchronization, and the computational power in the chaotic time series inference tasks. As a result, we clarify the close relationship between these quantities, especially a remarkable computational performance near the phase transitions, which is realized even near a nonchaotic transition boundary. These results may provide us with a new perspective on the designing principle for the RC.