Table of contents

The von Neumann entropy of a k-body-reduced density matrix γ_k quantifies the entanglement between k quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of k; it is concave for all $1\unicode{x2A7D} k\unicode{x2A7D} N$ and non-decreasing until the midpoint $k\unicode{x2A7D} \lfloor{N/2} \rfloor$. The results hold for indistinguishable quantum particles and are independent of the statistics.

We determine the impurity-induced free energy and the impurity-induced zero-field susceptibility of the symmetric single-impurity Kondo model from weak-coupling perturbation theory up to third order in the Kondo coupling at low temperatures and small magnetic fields. We reproduce the analytical structure of the zero-field magnetic susceptibility as obtained from Wilson's renormalization group method. This permits us to obtain analytically the first two Wilson numbers.

When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps Δx, Δt in space and time, respectively. By applying large-deviation theory on the discretized dynamics, we analyze the numerical errors due to the discretization, and find that the (relative) errors are especially large in regions of space where the concentration of particles is very small. We find that the choice $\Delta t = {\Delta x}^2 / (6D)$, where D is the diffusion coefficient, gives optimal accuracy compared to any other choice (including, in particular, the limit $\Delta t \to 0$), thus reproducing the known result that may be obtained using truncation error analysis. In addition, we give quantitative estimates for the dynamical lengthscale that describes the size of the spatial region in which the numerical solution is accurate, and study its dependence on the discretization parameters. We then turn to study the advection–diffusion equation, and obtain explicit expressions for the optimal Δt and other parameters of the finite-differences scheme, in terms of Δx, D and the advection velocity. We apply these results to study large deviations of the area swept by a diffusing particle in one dimension, trapped by an external potential ${\sim}|x|$. We extend our analysis to higher dimensions by combining our results from the one dimensional case with the locally one-dimension method.

We investigated the effective interaction potential (EIP) between charged surfaces in solvent comprised of dipole dimer molecules added with a certain amount of ionic liquid. Using classical density functional theory, the EIP is calculated and decoupled into entropic and energy terms. Unlike the traditional Asakura–Oosawa (AO) depletion model, the present entropic term can be positive or negative, depending on the entropy change associated with solvent molecule migration from bulk into slit pore. This is determined by pore congestion and disruption of the bulk dipole network. The energy term is determined by the free energy associated with hard-core repulsion and electrostatic interactions between surface charges, ion charges, and polarized charges carried by the dipole dimer molecules. The calculations in this article clearly demonstrate the variability of the entropy term, which contrasts sharply with the traditional AO depletion model, and the corrective effects of electrostatic and spatial hindrance interactions on the total EIP; we revealed several non-monotonic behaviors of the EIP and its entropic and energy terms concerning solvent bulk concentration and solvent molecule dipole moment; additionally, we demonstrated the promoting effect of dipolar solvent on the emergence of like-charge attraction, even in 1:1 electrolyte solutions. The microscopic origin of the aforementioned phenomena was analyzed to be due to the non-monotonic change of dipolar solvent adsorption with dipole moment under conditions of low solution dielectric constant. The present findings offer novel approaches and molecular-level guidance for regulating the EIP. This insight has implications for understanding fundamental processes in various fields, including biomolecule-ligand binding, activation energy barriers, ion tunneling transport, as well as the formation of hierarchical structures, such as mesophases, micro-, and nanostructures, and beyond.

A microscopic model for a translational Brownian motor, dubbed a Brownian translator, is introduced. It is inspired by the Brownian gyrator described by Filliger and Reimann (2007 Phys. Rev. Lett.99 230602). The Brownian translator consists of a spatially asymmetric object moving freely along a line due to perpetual collisions with a surrounding ideal gas. When this gas has an anisotropic temperature, both spatial and temporal symmetries are broken and the object acquires a nonzero drift. Onsager reciprocity implies the opposite phenomenon, that is dragging a spatially asymmetric object into an (initially at) equilibrium gas induces an energy flow that results in anisotropic gas temperatures. Expressions for the dynamical and energetic properties are derived as a series expansion in the mass ratio (of gas particle vs. object). These results are in excellent agreement with molecular dynamics simulations.

We explore the emergence of a discrete time crystalline (DTC) order and its stability against thermal fluctuations in a driven kinetic Ising model on a two-dimensional square lattice using the drive protocol invented in a recent work (Gambetta et al 2019 Phys. Rev. E 100 060105(R)). The DTC order is found to be quite robust in the presence of thermal fluctuations. We construct the resulting three-dimensional phase diagram for the DTC order, which manifests a striking resemblance to the jamming phase diagram proposed by Liu and Nagel. This finding may suggest a new way to view the DTC order as a new type of nonequilibrium soft matter. The quench dynamics exhibits a unique feature due to the nature of the employed drive protocol, namely, breakdown of the inverse relationship between the domain growth and defect relaxation, which holds in the usual quench dynamics of the kinetic Ising model.

We point out that Percus's collision integral for one-dimensional hard rods (Percus 1969 Phys. Fluids12 1560–3) does not preserve the thermal equilibrium state in an external trapping potential. We derive a revised Enskog equation for hard rods and show that it preserves this thermal state exactly. In contrast to recent proposed kinetic equations for dynamics in integrability-breaking traps, both our kinetic equation and its thermal states are explicitly nonlocal in space. Our equation differs from earlier proposals at third order in spatial derivatives and we attribute this discrepancy to the choice of collision integral underlying our approach.

We propose a new model of boundary-constrained intersecting pedestrian flow based on the collision-free velocity model, named the collision-aware deflection model (CADM). The movement of pedestrians in the new model depends on the positions and velocities of other pedestrians ahead. A pedestrian walks in the desired direction at a free speed until an obstacle appears in the desired direction. When there is an obstacle in the desired direction, pedestrians tend to choose the direction with the smallest deflection angle. When the decision of a pedestrian conflicts with the movement of the nearest neighbor in front, the pedestrian stops moving. Comparing CADM with other models, the evacuation time of CADM during the simulation is very close to the time in the experiment. CADM also successfully reproduced the stripe phenomenon in boundary-constrained intersecting pedestrian streams, which was difficult to accomplish with the compared model. CADM also inherits several advantages of the original model, in that it can reproduce the corresponding self-organization phenomena in straight corridors and bottlenecks.

This study investigates the behavioral patterns of children during emergency evacuations through a dual approach comprising controlled experimental evacuations within a classroom and computational modeling via a cellular automaton (CA) model. Observations from the experiments reveal several characteristic behaviors among children, including preferences for destinations, the impact of obstacles on their movement, as well as patterns of exit utilization, running and pushing during the evacuation process. Drawing upon these empirical findings, a CA model is developed to encapsulate these observed behaviors. A novel algorithm is introduced within this model to simulate the pushing behavior of children during emergency evacuations. Numerical simulations are conducted to validate the capability of the model to replicate the observed behaviors. The simulation results confirm that the model accurately reproduces the child behavior during evacuations. Furthermore, the results indicate that the total evacuation time is directly influenced by both the proportion of children exhibiting pushing behavior and the strength of the pushing force. These insights advance our understanding of child behavior in emergency situations and have significant implications for enhancing public safety.

Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits. Here, we derive closed-form bounds for community detection in hypergraphs. Using a message-passing formulation, we demonstrate that detectability depends on the hypergraphs' structural properties, such as the distribution of hyperedge sizes or their assortativity. Our formulation enables a characterization of the entropy of a hypergraph in relation to that of its clique expansion, showing that community detection is enhanced when hyperedges highly overlap on pairs of nodes. We develop an efficient message-passing algorithm to learn communities and model parameters on large systems. Additionally, we devise an exact sampling routine to generate synthetic data from our probabilistic model. Using these methods, we numerically investigate the boundaries of community detection in synthetic datasets, and extract communities from real systems. Our results extend our understanding of the limits of community detection in hypergraphs and introduce flexible mathematical tools to study systems with higher-order interactions.

We investigate several earthquake models in one and two dimensions of space and analyze in these models the stress spatial distribution. We show that the statistical properties of stress distribution are responsible for the distribution of earthquake magnitudes, as described by the Gutenberg–Richter (GR) law. A series of predictions is made based on the analogies between the stress profile and one-dimensional random curves or two-dimensional random surfaces. These predictions include the b-value, which determines the ratio of small to large seismic events and, in two-dimensional models, we predict the existence of aftershocks and their temporal distribution, known as the Omori–Utsu law. Both the GR and Omori–Utsu law are properties which have been extensively validated by earthquake observations in nature.

The double Pareto distribution is a heavy-tailed distribution with a power-law tail, that is generated via geometric Brownian motion with an exponentially distributed observation time. In this study, we examine a modified model wherein the exponential distribution of the observation time is replaced with a continuous uniform distribution. The probability density, complementary cumulative distribution, and moments of this model are exactly calculated. Furthermore, the validity of the analytical calculations is discussed in comparison with numerical simulations of stochastic processes.