Abstract During the detachment of a polymer chain initially anchored at both ends to an impenetrable substrate, the loop structure degenerates into a tail structure as one end detaches, ultimately resulting in complete detachment from the substrate. Many previous studies on the dynamics of polymer detachment have focused on tail structures anchored to the substrate at one end, whereas the mechanisms and kinetics of loop detachment remain incompletely understood. To understand the dynamics by which the loop gradually detaches to form a tail, it is necessary to determine the detachment time of a single breakable link, which is modeled as a spring. Compared with the escape of a Brownian particle from the potential well of a spring, geometric constraints significantly reduce the conformational entropy of a loop structured polymer adsorbed on the hard-wall, thereby accelerating its detachment. In this work, we investigate the detachment rate of polymer loop structures anchored to an impenetrable hard-wall, derive an analytical expression for the mean detachment time of the breakable link, and examine how the detachment time depends on parameters such as chain length and anchor-point separation. We find that the detachment time is strongly sensitive to changes in chain length, whereas the anchor-point separation has little influence.
Abstract Percolation properties of two types of inhomogeneous k -mers with different arrangements of conductive and nonconductive sites on a triangular lattice is studied by Monte Carlo simulations. The depositing objects are ‘Janus’ k -mers, with one conductive and one nonconductive side, and ‘patchy’ k -mers, with conductive ends and a nonconductive middle. We find that the percolation threshold strongly depends on the k -mer length, the number of nonconductive sites, and their spatial distribution. For both object types, the percolation threshold increases with the fraction of nonconductive sites. For fixed number of nonconductive sites, the threshold decreases monotonicaly with the object length. The presence of pre-existing conductive objects on the substrate can either hinder or enhance percolation, depending on their size and concentration.
A novel methodology for determining both the translational and rotational rheology of granular media is derived using an approach analogous to microrheology. This methodology is applied to simulated granular submonolayers at interfaces. A rich behaviour is found and is characterized in terms of simple models.
The Daydreaming algorithm has been recently proposed in Serricchio et al (2025 Neural Netw. 186 107216) as a learning rule that simultaneously reinforces stored patterns and suppresses spurious attractors to improve the storage capacity of the Hopfield model. Its effectiveness has been reported for both uncorrelated and correlated data. However, the existing formulation has mainly assumed unbiased patterns, and the formulation for biased patterns has not yet been sufficiently established. Biased patterns are known to be much more problematic for models of associative memories. In this study, we reformulate Daydreaming for biased patterns motivated by the underlying rationale of the pseudo-inverse rule. Specifically, we introduce the retrieval dynamics and an energy function based on the centered representation, and we derive a corresponding update rule for centered Daydreaming. We compare the centered pseudo-inverse rule with centered Daydreaming for biased patterns and examine the retrieval maps and eigenvalue distributions of the coupling matrices. As a result, the centered Daydreaming yields larger basins of attraction than the centered pseudo-inverse rule, and such a beneficial property seems to be due to the broadness of the eigenvalue spectrum of the coupling matrix. To better understand this connection, we construct modified coupling matrices whose spectra interpolate between a pseudo-inverse-like spectrum and the Daydreaming one. The results clearly indicate that the broader spectrum generated by Daydreaming contributes to the enlarged basin of attraction.
These notes accompany lectures given in June 2025 at the summer school Fundamental Problems in Statistical Physics XVI. They offer a short introduction to random quantum circuits as simple models for generic many-body quantum systems. They give an outline of the motivation for introducing these models, starting from ideas of random matrix theory. They also provide a sketch of calculations of some of the quantities of most physical interest, based on an average over an ensemble of systems. These quantities give insights into operator spreading, entanglement dynamics and spectral correlations.
The phenomenon of aging is an interesting property of non-equilibrium statistical mechanical systems whose relaxation slows down while time increases, meaning that time-translation invariance is broken. This phenomenon is observed in various systems, such as glasses and spin systems. In this work we review the aging properties of two related long-range spin models in one dimension: the voter model, where an agent copies the state of another at distance r with a probability P(r)proportional to r-alpha, and the Ising model with the interaction between spins decaying with an analogous power law J(r)proportional to r-alpha. In particular we focus on the autocorrelation function A(t,t ') and the Fisher-Huse exponent lambda, showing how the two models, which are equivalent in the case of nearest-neighbor interactions, behave differently as the interaction range increases (decreasing alpha).
We derive and classify properties of the power-spectrum tensor for systems in general steady-states, including stationary states not necessarily corresponding to equilibrium configurations. This allows us to establish a rigorous connection between the power-spectrum tensor and other quantities that characterize these systems, providing a systematic comparison with their equilibrium counterparts. As a physical application, we investigate the problem of quantum friction, describing the contactless quantum-electrodynamic drag acting on a particle moving in close proximity to material bodies at zero temperature. Specifically, we demonstrate how including additional information about the system's physical properties facilitates the derivation of more precise constraints on the power spectrum and its functional dependencies.
We provide strong numerical evidence for a dynamical bulk-boundary correspondence in two-dimensional topological matter which manifests itself as boundary contributions to the dynamical free energy and is governed by a two-dimensional non-Hermitian dynamical Loschmidt matrix-a setting largely unexplored beyond one dimension. Following a quantum quench, in-gap bands emerge in the spectrum of the Loschmidt matrix between successive dynamical quantum phase transitions when the time-evolving Hamiltonian is topological, while they are absent for quenches into the trivial phase in all cases we have studied. By fitting these in-gap bands, we show that they account for the observed boundary contributions to the dynamical free energy thus supporting a direct connection between the spectrum of a non-Hermitian dynamical matrix and topological boundary contributions. Taken together with earlier studies of the one-dimensional case, our results provide a framework to understand and classify dynamical topological phenomena based on the spectral properties of certain non-Hermitian matrices.
This paper investigates the small-parameter limits of the generalized Langevin equation (GLE). It primarily covers two aspects: 1. We studied the white-noise limit of the GLE with state-dependent coefficients and a rich class of memory kernels that can be represented as the sum of infinite exponentials. The limiting equations are driven by white-noise. 2. To study the relationship between the white-noise limit and the small-mass limit, we investigated a one-dimensional GLE. First, we successively take the white-noise and small-mass limits for this equation, then reverse the order of limit-taking. The resulting limiting equations differ. Next, we simultaneously take the white-noise and small-mass limits with different convergence rates. When the convergence rates of the two parameters vary, the limiting equations are identical. The second part provides an intuitive guide for further study of the first part and its relationship to the small-mass limit. We used a technique of integrals of semimartingales established by Kurtz and Protter.
We propose a rumor propagation model which generalizes the k-spreading Maki-Thompson model (Rada et al 2021 SIAM J. Appl. Dyn. Syst. 20 1209-31) by assuming k as being random. In this setting, individuals within a homogeneously mixed population can assume one of infinitely many possible states. To analyze this model, we extend the classical law of large numbers for density-dependent population models in Rd (Ethier and Kurtz 2009 Markov Processes: Characterization and Convergence (John Wiley & Sons)) to an infinite-dimensional setting. Specifically, we prove a convergence result for stochastic processes in the space of p-summable real sequences, generalizing the finite-dimensional theory. We derive the asymptotic proportions of individuals in each state at the end of a rumor outbreak. Furthermore, we characterize the maximum proportion of individuals actively spreading the rumor and explore conditions under which the model exhibits waves of rumor propagation.
Within the full replica-symmetry-breaking (fullRSB) solution of dense hard spheres in infinite dimension, Charbonneau, Kurchan, Parisi, Urbani, and Zamponi (J. Stat. Mech. P10009, 2014) introduced three critical exponents a, b, c governing the matching region of the fullRSB profile near the jamming transition. These exponents satisfy two scaling relations. The first, b=(1+c)/2, was established analytically by the diffusion-drift balance in the scaling ansatz. The second, a+b=1, was observed numerically to arbitrary precision but could not be proven. The exponents a,b,c of the scaling fullRSB ansatz are related to the physical exponents alpha,theta,kappa that control the gap, force, and overlap distributions by the relations alpha=a/b, theta=(c-a)/(b-c), kappa=c+1. Crucially, the relation a+b=1 yields the scaling relations alpha=1/(2+theta) and kappa=2-2/(3+theta) predicted on independent grounds by the mechanical-marginal-stability arguments of Wyart and collaborators. Here, we give an analytic proof of the identity a+b=1 from the scaling fullRSB equations. The proof was obtained through interaction with Claude (Sonnet 4.6 and Opus 4.7) and verified by us.
We adapt the mode-coupling theory of the glass transition, originally developed for modulated liquids with Newtonian dynamics, to colloidal liquids. The modulation reduces continuous translational invariance to a discrete lattice symmetry, which we encode by resolving density fluctuations into Brillouin-zone wave vectors and reciprocal-lattice indices. Using the Mori-Zwanzig projection-operator formalism, we derive exact equations of motion for generalized intermediate scattering functions. For Brownian dynamics, the memory kernel naturally decomposes into an irreducible part that reflects anisotropic transport parallel and perpendicular to the modulation. Within the mode-coupling closure, these irreducible kernels assume the same bilinear form as in the Newtonian theory. Consequently, the slow structural relaxation near the glass transition, including scaling laws and critical exponents, is universal and independent of microscopic dynamics. Differences between Brownian and Newtonian cases are confined to short-time propagators. This framework unifies glassy dynamics in modulated colloidal and atomic systems and facilitates quantitative comparison with experiments and simulations.
We study first-return statistics for photons undergoing three-dimensional (3D) Henyey-Greenstein scattering in a semi-infinite medium. In previous work, we showed that one-dimensional (1D) first-passage probabilities expand in Catalan and Motzkin generating functions. Extending to three dimensions requires a boundary truncation factor (BTF) that accounts for the restricted angular phase space imposed by the boundary. Extensive Monte Carlo simulations are used to determine the BTF empirically as a function of scattering order and anisotropy. For moderate anisotropy, the BTF is accurately described by a Cauchy kernel with parameters depending only on the Henyey-Greenstein asymmetry factor. This closed-form expression reproduces Monte Carlo results to 1%-2% accuracy over a broad range of scattering orders. At higher anisotropy, systematic deviations from the Cauchy form are observed and can be reduced using a one-parameter generalized kernel. We further extend the framework to oblique incidence by replacing the normal-incidence return probability with a Legendre-series formula; the BTF parameters and Motzkin counting machinery are independent of incidence angle, so only the anchor point of the algorithm changes. The resulting framework provides a computationally efficient mapping from 3D anisotropic transport at arbitrary incidence to 1D combinatorial first-passage theory.
We present steps towards an ab initio derivation of generalized hydrodynamics (GHD) in quantum integrable models, starting from the Bethe wave functions, and explained on the example of the repulsive Lieb-Liniger model. This includes an identification of the GHD quasi-particles as wave packets in the quantum model. These wave packets evolve according to a classical particle model and collect two-particle scattering shifts similar to solitons in integrable PDEs. We then discuss potential routes to obtain the GHD equation for average conserved densities in long-wavelength states from this description. As part of this, we provide an explicit formula for the action of the spectral phase-space density operator on Bethe wave functions, and show that it generates local conserved densities.
Understanding the generalization properties of neural networks on simple input-output distributions is key to explaining their performance on real datasets. The classical teacher-student setting, where a network is trained on data generated by a teacher model, provides a canonical theoretical test bed. In this context, a complete theoretical characterization of fully connected one-hidden-layer networks with generic activation functions remains missing. In this work, we develop a general framework for such networks with large width, yet much smaller than the input dimension. Using methods from statistical physics, we derive closed-form expressions for the typical performance of both finite-temperature (Bayesian) and empirical risk minimization estimators in terms of a small number of order parameters. We uncover a transition to a specialization phase, where hidden neurons align with teacher features once the number of samples becomes sufficiently large and proportional to the number of network parameters. Our theory accurately predicts the generalization error of networks trained on regression and classification tasks using either noisy full-batch gradient descent (GD) (Langevin dynamics) or deterministic full-batch GD.
Motifs are recurrent, statistically significant small subgraphs serving as higher-order structural building blocks of complex networks. Ranging from simple triangles to intricate topologies, they regulate key network properties such as information propagation and structural robustness. Accurately identifying influential motifs remains challenging due to their structural heterogeneity. We propose a distance-based motif ranking algorithm (DMR): we define the motifs' distance via cumulative node shortest paths, construct a motif distance matrix, and rank motifs using the eigenvector of the matrix's largest eigenvalue. Taking the number of remaining motifs as the core metric, experiments confirm that removing DMR-prioritized motifs leads to a faster decline in this metric.
With the improvement of urban non-motorized transportation systems, pedestrian-bicycle mixed flows have become increasingly prevalent in scenarios such as campuses and shared streets. Due to differences in speed and movement characteristics, turning sections of such mixed flows often suffer from inefficiencies and safety risks, becoming critical bottlenecks that restrict green travel experiences. To reveal the influence mechanism of channel width and turning angle on the turning characteristics of unidirectional pedestrian-bicycle mixed flows, this study systematically analyzed the dynamic characteristics of pedestrian flow, bicycle flow, and mixed flow under channel widths of 2.0 similar to 3.5 m and turning angles of 30 degrees, 60 degrees, and 90 degrees(including left and right turns) through controlled experiments. Based on high-precision trajectory data, quantitative analyses were conducted from the dimensions of speed-density evolution, traffic efficiency, and boundary proximity behavior. The results show that, for every 0.5 m increase in channel width, the passing times of the three types of traffic flows decrease by 0.75 s, 4.80 s, and 2.68 s, respectively, with bicycle flow being the most sensitive to width changes. Increasing turning angles significantly prolongs bicycle flow passing time (a right turn at 90 degrees increases it by 25.85% compared to a 30 degrees turn), while pedestrian flow is less affected (an increase of 3.31%). Bicycle flow passing time is longer in left-turn scenarios. Boundary behavior analysis reveals distinct kinematic constraints: cyclists consistently require a larger turning radius and greater boundary clearance compared to pedestrians, who tend to cut corners tightly. Furthermore, in wider channels (W >= 3.0 m), the trajectories of both groups shift outward, maintaining an average clearance of over 0.5 m from the inner corner. This phenomenon indicates the existence of a spontaneous comfort buffer when spatial constraints are relaxed.
We investigate the first two moments of the critical internal energy $E$ in a weakly disordered two-dimensional Baxter eight-vertex model as a function of the system size $L$, evaluated at the pseudo-critical point. Disorder is introduced via an equivalent representation of the pure eight-vertex model in terms of two ferromagnetic Ising models coupled by a four-spin interaction of strength $g_0$, where the Ising couplings consist of a uniform ferromagnetic part $J>0$ supplemented by weak Gaussian spatial disorder. In the critical regime, the model is formulated in terms of interacting Grassmann-Majorana spinor fields with quartic interactions and analyzed, for small positive $g_0$, using a combination of replica and renormalization-group methods. We also run extensive numerical simulations measuring the critical internal energy. Our results show that its relative variance increases with $L$ and approaches a finite constant as $L \to \infty$ for both $\pm g_0$. Hence, fluctuations remain relevant independently of the sign of $g_0$ (and thus of the specific-heat exponent), implying a lack of self-averaging of both the critical internal energy and the free energy. Consequently, reliable estimates of these quantities require averaging over many disorder realizations. In addition, we numerically confirm earlier predictions concerning the absence of self-averaging of the critical internal energy in the disordered Ising model.
