In this paper, we propose a $D$-dimensional topological Kuramoto model and investigate its synchronization on simplicial complexes. This model extends the higher-order Kuramoto model [Phys. Rev. Lett. 124, 218301 (2020)] to the $D$-dimensional sphere, where dynamics defined on simplices of different dimensions are governed by the $D$-dimensional Kuramoto model. By adopting an adaptive coupling, new phenomena of phase transitions are observed. Specifically, for nodal dynamics of odd dimensions, a double discontinuous synchronization transition is observed, whereas for the Kuramoto model defined on links, a single discontinuous synchronization transition occurs. Rigorous theoretical analysis reveals that the double discontinuous transition originates from the loss of stability of the incoherent state and a saddle-node bifurcation in the parameter space. Furthermore, for the $D$-dimensional Kuramoto model defined on links with $D>2$, synchronization is unattainable because of the inability to project dynamics onto adjacent dimensional simplices. Our findings provide insights into collective behaviors in high-dimensional spaces, such as collective defense mechanisms or social synchronization in insect swarms, mediated by higher-order signal transmission or environmental coupling.

Mode-pairing (MP) quantum key distribution (QKD) eliminates the requirements of phase locking and phase tracking compared with twin field (TF) QKD while still surpassing the fundamental rate-distance limit of QKD. The complexity of the experimental implementation is reduced while the efficiency can still be guaranteed. In MP-QKD, two communication parties need to pair two effective rounds according to the announced results by the third party. Therefore it is not intuitive how to provide an entanglement protocol equivalent to the prepare-and-measure protocol for proving security. At present, the security of MP-QKD is rigorously proven by examining the consistency of the states detailly between MP-QKD and the fixed-pairing scheme under all of Eve's possible interference to obtain the equivalence, and verifying the security of the latter. Here, we directly present an entanglement model for MP-QKD by proposing a free-pairing entanglement scheme that is equivalent to MP-QKD. This entanglement model simplifies the security proof and provides a clearer insight into the foundation of MP-QKD. Besides, it could provide a theoretical framework for the comprehensive analysis of MP-QKD, such as facilitating practical security analysis. Additionally, we propose an optimized pairing strategy based on the entanglement model. The simulation results show an enhancement of 163% in pairing efficiency with a reasonable pairing interval $2\times {10}^5$.

In plasma wakefield accelerators, the structure of the blowout sheath is vital for the blowout radius and the electromagnetic field distribution inside the blowout. Most previous theories assume artificial distribution functions for the sheath, which are either inaccurate or require prior knowledge of parameters. In this paper, we use an adiabatic sheath model based on force balancing to overcome these limitations. This model gives self-consistent forms of the sheath and pseudopotential distribution and estimates the balancing radius of the blowout channel better than previous models. Our findings not only enhance the understanding of sheath dynamics but also offer a self-consistent theoretical foundation for future studies on nonlinear phenomena in the blowout channel.

We explore the impact of spatial separation between two sensor qubits on quantum sensing performance within a quasi-one-dimensional Bose-Einstein condensate reservoir. By analyzing the quantum Fisher information and quantum signal-to-noise ratio for sensor qubits initialized in both entangled and product states, we reveal distinct behaviors in estimating key reservoir parameters, including spectral density coupling strength and temperature. For coupling strength estimation, smaller spatial distances between the sensor qubits enhance sensing precision. In contrast, for temperature sensing, the spatial separation emerges as a valuable resource, enabling significant improvements in estimation accuracy. Additionally, we discover that product states may outperform entangled states for parameter estimation in quantum reservoir sensing. These findings provide insights into leveraging spatial configurations and state initialization for optimizing quantum sensing protocols in quantum reservoirs.

We consider spin chain models with local Hamiltonians that display weak ergodicity breaking. In these models, the majority of the eigenstates are thermal, but there is a distinguished subspace of the Hilbert space in which ergodicity is broken. We achieve such a weak breaking by embedding selected integrable models into larger Hilbert spaces of otherwise chaotic models. The integrable subspaces do not have a tensor product structure with respect to any spatial bipartition, therefore our constructions differ from certain trivial embeddings. We consider multiple mechanisms for such an embedding, and we also review previous examples in the literature. Curiously, all our examples can be seen as perturbations of models with Hilbert space fragmentation, such that the perturbed models are not fragmented anymore.

Recently, tight-binding models on hyperbolic lattices (discretized anti–de Sitter space) have gained significant attention, leading to hyperbolic band theory and non-Abelian Bloch states. In this paper, we investigate these quantum systems from the perspective of quantum information, focusing particularly on the scaling of entanglement entropy (EE) that has been regarded as a powerful quantum-information probe into exotic phases of matter. It is known that on a $d$-dimensional translation-invariant Euclidean lattice, the EE of band insulators scales as an area law ($\sim L^{d-1}$, where $L$ is the linear size of the boundary between two subsystems). Meanwhile, the EE of metals [with a finite density of state (DOS)] scales as the renowned Gioev-Klich-Widom scaling law ($\sim L^{d-1}lnL$). The appearance of logarithmic divergence, as well as the analytic form of the coefficient $c$, is mathematically controlled by the Widom conjecture of asymptotic behavior of Toeplitz matrices and can be physically understood via the Swingle's argument. However, the hyperbolic lattice, which generalizes translational symmetry, results in the inapplicability of these analytic approaches and the potential nontrivial behavior of the EE. Here we make an initial attempt through numerical simulation. Remarkably, we find that both cases adhere to the area law, indicating the effect of background hyperbolic geometry that influences quantum entanglement. To achieve the results, we first apply the vertex-inflation method to generate a hyperbolic lattice on the Poincaré disk, and then apply the Haydock recursion method to compute the DOS. Finally, we study the scaling of the EE for different bipartitions via exact diagonalization and perform finite-size scaling. We also investigate how the coefficient of the area law is correlated to the bulk gap in the gapped case and to the DOS in the gapless case, respectively. Future directions are discussed.

Nanoparticles, such as viruses, can enter cells via endocytosis, a process by which the cell membrane wraps around them. The role of nanoparticle size and shape on endocytosis has been well studied, but the biophysical details of how extracellular proteins on the cell membrane surface mediate uptake are less clear. Motivated by recent discoveries regarding extracellular vimentin in viral and bacterial uptake and the structure of coronaviruses, we construct a computational model with a cell-like and virus-like construct containing filamentous protein structures protruding from their surfaces. We study the impact of these additional degrees of freedom on viral wrapping. The cell surface is modeled as a deformable sheet with bending rigidity, and extracellular vimentin as semiflexible polymers, or extracellular components (ECC), placed randomly on the sheet. The virus is modeled as a deformable shell that also has explicit, freely rotating spike filaments on its surface. Our results indicate that cells with optimally populated filaments are more susceptible to infection as they take up the virus more quickly and utilize a relatively smaller area of the cell surface. At optimal ECC density, the cell surface forms a fold around the virus, which is faster and more efficient at wrapping than localized crumples. Additionally, cell surface bending rigidity aids in the generation of folds by increasing force transmission across the surface. Changing other mechanical parameters, such as the stretching stiffness of filamentous ECC or virus spikes, can result in localized crumple formation on the cell surface. We conclude with the implications of our study on the evolutionary pressures of virus-like particles, with a particular focus on the cellular microenvironment.

Tightly packed granular particles under shear often exhibit intriguing intermittencies, specifically, sudden stress drops that we refer to as quaking. To probe the nature of this phenomenon, we prototype a circular shear cell that is capable of imposing a uniform and unlimited shear strain under quasistatic cyclic driving. Spherical PDMS (polydimethylsiloxane) particles, immersed in fluid, are driven in a fixed total volume at a wide range of shear rates, with particle trajectories captured in three-dimensional space via refraction-index-matched fluorescent tomography. Statistics on the magnitude of fluctuating displacements of individual particles show a distinct dependence on the shear rate. Particles move smoothly at high shear rates. At intermediate shear rates, quaking emerges with clusters of particles exhibiting relatively large displacements. At low shear rates, a cluster can span the entire system. and the cluster exhibits substructures in view of localized particle movements. Overall, we have confirmed that the quaking phenomena in the current setup are consistent with our previous work [Phys. Rev. Lett. 126, 128001 (2021)] and that the dimensionless shear rate that we have defined [Phys. Rev. Res. 6, 023065 (2024)] is indeed a good parameter for unifying the transitions observed in different experimental geometries.

Motile bacteria can migrate along chemical gradients in a process known as chemotaxis. When exposed to uniform environmental stress, Escherichia coli cells coordinate their chemotactic responses to form millimeter-sized condensates containing hundreds of thousands of motile cells. In this study, we combined experiments with mathematical modeling based on modified Keller-Segel equations to investigate the dynamics of this collective behavior across three distinct timescales: the shortest timescale, where spatial instability emerges; an intermediate timescale, where quasistationary bacterial condensates form; and finally, a longer timescale, during which neighboring bacterial accumulations coalesce. The model closely agrees with experimental results, quantitatively capturing the observed instability, the shape of mature condensates, and their coalescence dynamics. Specifically, we found that the force between neighboring bacterial accumulations decays exponentially with distance due to screening effects. We suggest that the model presented here could describe more broadly the dynamics of stress-induced condensation mediated by bacterial chemotaxis.

Magnetic colloids can be driven with time-varying fields to form clusters and voids that re-organize over vastly different timescales. However, the driving force behind these nonequilibrium dynamics is not well-understood. Here, we introduce a topological framework that predicts protected edge flows despite strong thermal motion. Notably, these edge flows produce shear stress that creates global rotation of clusters but not of voids. We verify this theory experimentally using micrometer-sized superparamagnetic colloids to demonstrate these emergent physical predictions and show how they drive system reorganization differentially at long timescales. Our results elucidate fundamental principles that shape and control nonequilibrium colloidal aggregates.

The skin color patterning of lizards with monochromatic skin scales can be modeled computationally with at least two different mathematical frameworks: Turing's reaction-diffusion model (relying on interaction data among colored cells), and the Lenz-Ising model (based on effective mesoscopic interactions among individual skin scales). However, a mechanistic connection between these very different descriptions remains elusive. Capitalizing both on the biological interpretability of the reaction-diffusion model and on the geometric interpretability of the Lenz-Ising model, we develop a computational approach to bridge this gap in a series of evolutionary divergent lizards. First, by combining mathematical and computational methods to perform a mapping between the two models, we show that a four-parameter extension of the classic Lenz-Ising model efficiently captures statistical aspects of color patterning in all species. Second, we show that the Lenz-Ising model parameters acquire an effective interpretation, in terms of cell interactions, by observing how these parameters change when tuning the reaction-diffusion parameters optimized for each species studied here. Taken together, our findings establish quantitative links between the strength and length scales of microscopic interactions among colored cells, and the scale-by-scale lizard skin color patterns visible to the naked eye.

Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D nanomagnetism, both volume and surface topological numbers must be considered, requiring the identification of a proper global topological invariant to support categorization. Here we consider domain walls in cylindrical nanowires as an excellent playground for 3D nanomagnetic systems, excited by a charge current, that generates an Œrsted field. We first provide experimental evidence of previously unreported domain-wall transformations of topology occurring at the nanosecond timescale. We investigate these transformations with micromagnetic simulations, tracking both bulk and surface topological signatures. We demonstrate a topological invariant combining both signatures, while the topological charge varies from bulk to surface during the dynamics. The experimental change of topology is reproduced when the pulse duration matches the timescale of the internal transformations of the wall, and the current is switched off before the transformation is complete. We expect that the topological categorization and dynamical exploitation apply to any 3D nanomagnetic system.

Adaptive physics-constrained superresolution diffusion is developed for noninvasive virtual diagnostics of the six-dimensional (6D) phase space density of charged particle beams. An adaptive variational autoencoder embeds initial beam condition images and scalar measurements to a low-dimensional latent space from which a ${32}^6$ pixel 6D tensor representation of the beam's 6D phase space density is generated. Projecting from a 6D tensor generates physically consistent two-dimensional projections. Physics-guided superresolution diffusion transforms low-resolution images of the 6D density to high resolution $256\times 256$ pixel images. Unsupervised adaptive latent space tuning enables tracking of time-varying beams without knowledge of time-varying initial conditions. The method is demonstrated with experimental data and multiparticle simulations at the HiRES UED. The general approach is applicable to a wide range of complex dynamic systems evolving in high-dimensional phase space. The method is shown to be robust to distribution shift without retraining.

A novel generalized mean-field approximation, called the small-coupling dynamic cavity (SCDC) method, for epidemic inference and risk assessment is presented. The method is developed within a fully Bayesian framework and accounts for noncausal effects generated by the presence of observations. It is based on a graphical model representation of the epidemic stochastic process and utilizes dynamic cavity equations to derive a set of self-consistent equations for probability marginals defined on the edges of the contact graph. By performing a small-coupling expansion, a pair of time-dependent cavity messages is obtained, which capture the probability of individual infection and the conditioning power of observations. In its efficient formulation, the computational cost per iteration of the SCDC algorithm is linear in the duration of the epidemic dynamics. While the method is derived for the susceptible-infected (SI) model, it is straightforwardly applicable to many other Markovian epidemic processes, including recurrent ones. This linear complexity is particularly advantageous for recurrent epidemic processes, where inference methods are typically exponentially complex in the duration of the epidemic dynamics. The method exhibits high accuracy in assessing individual risk, as demonstrated by tests on the SI model applied to various classes of synthetic contact networks, where it performs on par with belief propagation techniques and generally exceeds the performance of individual-based mean-field methods. Additionally, the method was applied to recurrent epidemic models, where it showed interesting performance even for relatively large values of the infection probability, highlighting its versatility and effectiveness in challenging scenarios. Although convergence issues may arise due to long-range correlations in contact graphs, the estimated marginal probabilities remain sufficiently accurate for reliable risk estimation. Future work includes extending the method to non-Markovian recurrent epidemic models and investigating the role of second-order terms in the small-coupling expansion of the observation-reweighted dynamic cavity equations.

We present estimates for the number of ions needed to implement fault-tolerant lattice surgery between spatially separated trapped-ion surface codes. Additionally, we determine attainable lattice surgery rates given a number of dedicated “communication ions” per logical qubit. Because our analysis depends heavily on the rate that syndrome extraction cycles take place, we survey the state-of the art and propose three possible cycle times between 10 and $1000\mu \mathrm{s}$ that we could reasonably see realized provided certain technological milestones are met. Consequently, our numerical results indicate that hundreds of resource ions will be needed for lattice surgery in the slowest case, while close to a hundred thousand will be needed in the fastest case. The main factor contributing to these prohibitive estimates is the limited rate that ions can be coupled across traps. Our results indicate an urgent need for optical coupling to improve by one or more orders of magnitude for trapped-ion quantum computers to scale.