Papers

We develop a semiclassical Boltzmann framework for second-order extrinsic spin transport in the presence of skew scattering. The conventional relaxation-time approximation reduces the full collision integral to a single phenomenological timescale and thereby neglects the angular structure of impurity scattering. While the transport relaxation time primarily characterizes the leading angular harmonic of the nonequilibrium distribution, nonlinear response is sensitive to its higher angular harmonics, which are governed by distinct components of the collision operator. We therefore retain the angular and band dependence of the scattering kernel and decompose both the collision integral and the distribution function into Fourier harmonics. The resulting coupled algebraic equations allow the symmetric and skew-scattering corrections to the distribution function to be obtained recursively order by order in the electric field. We apply this formalism to the gapped surface states of a topological insulator with spin-dependent impurity scattering and evaluate the corresponding second-order extrinsic spin-current response. Our results show that higher angular harmonics of the nonequilibrium distribution and scattering between distinct constant-energy contours play an essential role in extrinsic nonlinear spin transport beyond the single-relaxation-time approximation.

We investigate the dynamics of bound pairs in an extended Hubbard model at resonance. We show that a single fermion and a singlet bound pair possess identical dispersion relations and scatter off each other. In contrast, a neighboring doublon pair is dynamically pinned in the strong-interaction regime. Remarkably, a single fermion and a singlet bound pair exhibit fundamentally different scattering behaviors when encountering a pinned doublon pair acting as a scattering center. While the singlet bound pair undergoes perfect transmission, the single fermion is completely reflected. These results demonstrate that a neighboring doublon pair functions as an efficient filter that separates bound pairs from single particles. Numerical simulations fully support the analytical predictions. Our findings provide a dynamical mechanism for generating and manipulating bound-pair states.

We investigate analytically and numerically a one-dimensional periodically driven free-fermionic system subjected to monitoring of the local particle density. Based on the analytical approach that describes the long-wavelength physics of the time-dependent Hamiltonian in the field-theoretical language using the nonlinear sigma-model (NLSM), we reveal that driving does not alter the universality class of the problem. As a consequence, the system retains the area-law behavior in the thermodynamic limit, with an intermediate diffusive regime giving rise to logarithmic growth of entanglement entropy for a small monitoring rate. At the same time, driving leads to a renormalization of the bare coupling constant of the NLSM, which controls the space-time “conductivity” in the diffusive regime. We derive the analytic form of this renormalization, which becomes particularly strong in the case of a “maximally symmetric” drive and sufficiently short driving period. In addition, we employ the Wiener-Hopf method to investigate the ballistic-diffusive crossover. These analytical predictions are corroborated by numerical simulations of the von-Neumann entanglement entropy and the density correlation function. Our numerical results clearly demonstrate that, with an increase in the system size, there are successive crossovers from ballistic to diffusive behavior and ultimately to localization. Furthermore, in the diffusive regime, we observe weak-localization corrections that are in agreement with the analytical predictions of the NLSM. Overall, our results provide a unified analytical and numerical framework for understanding the effects of monitoring in time-modulated fermionic systems, paving a way for broader investigations of driven quantum matter.

We propose a theoretical scheme for realizing a tunable nonreciprocal Goos-Hänchen shift (GHS) in a hybrid cavity magnomechanical system. The setup consists of a rotating yttrium iron garnet sphere embedded in a microwave cavity, with magnetic-dipole and magnetostrictive interactions mediating magnon-photon and magnon-phonon couplings, respectively. Owing to the Barnett effect, the magnon frequency acquires a rotation-induced shift whose sign can be reversed by changing the direction of the bias magnetic field. We show that the output probe spectrum exhibits a Fano resonance, while the associated GHS responds asymmetrically to opposite field directions, providing a controllable mechanism for nonreciprocal beam shifts. The magnon-photon and magnon-phonon interactions are found to affect the GHS in opposite ways, while the cavity length offers an additional degree of tunability. These results provide a route toward magnetically reconfigurable microwave photonic devices and sensitive detection of Barnett-induced effective fields.

Topological states and criticality have long been regarded as incompatible ingredients: the former requires a finite spectral gap, whereas the latter demands its closure. Guided by this view, topological photonics has focused almost exclusively on gapped phases, treating gap-closing transitions as mere phase boundaries. In this work, we propose a class of topological states in which topology coexists with criticality in experimentally accessible synthetic-frequency photonic platforms. In a one-dimensional (1D) synthetic lattice, we identify such critical topological photonic states through midgap degeneracies in the single-particle entanglement spectrum, and uncover a topology-enforced multicritical point that reorganizes the topology of neighboring critical states. We further extend this framework to two dimensions (2D). Our work provides an experimentally accessible route to critical topological photonics, and may also inspire novel applications such as critical topological sensing.

The exploitation of crystal-lattice symmetries to engineer angular momentum transfer between structured light and magnons marks a novel frontier for optomagnonic research. In Brillouin light scattering, when focused light propagates parallel to an external magnetic field and interacts with ferromagnetic uniform magnons, only optical-vortex scattering is expected to be permitted. Due to the combined effects of magneto-optical coupling and optical spin-orbit interaction, the transfer of magnon spin angular momentum to photon orbital angular momentum allows for this distinctive scattering phenomenon. Here, we experimentally demonstrate that, for a specific ferromagnetic crystal orientation, Gaussian-beam scattering coexists with the optical-vortex scattering, contrary to conventional expectations based on angular momentum conservation between magnons and photons. We show that the crystal lattice, via the rotational Umklapp process, provides the missing angular momentum required for the Gaussian-beam scattering. Furthermore, we predict that as the degree of light focusing increases, the relative efficiencies of the Gaussian-beam and optical-vortex scattering processes reverse.

We study one-dimensional run-and-tumble particles confined by a harmonic potential and coupled to an equilibrium thermal bath. Exploiting the coupling of active and thermal degrees of freedom through the Ornstein-Uhlenbeck propagator, we show that the position distribution factorizes, as a convolution, into the Ornstein-Uhlenbeck distribution and the distribution of the athermal run-and-tumble problem. This yields closed-form results, correcting expressions from earlier treatments by identifying the Ornstein-Uhlenbeck propagator, rather than the free-diffusion one, as the correct kernel. Results are confirmed both in Fourier space and by direct Langevin simulation. We further focus our analysis on the stationary regime, characterized by two dimensionless parameters–the ratio of trapping to persistence length, and the ratio of thermal to active diffusion–which control the crossover from a non-Gaussian, boundary-peaked distribution to the Gaussian, equilibrium-like limit. Energy fluctuations and the Kullback-Leibler divergence from the equilibrium distribution quantify the resulting non-equilibrium character of the confined active particle.

While the interaction-induced breakdown of Aharonov-Bohm (AB) cage is typically attributed to uniform bound-pair transport, systems with inhomogeneous exchange interactions realized with Rydberg synthetic lattices exhibit more complex dynamics. Employing the evolution-path symmetry (EPS) framework developed recently, we analyze the two-particle dynamics via path interference in Fock space. We find that a homogeneous nearest-neighbor exchange interaction cannot break the AB cage, regardless of whether the long-range exchange interaction is present or not. In contrast, we demonstrate that inhomogeneous nearest-neighbor exchange interaction breaks the destructive-interference EPS, and lifts the degeneracy of many-body compact localized states, thereby generating non-local dispersive eigenstates. Consequently, the initial state gains a non-zero overlap with these dispersive states, enabling delocalized transport. Furthermore, while long-range exchange interaction alone preserves the AB cage, its coupling with nearest-neighbor inhomogeneous exchange interaction opens non-canceling pathways that alter the diffusion profile. Our work connects microscopic path interference with macroscopic spectral reorganization, offering an analytical understanding of the mechanism underlying exchange-interaction-induced transport in Rydberg synthetic lattices.

The dynamic magnetic pair-density function (DymPDF) $D_{\rm M}(r, E)$ is derived by extending the static magnetic pair distribution function (mPDF) to finite energy transfer. The analytical DymPDF of a one-dimensional Heisenberg ferromagnet is obtained from the magnon dispersion and compared with simulations performed using {\textsc SpinW}. Excellent agreement is achieved for energy dependence of the nearest-neighbor spin-pair correlation, demonstrating that the DymPDF changes sign at the magnon-mode transition occurring at one-half of the maximum magnon energy. The r-dependence of DymPDF at low energy is also reproduced with a model including magnon correlation length and Fourier-termination effects. These results establish the theoretical foundation of DymPDF analysis for investigating local spin dynamics in magnetic materials.

Conventional probabilistic Ising machines often suffer from inefficient exploration of configuration space, while replica-based quantum Monte Carlo methods reduce sampling bottlenecks at the cost of large hardware overhead. Here we propose a time-dimensional exchange coupling (TEC) that replaces spatial replica coupling with a temporal exchange interaction between successive spin configurations of a single p-bit network. This TEC improves sampling efficiency without duplicating replica hardware. At low temperatures, antiferromagnetic TEC expands sampling range; at high temperatures, ferromagnetic TEC stabilizes the optimal state. For MaxCut problems with up to 2000 vertices, TEC significantly accelerates convergence speed. SPICE simulations confirm hardware feasibility. TEC offers a scalable, hardware-efficient strategy to enhance combinatorial optimization on existing Ising machines.

It has long been known that well-trained neural networks can be compressed very strongly without affecting their performance, an important phenomenon that remains poorly understood. We prove a uniform compressibility theorem for deep multilayer perceptrons with analytic activations. For a deep, wide fixed teacher network, there exists a narrow (same depth) network that approximately represents the same function as the original. The reachable compressed width is strikingly independent of the original width, but is $O((\log(1/\varepsilon))^{d_{in}})$, where $\varepsilon$ is the error budget and $d_{in}$ is the effective input dimension. Our construction involves a novel derivative-matching technique which is aware of the low-dimensional input, and a layer-wise reweighting that preserves the input-output mapping.

We present a reduced-order semi-analytical model for reorientational nonlinearity in chiral nematic liquid crystals, showing that the chiral pitch acts as the dominant physical length scale governing the onset of nonlinear self-focusing and soliton formation. Starting from the full Frank-Oseen equation, we derive a closed-form expression for the optically induced molecular rotation that captures the essential saturable response of the medium while reducing computational cost by more than two orders of magnitude compared with standard relaxation-method solvers. Despite its simplicity, the model reproduces the essential features of the numerically obtained nonlinear refractive index, the onset of self-localization, and the transition from discrete to continuous solitons in one and two dimensions. It further predicts the formation of fully localized astigmatic nematicons with only minor shifts in the self-localization threshold due to the neglect of nonlocal effects. The proposed model provides direct physical insight into light-matter interactions with soft matter media and offers a computationally efficient tool for the design and optimization of nonlinear photonic devices.

Diamond was grown from a liquid Ga-Fe-Ni-Si alloy near 1 atm, although bulk graphite is thermodynamically more stable under those conditions. This Perspective asks what must be true for a diamond growth front to continue advancing in such a metastable regime. I define a finite-difference transfer free energy for a specified interfacial event and identify the completed attachment of one carbon atom at a kink as the repeatable event that governs sustained growth. In the macroscopic limit, surface terms cancel, and the required carbon activity is fixed by the bulk free energy of diamond. On a graphite-normalized scale, the diamond equilibrium threshold is about 2.0 at 1300 K, whereas graphite saturation occurs at unity. Diamond growth therefore requires kinetic selection above the graphite threshold, not a reversal of bulk phase stability. The analysis distinguishes thermodynamic driving force, kinetic accessibility, experimental detection limits, and the carbon retained after an experiment. It gives isotope-resolved tests for distinguishing sustained diamond growth from seed survival, transient carbon attachment, or failure to detect graphite. A $^{13}\mathrm{C}$-enriched diamond seed provides a test of natural-abundance gas or condensed carbon sources: a registered, crystallographically continuous $^{12}\mathrm{C}$-rich layer outside the original seed can establish source-attributed overgrowth without isotopically labeling each feed. The same accounting is extended to cubic boron nitride. Separate boron and nitrogen chemical potentials are required, and $^{10}\mathrm{B}/^{11}\mathrm{B}$ and $^{15}\mathrm{N}$ contrasts could distinguish reservoir supply from seed loss for each element. The resulting criteria make low-pressure metal-flux growth claims quantitatively testable and guide experiments, thermodynamic modeling, and atomistic simulation.

Polyethylene (PE) is one of the most commonly used synthetic polymers. While the synthesis and processing protocols for PE are well established, precise experimental assignment of microscopic structures at atomistic resolution (i.e., the position of each atom) remains largely limited to highly crystalline systems. This gap is often addressed via computer simulations using empirical interatomic potentials, which use approximate but efficient descriptions of interatomic interactions to reach the length and time scales needed to describe macromolecules. These empirical potentials typically perform well for bulk and/or collective properties but face challenges with chemical realism for complex systems, e.g., during reactive processes. In this work, we address this challenge by combining the computational efficiency of a deep potential (DP) machine-learning force field and the chemical realism of first-principles van der Waals (vdW) corrected hybrid density functional theory (DFT) enabled by a SeA high-throughput framework. Using this approach, we study the structure and dynamics of PE oligomers and polymers in an ethylene solvent under common high-pressure (supercritical) radical polymerization conditions. We found that the local solvation environment of radical-containing PE oligomers converges for chain lengths greater than (n~6), suggesting extensibility of our oligomer-trained MLFF to significantly longer polymers. We then confirmed the extensibility of these models to long PE chains by characterizing the molecular weight scaling of single-chain structure and dynamics, which showed classic good solvent behavior. Our PE MLFF retained a consistent level of fidelity and stability across a wide range of thermodynamic state points and chain lengths, at full atomistic resolution, therefore paving the way towards first-principles-based polymer structure and property prediction.

Localized forcing in the fluid inside or outside a viscous drop can drive drop translation. Using the Lorentz reciprocal theorem, we derive an integral expression for the translational velocity of a spherical Newtonian drop subject to localized force and source distributions in either fluid and to interfacial traction. For a clean drop, we obtain explicit responses to Stokeslets, force dipoles, rotlets, general second force moments, and source dipoles as functions of position, orientation, and viscosity ratio. Interior forcing obeys a finite selection rule: only force moments through second order and the first source moment contribute directly to translation. Exterior forcing can couple to multipoles of all orders and produces distance-dependent responses. Although different enclosed singularities can produce the same drop velocity, resolving their exterior flows in drop-centered spherical Stokes modes provides additional constraints on the underlying forcing. We also distinguish regularized force distributions, governed by prescribed kernel moments, from resolved rigid particles, governed by low-order surface-traction moments and prescribed slip. The framework unifies these representations and shows how exterior-flow measurements provide information beyond drop translation, laying the foundation for constructing squirmer-like viscous drop solutions with controllable far-field behaviors.

Ureilites are ultramafic achondrites interpreted as fragments of a differentiated parent body, yet their origin and evolution remain debated because textural equilibrium coexists with chemically primitive compositions. Here we report mineralogical, isotopic, and microstructural observations from polymict ureilite Elephant Moraine (EET) 87720. The sample contains unusually magnesian olivine (Mg# up to 98.7), Ca-poor pyroxene (Wo as low as 1.0), and rare coarse-grained pink aluminous spinel containing 56.4-58.7 wt% Al2O3 and 11.3-11.8 wt% Cr2O3. In situ triple oxygen isotope measurements of spinel and associated forsteritic olivine plot along the ~1-slope Carbonaceous Chondrite Anhydrous Mineral (CCAM) line, consistent with bulk ureilites. The clasts also follow the ureilitic Fe-loss/addition trend, with near-constant chondritic Mn/Mg ratios. These observations demonstrate that the clasts are indigenous to the ureilite parent body and extend the known ureilite oxygen isotope range to delta18O ~9.7 per mil. Three-dimensional dark-field X-ray microscopy reveals a hierarchical deformation microstructure in the spinel, comprising distributed lattice curvature, localized slip-band-like boundaries, and coherent mosaic-domain boundaries, indicating multiscale accommodation of shock-induced crystal-plastic deformation. We propose that the aluminous spinel crystallized from a locally Al-rich, Ca-poor melt under low oxygen fugacity. Al partitioning between coexisting spinel and olivine yields a crystallization temperature of 1318 +/- 43 K, consistent with a thermally elevated parent body. The spinel may therefore preserve a rare crystallization product of an early aluminous melt that has largely disappeared from the ureilite record, providing an archive of early planetary differentiation.

We study the superdiffusive behavior of random walks on the randomly oriented Manhattan lattice, i.e., the $d$-dimensional integer lattice $\mathbb{Z}^d$ where each axis-aligned line is independently assigned a random direction (forward or backward) with equal probability. The walker takes nearest-neighbor steps, choosing an axis randomly and moving along the assigned direction of that axis's line, with equal probabilities for each axis. We show that, in the critical dimension $d=3$, the diffusion coefficient of the random walk diverges in the Tauberian sense as $\sqrt{\log t}$ with a multiplicative correction $(\log\log t)^{\pm(2+\varepsilon)}$ as time $t\to\infty$. This gives an answer to a conjecture by Ledger, Tóth and Valkó (2018).

We investigate the impact of charge regulation (CR) on the non-uniform swelling behavior of polyelectrolyte hydrogels. The Poisson-Boltzmann theory with electro-elastic coupling between the local polymer density and elastic deformation is considered. We investigate the spatial distributions of the elastic displacement and polymer density under different salt concentrations and compare charge-regulated gels with fixed-charge (non-CR) gels of the same net charge. Our results show that the CR induces spatially varying charge fractions, which strengthen the electro-elastic response and lead to stronger non-uniform swelling compared with non-CR gels. These findings provide a theoretical basis for understanding and controlling non-uniform swelling in responsive polyelectrolyte hydrogels.

Anomalous heat transport in strongly anharmonic crystalline solids poses both a fundamental challenge to the theoretical understanding and an opportunity for thermoelectric and thermal barrier coating applications. Although Green-Kubo theory reproduces experimental thermal conductivity ($\kappa$) at high temperatures, it lacks microscopic insight and neglects the Bose-Einstein statistics of lattice vibrations. On the other hand, the conventional Boltzmann transport equation (BTE) framework, based on a phonon-gas picture, fails due to strong anharmonicity-induced overdamped phonons. Herein, the thermal transport properties in TlAgSe, a metal chalcogenide, and Cs$_2$PbI$_2$C$_2$, an all-inorganic layered Ruddlesden-Popper perovskite, are investigated by explicitly accounting for temperature-dependent lattice dynamics through machine learning interatomic potentials and employing the Wigner transport equation (WTE) framework. Crucially, heat conduction is governed not only by higher-order phonon scattering-dominated populations' transport channel described within the BTE, but also by a coherences' channel in the WTE framework arising from wave-like interbranch coherence between eigenstates. Incorporating four-phonon scattering, WTE predicts average room-temperature $\kappa$ values of 0.31 Wm$^{-1}$K$^{-1}$ (TlAgSe) and 0.38 Wm$^{-1}$K$^{-1}$ (Cs$_2$PbI$_2$C$_2$), in excellent agreement with experiments. Phonon scattering-rate analysis reveals strong coherences' contributions and prevalent overdamped phonon modes, demonstrating the breakdown of the conventional BTE framework based on the phonon quasiparticle picture with only first-order anharmonic perturbation. This computational approach provides a unified description of heat transport in ultralow-$\kappa$ materials, offering a basis for the rational design of phononic and thermoelectric devices.

Shannon–Rényi entropies probe the full measurement distribution of a quantum many-body state, but their microscopic evaluation remains difficult even in free-fermion systems. We show that the Born distribution of the critical transverse-field Ising chain is exactly the parity boundary of a weak inverse-square classical Ising model, a structure revealed by the Cauchy form of its probability kernel. The construction is exact at finite size for every real $n>0$ and isolates the long-distance sectors controlling the $n>1$ thermodynamics. Cutting a finite interval generates the universal $c\,n/[8(n-1)]$ logarithm directly from the missing $1/r^2$ interactions, with $c=1/2$ the Ising central charge. On the ring, the explicit finite-size factor has no constant term, while any additional noninteger singularity is confined to a residual cycle-only free energy. All explicit long-distance contributions become marginal only at $n=1$.

Discrete energy-level structures in Coulomb-like localized bound states are conventionally obtained by direct diagonalization of the Schrödinger equation or by semiclassical approximations that fail at low energies. Here we develop a geometric phase-space framework that recovers the exact discrete energy levels and shell degeneracy of three-dimensional Coulomb bound states from classical symplectic geometry and global boundary constraints, bypassing explicit operator diagonalization. Using Kustaanheimo–Stiefel regularization, we map negative-energy Kepler orbits to four-dimensional isotropic harmonic oscillators. The group composition law of the symplectic flow determines an integral kernel built from the classical two-point action and Van Vleck amplitude, whose infinitesimal generator satisfies an exact linear evolution equation—a property we term quadratic closure. Imposing three geometric constraints—decay at infinity, regularity at the origin, and fiber invariance under the Hopf fibration—we recover the exact $E_n/E_1=1/n^2$ scaling and $g_n=n^2$ degeneracy. The phase scale $\alpha$ sets the action unit; all spectral structural features are independent of its value. This framework offers a symmetry-transparent route to spectral data: for quadratic Hamiltonians, the classical kernel incurs zero semiclassical error even at ground-state energies, and the geometric constraints directly identify symmetry-protected degeneracies without diagonalization. We apply the method to shallow impurity states, moiré superlattices, and semiclassical transport, demonstrating how geometric screening rules simplify spectral analysis in condensed-matter environments.

We provide a perspective into measuring the quantum information spreading by introducing N-operator correlators. Leveraging the idea from N-point correlation function from cosmology, we formulate a generalized Out-of-Time-Ordered Correlator (OTOC), called N-Operator Correlator (NOC). Such formulation can reduce the effect of restricted analysis associated with selecting only two operators for OTOC. NOC can take into account a larger set of measurement probes in measuring the degree of quantum information spreading. We demonstrate these concepts with two analytically tractable toy systems with computing thermal averages of operator time evolutions at a finite temperature: a single qubit in longitudinal field and XYZ two-qubit system. Our perspective serves as a basic introduction to generalized operator correlators in quantum mechanics.

For nonautonomous open systems described by macroscopic stochastic thermodynamics, we derive an emergent second law that constrains time-dependent macroscopic fluctuations by the entropy production along the most probable evolution under the time-reversed driving protocol. We show that this bound can be understood as a macroscopic consequence of the fluctuation theorem: the time reverse of this evolution provides a possible fluctuation path under the forward dynamics. In the linear-response and slow-driving regime, the bound becomes an equality to first order and generalizes the McLennan-Zubarev formula to the time-dependent probability density of nonautonomous systems with weak nonconservative affinities. We illustrate our results in a bistable system under sudden quenches and periodic driving.

Multilevel non-volatile memory technologies face recurring trade-offs among information density, endurance, retention, and switching energy. We investigate an alternative state variable based on the discrete vortex configuration of self-organized vortices in a boundary-driven electron fluid. A dissipative point-vortex model derived from magnetohydrodynamic dynamics yields six reproducible vortex codewords, corresponding to 2.585 bits per cell, whose write fidelity, noise sensitivity, 100-cycle endurance, and effective information capacity are quantified. The ordering of their finite-amplitude basin radii $r_{50}$ differs from that predicted by both fixed-circulation and fully coupled linear-stability spectra. A nonlinear saddle-point construction based on the reduced dynamics likewise does not recover the measured basin ordering. The discrepancy is associated with escape pathways involving coupled position–circulation dynamics that are absent from the fixed-circulation description. These results show that local stability alone does not determine the finite perturbation tolerance of the vortex states considered here. The proposed memory requires active hold power, and passive retention remains to be established experimentally.

Quantitative charge-transport modelling in crystalline pi-conjugated polymers requires an electronic representation that captures extended conjugation and material-specific electron-phonon interactions on equal footing. We present a Wannier-orbital-based formulation of the transient-polaron-localization (TPL) framework for quantitative charge-transport simulations in crystalline pi-conjugated polymers. By expressing all interactions directly in a Wannier representation derived from first-principles calculations, the approach avoids artificial fragmentation of polymer backbones and enables a consistent, material-specific description of electronic couplings and electron-phonon interactions. Low- and high-frequency vibrational modes are incorporated within a mode-resolved TPL formalism, yielding an effective electronic Hamiltonian that captures both dynamic disorder and polaronic renormalization. The methodology is demonstrated for the ambipolar crystalline naphthalenediimide-bithiophene copolymer, enabling a direct comparison of electron and hole transport along the polymer backbone and pi-stacking directions. The simulations reproduce key transport features, including pronounced anisotropy and higher electron than hole mobility. Additional studies on single- and bi-chain systems reveal the essential role of inter-chain coherence in supporting efficient transport along the polymer backbone. Beyond this specific system, the Wannier-orbital-based TPL framework provides a transferable route to disentangle intrinsic charge-transport mechanisms in crystalline pi-conjugated materials and establishes a foundation for future work.

Network Hamiltonian Models (NHMs) provide an efficient framework for modeling the aggregation of interacting particles (e.g., the condensation of proteins into gel-like, oligomeric, or fibrillar states), representing the system as a network whose edges represent bound interactions. Terms within the network Hamiltonian represent multi-body interactions governing aggregation behavior, and are specified via topological degrees of freedom. Because motional degrees of freedom are not explicitly represented within the NHM, their influence must be indirectly accounted for by introduction of corresponding terms to the Hamiltonian. Here, we describe specifications for terms representing motional degrees of freedom of two, three, and four-body interactions. We also consider the impact of these terms on the aggregation states of a minimal system governed only by a pairwise edge potential, showing that three and four-body interactions favor condensation of the system into small droplet-like structures at low temperature.

The kagome $R$Mn$_6$Sn$_6$ material family has attracted significant attention as high-temperature metallic magnets with a host of different magnetic orderings and anisotropy. Theoretical studies point to the rare-earth ($R$) as the determining factor for both the direction of magnetic anisotropy and the type of magnetic ordering in a given compound. This motivates studying high-entropy forms of $R$Mn$_6$Sn$_6$ to examine how the interplay of several rare-earth elements leads to different magnetic states in a single crystal. Here, we present a rare-earth mix of Tb, Dy, Ho, Er, Tm, and Lu that produces phase transitions from a paramagnet to an easy-plane ferrimagnet (FiM) below $T_{\text{C}}$ = 380 K, then to a FiM easy-axis state at $T_{\text{SR1}}$ = 207 K, to a canted FiM ground state below $T_{\text{SR2}}$ = 79 K. This behavior is consistent with previously reported high-entropy $R$Mn$_6$Sn$_6$ compounds; however, uniquely, the rare-earth mix studied here exhibits a broad transition from easy-plane to easy-axis anisotropy from 270 K to 170 K, and reveals a nonmonotonic magnetoresistance. Using neutron scattering data, we found that both observations correlate with an incommensurate modulated contribution to the spin state due to competing rare-earth interactions. This magnetoresistive behavior and the correlated spin structures underscore the potential for rare-earth engineering of magnetism.

For decades, debate has surrounded the electrostatic persistence length (EPL) controlling local polyelectrolyte stiffening, centered on two competing power laws: the linear BJ prediction, $\textbf{l}_\mathrm{e} \sim r_\mathrm{D}$, and the quadratic OSF/KK scaling, $\textbf{l}_\mathrm{e} \sim r_\mathrm{D}^{2}$, where $r_\mathrm{D}$ is the Debye screening length. Building on the asymptotic scaling theory developed in the accompanying paper, we validate a complete diagram of limiting regimes using large-scale coarse-grained Monte Carlo simulations of ideal chains with charged monomers interacting through a screened Coulomb potential. By simulating long chains of up to $N \simeq 10^{4} - 10^{5}$ Kuhn segments, we demonstrate that the electrostatic stiffening of both semiflexible and flexible polyelectrolytes obeys the same quadratic OSF/KK law. We track the exponent $\alpha$ which measures how the chain size $R$ grows with the Debye radius, $R \sim r_\mathrm{D}^{\alpha}$. For both cases, in agreement with the OSF/KK theory, $\alpha$ rises past 3/5 and slowly approaches 1 as the chain length increases, whereas within the BJ theory it can never exceed 2/5. We further find that three common size measures, the end-to-end distance $R_\mathrm{ee}$, radius of gyration $R_\mathrm{g}$, and hydrodynamic radius $R_\mathrm{h}$, reach this asymptotic behavior at progressively increasing chain lengths. Consequently, for any real polyelectrolyte, the apparent exponents obey $\alpha_\mathrm{ee} \geq \alpha_\mathrm{g} \geq \alpha_\mathrm{h}$, making $R_\mathrm{g}$ a sharper experimental probe than $R_\mathrm{h}$. Finally, we re-analyze the available experimental data and show that they rule out the linear BJ law and support the quadratic KK scaling, thereby resolving contradictions that stem from mistaking the apparent slopes measured for short chains for the true asymptotic exponent.

Predicting mobile-ion self-diffusivity $D^*$ from molecular dynamics (MD) simulations is essential for identifying promising solid-state electrolytes, but directly simulating ion diffusion is computationally expensive, particularly with high-accuracy machine learning interatomic potentials (MLIPs). Diffusion is a slow, emergent process that requires long trajectories to converge. Thermodynamic properties, by contrast, converge much faster: the enthalpy $h$, vibrational entropy $s_{vib}$, and 2-body, excess configurational entropy $s^{ex}_{2,config}$ can be extracted from comparatively short MD trajectories, and they encode rich information about the free energy landscape from which transport properties like self-diffusivity ultimately arise. Intuitive correlations are discussed between these thermodynamic properties and ion diffusion, motivating a data-driven approach to exploit this link. A simple neural network was trained to predict diffusivity from features computed over short MD trajectories: a vibrational fingerprint (the vibrational density of states, VDOS) and a structural fingerprint (the radial distribution function, RDF), conditioned on chemistry information encoded in the MLIP embedding. This combination allows the model to predict the converged $\log_{10} D^*$ (cm$^2$/s) \textemdash\ normally obtained from significantly longer MD simulations \textemdash\ with a mean absolute error of 0.398 and a Spearman's rank correlation $\rho$ of 0.844.

The problem of single-chain conformations of polyelectrolytes in salt-added dilute solutions, and the associated concept of the electrostatic persistence length $\textbf{l}_\mathrm{e}$, has remained unresolved for decades. To address this challenge, we develop a comprehensive scaling theory and corroborate it with simulations. A unified scaling diagram is constructed that encompasses both flexible and intrinsically semiflexible/stiff polyelectrolytes. Nine distinct scaling regimes are identified, each characterized by different conformational statistics. The concept of the Gaussian electrostatic blob $\xi_\mathrm{e}$ used in the description of flexible polyelectrolytes is extended to the semiflexible case, and the new characteristic length $\xi_\mathrm{e}^{|}$ referred to as the rodlike electrostatic blob is introduced. This enables delineating the important crossovers and showcasing an analogy between semiflexible and flexible chains. The concept of electrostatic excluded volume is also reconsidered and generalized. Upon increasing the salt concentration, i.e., decreasing the Debye length $r_\mathrm{D}$, chain conformations evolve from (i) rodlike stretches to (ii) Gaussian and then (iii) swollen coils with local electrostatic stiffening characterized by $\textbf{l}_\mathrm{e}$, followed by (iv) swollen coils without stiffening but with electrostatic exclude volume, and finally to (v) quasi-neutral Gaussian coils. In regimes of type (ii) and (iii), the electrostatic persistence length scales quadratically with $r_\mathrm{D}$, in agreement with the OSF and KK predictions for semiflexible and flexible chains, respectively: $\textbf{l}_\mathrm{\mathrm{OSF}} \simeq r_\mathrm{D}^{2}/\xi_\mathrm{e}^{|}$ and $\textbf{l}_\mathrm{\mathrm{KK}} \simeq r_\mathrm{D}^{2}/\xi_\mathrm{e}$. These asymptotic scalings are confirmed by coarse-grained simulations presented in the accompanying article.