Papers

Slowly sheared granular materials generally store mechanical energy and dilate between abrupt failures that release energy and compact the material. Here, simultaneous measurements of torque, layer thickness, acoustic emission, and photoelastic force networks reveal all four combinations of energy release or storage with contraction or dilation in a compressed granular fault. Most strikingly, some avalanches both dilate the layer and increase the elastic energy transmitted to the resisting boundary. These events reorganize force chains beyond the shear band and produce a distinct acoustic response. The results show that an avalanche need not relax a driven disordered material; it can instead redistribute stress into a more highly loaded configuration, a mechanism with potential relevance to the physics of both laboratory and natural faults.

We introduce high-order Winfree models for oscillatory associative memory. We characterize memory performance through the local-stability dichotomy between stored and unstored patterns. Using this criterion, we show that crosstalk noise drives a cascade of ferromagnetic, mixed, and spin-glass transitions as the memory load increases. For both polynomial and exponential Winfree models, we derive the phase boundaries and develop auxiliary-field modulation schemes adapted to the different phases. We further present corresponding circuit designs and numerical simulations that support our theoretical predictions.

We give a quantitative disorder comparison for the zero-field Sherrington–Kirkpatrick model at inverse temperature one. For any fixed number of replicas, replacing Gaussian couplings by independent couplings from a bounded symmetric variance-one law changes a bounded replica expectation by at most a constant times the Gaussian overlap second moment plus $N^{-1}$. A multiplicative comparison for nonnegative observables controls the tails. The proof uses Talagrand's positive-observable estimates and Yu-Ting Chen's fourth-order replica cancellation. Assuming the Gaussian critical overlap limit stated by Du and Huang, we obtain the same limit for the random quenched overlap measure in the iterated Wasserstein-2 topology. No separate moment assumption is needed for this transfer. Their additional exponential moment bound gives convergence of the rescaled spin-glass susceptibility in every finite Wasserstein distance. The coupling class includes fair signs, uniform disorder, and signs thinned at any fixed positive density.

Classical theories of random neural networks typically assume independent connectivity, overlooking the local motif structures prevalent in biological circuits. Here, we investigate how four second-order synaptic motifs (chain, reciprocal, convergent, and divergent) shape the dynamics of nonlinear firing-rate networks. While previous studies have established that chain correlations generate outlier eigenvalues, we demonstrate that these motifs also jointly reshape the Jacobian eigenvalue bulk. Using the path-integral formalism, we derive a dynamic mean-field theory which reveals that the chain motif acts as a retarded feedback of the ensemble-mean activity through the response kernel, producing a rich repertoire of dynamical regimes, including ferromagnetic states and limit cycles. At sufficiently large magnitude, negative chain correlations produce a glassy, multistable regime that was previously mainly associated with partially symmetric networks. Our theory also distinguishes convergent from divergent motifs: divergent correlations primarily rescale temporal noise, while convergent correlations suppress temporal chaos by converting nonzero mean activity into quenched heterogeneity. Finally, analyses of the Lyapunov spectrum and participation-ratio dimension show that motif structure changes the geometry of chaotic activity, reducing entropy production and attractor dimensionality even when the effective spectral edge is held fixed. Together, these findings establish second-order motifs as a fundamental structural mechanism governing the dynamical regimes of local cortical circuits.

The homogeneous form associated with a symmetric tensor, restricted to the sphere, is the objective of the best rank-one approximation problem and, with random coefficients, the energy of a mean-field spin glass. Its critical points have been studied extensively, but the global organization of the landscape they form is far less understood. We study this global structure for positive orthogonally decomposable tensors. We determine the persistent homology of the sublevel and superlevel filtrations in closed form, for every homological dimension $q$, every ambient dimension $D$ and every tensor order $k$, via a recurrence in the ambient dimension. Taking the coefficients to be random, we further prove laws of large numbers for the resulting persistence diagrams at dimension $0$ and $D-2$, giving an exact description of the typical global topology of a spin-glass-like energy landscape. We illustrate our results with numerical computations and simulations.

Scale-invariant avalanche dynamics are commonly associated with criticality and robust, universal size exponents. Dissipation is generally expected to drive the system away from the critical point, progressively suppressing large events. The Olami–Feder–Christensen (OFC) model challenges this picture: in its non-conservative regime, the avalanche-size exponent is non-universal and can exceed the mean-field value $\tau=3/2$, while system-spanning events persist even at large dissipation. Here, we show that these apparently anomalous features are also observed experimentally in a two-dimensional granular system displaying scale-invariant avalanche dynamics. By increasing interparticle friction, and therefore dissipation, the avalanche-size exponent increases from $\tau=1.58$ to $\tau=1.83$, while the upper cutoff remains proportional to the system size. We further identify similarities between experiment and the OFC model in their memory effects, local dynamics, and the emergence of better-than-random predictability of large events. The latter indicates that the system does not remain permanently critical, but instead evolves through configurations with different propensities to generate extreme events. Our results suggest that OFC-like dynamics are not merely an anomalous feature of a particular model, but may provide a relevant framework for understanding scale-invariant dynamics with $\tau>3/2$ in real dissipative systems.

We study the retrieval dynamics of an $n$-body asymmetric dense associative memory model, in which sequential retrieval is implemented by shifting one pattern index in the higher-order Hebbian interaction. The model exhibits sequential retrieval of the stored patterns, and the retrieval state corresponds to a stable limit-cycle attractor. The storage capacity is defined as the maximum loading rate for which this limit cycle remains stable. Using generating functional analysis, we derive the dynamical equations describing the sequential retrieval state. The generating functional analysis reveals that the retarded self-interaction term vanishes in the asymmetric model, and the resulting overlap dynamics is reproduced by an Amari-Maginu-type signal-to-noise analysis. Also, we find that for the interaction order $n\ge 3$, the normalized storage capacity decreases monotonically with increasing interaction order, in contrast to symmetric Modern Hopfield models.

We study rare nonresonant regions in a canonical one-dimensional disordered quantum spin chain by directly implementing the iterated Schrieffer-Wolff construction underlying the recent work of De Roeck, Giacomin, Huveneers and Prosniak on subdiffusive transport. For finite systems, we compute the probability that a disorder realization remains nonresonant through successive scales of the flow, while separately monitoring operator proliferation and the spatial localization of dressed local observables. The survival probability decays at most exponentially with system size over the numerically accessible regime. Resolving this decay scale by scale yields failure rates associated with successive Schrieffer-Wolff steps. The first rate is obtained analytically in excellent agreement with numerics, while higher-scale rates decrease rapidly throughout the regime studied. These results support the summability mechanism required for exponentially rare but parametrically long nonresonant regions, which provide the insulating bottlenecks responsible for subdiffusive transport. At the smallest couplings studied, the survival probability under our conditions exceeds the rigorous lower bound by six to seven orders of magnitude, demonstrating how conservative the constants required by the proof are while confirming that its underlying physical mechanism is quantitatively visible at accessible scales. More broadly, our results show how direct numerical implementations can provide an independent and physically transparent test of technically demanding constructive proofs, a methodology that may become increasingly useful as machine-assisted proofs become more common.

Within a random-matrix-theory (RMT) approach, we perform a detailed numerical study of the spectral statistics of fuzzy Erdos-Renyi (ER) random graphs. Specifically, we consider the membership values of the vertices and edges of a fuzzy ER graph model as random variables. In this way, the corresponding adjacency matrices become sparse matrices with random entries. Then, we apply standard RMT measures to characterize the eigenvalues and eigenvectors of ensembles of Hermitian and non-Hermitian adjacency matrices of both undirected and directed fuzzy graphs. We demonstrate that the average degree of the ER model serves as the scaling parameter of the spectral properties of the corresponding fuzzy setups.

The 3D digital reconstruction of multi-scale, heterogeneous porous media is traditionally limited by the resolution boundaries and artifacts of X-ray computed tomography (XCT). This paper introduces a physically consistent 2D to 3D pore space synthesis framework that supersedes conventional geometric shuffling with dynamic Newtonian gravitational deposition using a high-performance rigid-body mechanics engine. To honor strict physical contact mechanics, statistical 2D targets, and morphological constraints, we develop a two-stage dynamic packing pipeline that combines realistic 3D grain shapes with a virtual sub-particle insertion engine. The framework is validated against synthetic and natural core benchmarks. First, we show that our stereological integral equation systematically converts size distributions; bypassing this inversion step induces a systematic 50% deviation in permeability predictions despite identical total porosities, independently altering flow channel topology. Second, temporary virtual spheres serve as architectural placeholders to stabilize large non-equilibrium dissolution voids, ensuring the reconstructed model satisfies target flow metrics within the prescribed tolerance. Finally, when applied to a fine-grained, weakly consolidated sandstone, the workflow exposes and suppresses systematic XCT artifacts, including phantom internal porosity. Ensembles of two-point correlation functions demonstrate that the hydrodynamically and structurally synthesized digital twins quantitatively exhibit closer structural proximity to the uncorrupted rock geometry than the reference XCT dataset itself. This methodology establishes a scalable foundation for high-fidelity multi-phase rock reconstruction, with potential extensions toward complex amorphous cement phases.

As a simple model of interacting systems of excitable degrees of freedom, we consider a threshold contact process on various lattices and networks, in which a successful activation event requires the presence of more than one active neighbors. We show by combining numerical simulations and a phenomenological theory that, in the two-phase coexistence region and for a sufficiently low initial activity, a slower-than-exponential temporal decay of the global density emerges, caused by the spontaneous formation of slowly vanishing and non-communicating clusters of activity. This slow-decay phenomenon is found to appear generally for regular lattices and also for finite-dimensional random lattices such as the Voronoi-Delaunay network. However, the slow-decay is impeded by small-world property, as demonstrated by simulations on random-regular networks. In the case of a power-law decay of the order parameter, which is valid among others on two-dimensional regular lattices, our phenomenological theory points out that the decaying state is stable against unbounded nucleation only if the decay exponent exceeds $1/2$. Besides the well-known Griffiths effects of quenched random systems, this slow-decay phenomenon rooted in the threshold condition provides an alternative mechanism of off-critical but scale-free dynamics, occurring also in the absence of disorder.

Recent studies of "deep thermalization" have revealed universal physics in quantum many-body dynamics beyond equilibration towards Gibbs states: maximally random quantum state ensembles can emerge on local subsystems, generated by measurements on their complement. In this work, we further identify a new form of universality exhibited in the "finer fingerprints" of quantum dynamics for local subsystems, induced by global unitary time-evolution. Specifically, we consider the projected Kraus ensemble, an ensemble of Kraus operators obtained by unraveling the quantum channel on a small subsystem with respect to knowledge of the classical configurations of its complement. Our central result is a one-parameter random matrix Ansatz that captures the ensemble's emergent statistical behavior along particular spacetime scalings, valid for generic 1D circuit dynamics without conservation laws: the ensemble is described by the product of a complex Ginibre random matrix and an independent log-normal random real scalar. The former encodes scrambling within the subsystem, captured by rotational invariance of the Ginibre measure, whereas the latter encodes fluctuations in the Born probabilities, arising from locality of the underlying dynamics. Our Ansatz can be established in the special cases of dynamics generated by global Haar random unitaries and dual-unitary circuits, while we motivate it for generic circuits using arguments of spacetime duality and the multiplicative ergodic theorem on long products of spatial transfer matrices. Extensive numerical simulations for random and Floquet circuit models verify these predictions. This universality in Kraus operators also provides a microscopic mechanism for deep thermalization in generic 1D quantum circuit dynamics, and has implications for local quantum information recoverability involving classical side information tied to knowledge of the bath.

The relationship between vibrational modes and glassy dynamics has been an important and controversial topic of study for many decades. We introduce a family of glass-forming model potentials that have identical molecular and swap dynamics but different low-frequency vibrational modes. In sufficiently small systems low frequency modes do not hybridize with phonons, and this enables us to study their statistical properties independently. We investigate i) the role of the optimization algorithm used to find a minimum; ii) that of the finite-size effects; iii) that of the truncation of the interaction potential; and, iv) that of the parent temperature. We find that models with identical supercooled liquid structure and dynamics can have dramatically different non-phononic vibrational modes at low frequency, based on how the potential is truncated. These findings challenge ideas relating the low-frequency non-phononic vibrational modes with the slow supercooled liquid relaxation.

Hierarchical correlations are a universal feature of any realistic model of data, and the question of how associative memory models may learn these correlations and generalize beyond them to construct new sensible images is an important step towards understanding more complex modern architectures such as diffusion models. We consider a hierarchical model for memories which are sampled and stored in a dense Hopfield network with polynomial activation. We analytically derive conditions for each level of this hierarchy to be locally stable - that is they are local energy minima. We use prototype reconstruction as a minimal model of generalization and we find that it takes only a quasi-polynomial amount of information to generalize beyond particular memories and even particular groups in the hierarchy. We observe a qualitatively analogous phase diagram in the number of memories, sharpness of the activation function (polynomial degree) for data from Fashion-MNIST.

Finite-component light-matter systems realize dissipative phase transitions in a single controllable atom-cavity setup, but how atomic dephasing - ubiquitous in real cavity- and circuit-QED devices - affects this criticality remains unknown. We study the anisotropic open Rabi model under cavity decay, spontaneous emission, and atomic dephasing together. We show that when spontaneous emission stabilizes a long-lived metastable superradiant phase, atomic dephasing actively competes with it - eroding its coherence and shortening the lifetime. This direct competition reveals that a dissipation channel's microscopic character, not its strength, controls its nonequilibrium criticality - a distinction directly tunable via independent spontaneous-emission and dephasing rates in circuit-QED and trapped-ion platforms.

Ultracold atomic systems offer a highly controllable platform for investigating quantum state transfer through the precise dynamical manipulation of system parameters. While quantized Thouless pumping has been extensively explored in these systems, adiabatic edge-to-edge transfer of localized quantum states remains largely unexplored. Here, we consider a one-dimensional ultracold atomic gas confined in a bichromatic optical lattice realizing a quasiperiodic Aubry–André–Harper system. We use its edge-localized winding states to implement quantum state transfer between opposite boundaries. Starting from the instantaneous spectral properties of the corresponding tight-binding model, we construct locally adiabatic protocols and extend the approach to higher protocol orders. We then simulate their dynamics under the full continuum bichromatic-lattice Hamiltonian. Our results reveal a tradeoff between edge localization and the minimum spectral gap: strongly localized states require longer transfer times, but can benefit substantially from higher protocol orders. We are also able to capture the main fidelity trends and coherent oscillations over a broad parameter regime using an effective two-level Landau–Zener description. Our results provide practical guidelines for selecting experimentally accessible parameters and tailoring quantum transfer protocols in quasiperiodic ultracold atomic systems.

We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the standardized moments of the Ising DOS as features for learning. We show that these moments count signed closed walks, are switching-invariant, and are size-free by construction. As a benchmark, we target learning the frustration index, an NP-hard measure of structural balance that can be labeled exactly at moderate size. At zero field, the models can be sampled classically, allowing the quantum extraction procedure to be certified against exact ground truth. We propose DOS-QPE, a phase estimation on a purified maximally mixed probe, which samples the spectral density with orders of magnitude fewer shots than Hadamard test-based trace sampling and feeds the resulting features directly into classically trained models. On $1.4\times10^5$ labeled graphs the exact DOS determines the frustration index, and five moments recover it with a mean error of 0.4, well below one sign flip. Beyond zero field, the underlying trace-estimation problem is DQC1-complete, providing access to spectral features for which no efficient classical sampling method is known. Our work opens routes towards quantum applications in social network balance analysis, spin-glass studies, correlation clustering, and protein-interaction networks.

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

Associative memory in the Hopfield network is attractor dynamics in a disordered many-body system, and higher-order and exponential extensions turn its retrieval update into softmax attention. The polynomial and exponential regimes have been analyzed by different methods, with no common architecture in which to ask what fixes the storage scale. In this paper we study the bipartite architecture of Krotov and Hopfield, which we call the class $H$, whose model is fixed by a Lagrangian for each layer, taking the hidden neurons as the order parameter of retrieval. At polynomial load the replica method yields the replica-symmetric phase diagrams and closed-form capacities, and the crosstalk moment is common to Ising and spherical visible neurons, so their differences come from the visible entropy. With a softmax hidden layer the load is exponential, and a copy representation maps the thermodynamics onto random-energy-model counting, with paramagnetic, condensed, and frozen phases. Heating destabilizes retrieval by quantized reassignments of attention, and typical Gaussian patterns remain metastable at every load. The regimes differ in their crosstalk statistics, central-limit at polynomial load and large-deviation at exponential load, and the class $H$ splits retrieval into two roles, the visible Lagrangian fixing stability and the hidden one the storage scale, two axes that may also guide the design of new Lagrangians.

Quasiperiodic order is characterized by irrational frequencies whose rational approximability known as irrationality measure defines distinct arithmetic classes. We establish that this arithmetic classification has direct physical consequences for long-wavelength charge fluctuations. In translation-covariant quasiperiodic systems, the infrared scaling of charge fluctuation is governed by the interplay between the irrationality exponent of irrational frequency and the large-harmonic decay of the hull charge profile: the latter determines the available charge weight, while the former controls how efficiently that weight is transferred to the infrared. Consequently, all algebraic irrational frequencies share the same arithmetic scaling, whereas exceptionally well-approximable transcendental frequencies can exhibit strongly enhanced infrared fluctuation scaling. We further prove that occupied states separated from the Fermi level by a gap stable throughout the hull contribute only an analytic infrared background, leaving the nontrivial scaling to near-Fermi states. Our results extend to general translation-covariant multi-frequency quasiperiodic systems.

When independent learners are trained on data from the same disordered system, finite and noisy samples can lead them to different descriptions of the underlying physics. We quantify the reproducibility of such descriptions through consensus, the degree of agreement among independently trained models. In a teacher-student framework on the two-dimensional random-bond Ising model, an ensemble of students each infers a single uniform effective coupling from a finite set of equilibrium configurations drawn from one quenched bond realization. Aggregating the inferred couplings across students and realizations yields the consensus distribution, whose width quantifies the agreement among learners. The variance of this distribution separates exactly into a finite-sampling contribution, bounded below by inverse of Fisher information, and a quenched-disorder contribution. Sum of these two variance is minimized near critical region, so the consensus width has a minimum near the pseudocritical temperature that sharpens with increasing disorder. The two minima arise from different mechanisms: the sampling term inherits the critical peak of the Fisher information, while the disorder term is temperature-independent at leading order and acquires its critical minimum only at fourth order in the disorder strength, through the covariance between the linear and cubic responses to the bond disorder. Because the students fit a uniform coupling to a heterogeneous lattice, the inferred coupling also carries a misspecification bias that survives in the infinite-data limit. This bias displaces the minimum of the mean-squared error above the consensus minimum, so the temperature at which independent learners agree most closely is not the temperature at which their shared answer is most faithful.

We demonstrate that designing a neural quantum state to be an exact eigenstate of the Hamiltonian's symmetries significantly improves both training speed and final variational energy. For the 2D electron gas, we design TorFormer, a neural network wavefunction which is an exact eigenstate of the total momentum. TorFormer describes both the Fermi liquid and Wigner crystal with no supervision and significantly outperforms Psiformer-based references up to large system sizes. For $r_s = 30.0$ and $40.0$ at $N=91$, we compare TorFormer trained for $8\mathrm{K}$ steps against the previous best NQS, which required $100\mathrm{K}$ training steps. Our improvement to the total energy at $r_s = 40.0$, excluding the trivial Madelung part, is $0.12\%$—enormous compared to the tiny differences separating phases. Relative to Slater-Jastrow-backflow diffusion Monte Carlo, TorFormer's energy decrease is roughly $9.8$ times that of the previous best NQS. Our work demonstrates that neural quantum states can both accurately and efficiently solve large-scale problems.

Exciton-polariton condensates combine ultrafast dynamics with strong optical nonlinearities, making them promising for optical neuromorphic computing. Here, we numerically demonstrate image recognition using the transient response of an exciton-polariton condensate. Downscaled MNIST images are encoded as optical pulse sequences, and the resulting condensate dynamics are sampled and processed by a linear classifier. For ten-class classification, condensate features achieve 92.2% accuracy, compared with 91.4% for raw-pixel linear classification. Combining both feature sets increases the accuracy to 93.2%. For the challenging binary classification of digits 7 and 9, the combined model reaches 97.3%, exceeding both the linear (95.5%) and feed-forward neural-network (96.6%) baselines. These results demonstrate that polariton dynamics can extract useful nonlinear features for ultrafast optical information processing.

We study the quenched pressure of the nearest-neighbor Edwards–Anderson Ising model with free and periodic boundary conditions. First, we prove that the infinite-volume pressure is $\beta d$-Lipschitz in the coupling law for the $1$-Wasserstein distance, yielding quantitative thermodynamic limits for spatially inhomogeneous disorder. Second, for periodic volumes, we prove that almost-sure convergence under every joint coupling of the finite-volume disorder arrays is equivalent to complete convergence of the one-volume pressure laws. Third, we prove that $\mathbb{E}\vert{}J\vert{}^{1+1/d}<\infty$ guarantees this universal-coupling conclusion. We further show that this exponent is optimal among uniform power-moment assumptions: for every $1\leq q<1+1/d$, there is a centered symmetric law with finite $q$-th moment for which canonical nested volumes converge almost surely, whereas independently resampled volumes with the same fixed-volume marginals converge in probability but not almost surely. Finally, in dimension one, we prove that the first-moment condition is also necessary for a finite limiting pressure.

In Euclidean space, universality classes of Anderson transitions are primarily determined by symmetry and spatial dimensionality. Here, we present evidence for a geometry-controlled universality class of non-Hermitian Anderson transitions on hyperbolic-like lattices. In this setting, critical behavior is influenced by the large-scale hyperbolic geometry, characterized by negative curvature, exponential volume growth, and a non-Euclidean notion of spatial scaling. Finite-size scaling of participation ratios across several distinct \( \{p,q\} \) tilings reveals one-parameter scaling collapses with a common critical exponent \( \nu\simeq1 \) within numerical accuracy. A complementary phenomenological coarse-grained Landau-Ginzburg analysis shows how exponential correlation-volume growth suppresses critical fluctuations, offering a rationale for the observed mean-field-like scaling. Our results suggest that spatial curvature can act as an additional organizing principle for Anderson-transition universality beyond the conventional dimensionality- and symmetry-based classification.

Quantum reservoir computing (QRC) is a machine learning approach which employs the internal dynamics of a physical system (the reservoir) to encode and process information. In this work, we explore the use of dual-unitary circuits in a brickwork architecture as a platform for QRC, well suited to current noisy intermediate-scale quantum devices. Dual-unitary circuits present both practical and conceptual advantages. Our results indicate that, under appropriate conditions, dual-unitarity can lead to an enhanced regime of operation: we numerically verify that it improves memory effects and nonlinear processing, and shields against finite-shot noise, mitigating exponential concentration. Moreover, dual unitarity offers an intuitive picture of how operator dynamics gives rise to memory and nonlinear processing in circuit-based reservoirs.

The effects of disorder on topological phases of matter are typically either preservation of topology or its destruction. For example, the quantum Hall effect's quantization and chiral edge mode remain robust until a strong-disorder percolation transition exits the topological phase. Disorder can also enlarge a preexisting topological phase, yielding a topological Anderson insulator (TAI). However, the reliance of TAI and other theoretical treatments on perturbatively averaging out long-wavelength randomness suggests that additional effects might appear when the disorder involves localized defects. Here we show that a finite density of randomly distributed defects can generate various new topological phase transitions. This route to disorder-induced topology can be viewed as the formation of topological impurity bands (TIB) and is applicable even if the initial clean model is a trivial band insulator. The theory relies on an orbital-dependent vorticity of impurity bound states, which we derive analytically near a generic Dirac cone phase transition as well as using the Chern insulator lattice models of Qi-Wu-Zhang and Haldane. Their numerically computed phase diagrams at 3% defect density show robust topological transitions in distinct TIB and TAI regimes, suggesting a local route to topological phases.

Two-dimensional massless Dirac systems, exemplified by graphene, are known to exhibit a divergent orbital diamagnetic susceptibility that scales linearly with system size. Motivated by viewing a chiral edge state as one half of an enlarged analogue of a benzene ring, we study Chern insulators under open boundary conditions and find the same divergent scaling. This giant diamagnetism is robust against disorder, revealing its topological nature. Our results further suggest a profound connection to the divergent diamagnetism of massless Dirac systems.

We numerically investigate how particle surface roughness affects the static and dynamic properties of a hard-particle fluid across a wide range of densities, rho. These simulations of a simple model of granular systems reveal that, although the amplitude and coverage of surface corrugation significantly influence the rho-dependence of system properties, the qualitative behavior of this dependence remains unchanged. These findings can be described quantitatively by introducing an effective particle size, which enables a direct mapping of the rough particle systems to equivalent hard-disk systems. Analytical calculations provide an explicit form of this mapping, and allow us to predict the static and dynamic properties of rough particles using standard liquid-state theories for hard disks.

Characterizing the time evolution of generic quantum many-body systems is a fundamental challenge, as representing the exact state requires exponentially scaling computational resources. While hydrodynamics and statistical mechanics successfully simplify this task by predicting the expectation values of local observables, these macroscopic frameworks provide no information about nonlinear characteristics of the quantum state. In this work, we demonstrate that for systems exhibiting a timescale separation, with dynamics governed by the transport of conserved charges, this lost information can be systematically recovered. By constraining the maximum-entropy Scrooge ensemble solely by the system's slow modes, we accurately reconstruct complex, nonlinear quantum properties of the global time-evolved state, including the half-chain entanglement entropy and the participation entropy in the computational basis. Our results generalize the paradigm of canonical typicality, revealing that a hydrodynamically bottlenecked system behaves as a typical pure state within a dynamically restricted submanifold of the Hilbert space - a phenomenon we term global restricted typicality.