Papers

A recurring principle in many-body physics is that sufficiently distributed interactions or correlations lead to an effectively mean-field description. For fermionic Gaussian states, we establish a quantitative version of this principle directly at the level of Majorana covariance matrices. The main observation is that the admissibility condition for fermionic covariance matrices imposes a quantitative monogamy constraint on two-point correlations: a fixed region has only a bounded covariance budget to distribute among many disjoint regions. We use this principle in three directions. First, for quadratic fermionic Hamiltonians on finite simple graphs of high degree, we obtain product-state approximations to both the ground-state energy and the finite-temperature free energy, with error of order \(D^{-1/2}\) for \(D\)-regular graphs. Second, we prove a finite fermionic Gaussian de Finetti theorem: a \(k\)-copy Gaussian state that is \(n\)-exchangeable under graded fermionic copy permutations is \(O(k/n)\)-close in trace norm to the product of its one-copy marginal. In particular, infinite exchangeability within the Gaussian class implies exact product structure. Third, for spatial fermionic Gaussian states with exponentially clustering mutual information, we prove that the conditional mutual information across a separating buffer decays as \(O(r^{-1})\), and hence, by recoverability, the state admits an \(O(r^{-1/2})\) trace-norm approximation by a recovered state. These results show that product and de Finetti approximations and recoverability estimates for fermionic Gaussian systems can all be derived directly from covariance-level structure.

We derive a generalized fluctuation-dissipation theorem (FDT) for vector fields in rotating thermal equilibrium from an exact phase-space Kubo-Martin-Schwinger (KMS) relation. The resulting FDT contains rotation-induced tensorial contributions beyond a scalar thermal factor. In the local transport limit, we obtain a model-independent generalized Einstein relation with rotation in which, through second order in thermal vorticity, symmetric momentum diffusion depends on low-frequency spectral information beyond that encoded in the rotation-dependent dissipative drag. Remarkably, we find a new Einstein-type relation linking zero modes in the spectral function to the nonrotating drag coefficient. These zero modes underlie a new mechanism for the orbital polarization of heavy quarkonium. The same FDT constraint yields a modified detailed-balance relation whose first-order vortical correction is governed by transition polarization, without explicit dependence on the bath model. Our findings establish microscopic equilibrium constraints for studying rotating quantum matter in various fields.

We discuss the triality between stochastic growth models in the KPZ universality class, the DSSYK model, and low dimensional dilaton gravity. The TASEP model, which will be our primary focus, is identified with the strong-coupling limit of two-dimensional quantum gravity. The Hamiltonian of DSSYK and the transfer matrix of ASEP coincide up to an additive constant, and we derive the exact expression for the resolvent of the corresponding transfer matrix in ASEP on a finite interval. We also mention the relation of cumulants with the Tutte polynomial $T(1,q)$ of the crossing graph dual to the chord diagram, which implies the relationship of the models considered with the $Q=0$ Potts model coupled with gravity. We further exploit the realization of all these models in terms of different versions of discrete and continuous random walks on two-dimensional manifolds, which parameterize the Hilbert spaces of the respective theories. The representation of TASEP as the growth model of heaps provides new insight into strong-coupling gravity, suggesting its interpretation as an emerging phenomenon. The new dualities between ASEP and q-TASEP models and heap models providing a useful growth interpretation have been developed.

We study the interplay between local stroboscopic measurements and the unitary quantum circuit dynamics of the deterministic Floquet-quantum East model. We derive exact analytical results for the probability of first detecting a subset of qubits back in their initial state. This is achieved via a renewal equation linking the first-detection probability to the subsystem Loschmidt echo, which encodes the effective open dynamics of the monitored qubits. The resulting statistics exhibit two regimes set by the competition between the measurement probing time and the relaxation timescale of the unitary circuit dynamics: while infrequent monitoring leads to geometric first-detection statistics, frequent monitoring induces correlations that manifest as deviations from this geometric behavior. These results provide a rare exact characterization of how local measurement backaction reshapes detection statistics in an interacting quantum many-body system. In our local protocol, return probabilities are controlled by the size of the monitored subregion and can therefore be accessed on digital quantum simulators via local mid-circuit measurements.

The active Brownian particle (ABP) model is one of the most widely used particle-based models in studies of scalar active fluids. A collection of interacting ABPs is known to exhibit intriguing phenomena that are absent in equilibrium counterparts. A prominent example is spontaneous phase separation, known as motility-induced phase separation (MIPS), which occurs even in the absence of explicit attractive interactions. In parallel, the large-scale behavior of scalar active fluids is often modeled using continuum descriptions, namely, scalar field theories. Such scalar active field theories are usually formulated in a top-down manner, and establishing their connections to particle-based models remains challenging, with these connections not yet fully understood. To advance the microscopic derivation of scalar active field theories, we revisit the connection between ABPs interacting via a two-body potential in two dimensions and scalar field theories that include all possible terms up to fourth order in spatial gradients. Our approach is based on a pressure expansion and the renormalization group (RG) method in the context of singular perturbation theory. The RG method provides a systematic way to eliminate fast variables and identify the dynamics on the slow invariant manifold. Within this framework, scalar field theories can be obtained as RG flow equations. We also apply this method to a chiral variant of the ABP model, the chiral ABP (cABP) model, in which a constant torque biases particle rotation to the left or right. We show that the scalar field theory corresponding to the cABP model contains two “odd” terms in addition to those present in the scalar field theory for ABPs. The method developed here may also be useful for deriving hydrodynamic descriptions of other types of active matter systems.

Event-chain Monte Carlo (ECMC) has revolutionised computational sampling over recent years, providing a powerful alternative to the molecular-dynamics (MD) and Hamiltonian Monte Carlo (HMC) algorithms. Each method outperforms the ubiquitous random-walk Metropolis algorithm by advancing particles along deterministic trajectories, but ECMC achieves this without being constrained by Newtonian dynamics. Recent advances exploited this dynamical freedom to induce a collective particle dynamics that relax local density variations on fast timescales. In a foundational model of $N$ pairwise-interacting particles on the 1D torus, this led to an $O(N^{3/4})$ improvement on the industry-leading computational efficiency of MD and HMC - but with an impractically small prefactor at low/high mean particle density for general attractive/repulsive interactions. Here we present a universal framework that generalises this high-efficiency sampling strategy to all translationally symmetric pairwise models on the torus - creating the potential to surpass MD and HMC as the state of the art. We also numerically elucidate the collective particle dynamics and discuss broad impact across the physical sciences and computational statistics.

Traffic movement on highways and data packet transmission across the Internet serve as prototypical examples of collective dynamical behavior in complex systems. Although enhancing traffic flow in complex networks has been extensively investigated, most existing studies focus on single-queue models. In this paper, we introduce a simple yet effective two-queue scheme with gate control that regulates vehicle entry and integrates it with the routing protocol. When vehicles arrive at a on-ramp gate, they first join a waiting queue and are permitted to enter the main flowing queue once it has emptied. This two-queue strategy is especially advantageous when highway inflow varies periodically with large fluctuations, as is commonly observed in real traffic. Moreover, it modifies the system's failure characteristics, replacing sudden, discontinuous jamming transitions with gradual, continuous ones. The approach is based on a simple rule using only local queue information, making it easy to implement and widely applicable. Beyond the specific setup studied here, it can be applied to other transportation networks under different conditions or extended to other queuing systems, such as Internet data packet routing.

We examine whether the perturbative renormalization group (RG) regime of stochastic turbulence can be continued from small $\varepsilon$ to the physical value $\varepsilon_{\mathrm{phys}}=2$, corresponding to large-scale forcing. Exploiting the simplifications of the large-$d$ limit, we calculate the correction exponent $\omega$ to five-loop order and find a simple structure suggesting a closed analytic form. This form implies that the fixed point stable near $\varepsilon=0$ ceases to be simultaneously real and infrared stable before reaching $\varepsilon_{\mathrm{phys}}=2$, pointing to a possible change of infrared regime rather than a controlled perturbative RG extrapolation.

Simulating microstructure evolution requires quantum-mechanical accuracy and mesoscopic reach in length and time scales, a combination that no current method achieves. Classical phase-field models provide this reach, but their accuracy is limited by phenomenological free energies and mobilities. Here we develop a framework for learning ab initio phase-field models, where the mesoscopic equation is not postulated but derived from a Mori-Zwanzig projection of molecular dynamics onto species-density fields under explicit assumptions. The nonlocal free energy and mobility left unspecified by this equation are parametrized by neural networks and learned from short molecular dynamics trajectories generated with machine-learning interatomic potentials of ab initio accuracy. We demonstrate the framework on an iron-boron melt and on hydrogen-helium mixtures under planetary conditions. For iron-boron, the model shows that the melt at the FeB$_4$ composition is spinodally unstable at ambient pressure but stabilized at 10 GPa, offering a thermodynamic rationale for why FeB$_4$ has been synthesized only under high pressure. For hydrogen-helium, the model predicts the immiscibility boundary and captures droplet nucleation and growth in helium-rain simulations of a column corresponding to 2.2 million atoms, far beyond the scale of atomistic modeling at comparable accuracy. Trained across compositions and conditions, such models could provide a mesoscopic counterpart to ab initio molecular dynamics.

We study the thermalization in the random free fermion model by a detailed random-matrix analysis. By computing the ensemble average and fluctuations of $\operatorname{Tr}(A\rho(t))$ for a single-particle observable $A$, we derive the thermalization function $g^2(t/\tau_\lambda)$ with $\tau_\lambda = \hbar/(2\eta\sqrt{N})$, prove its $|t|^{-3}$ asymptotic decay, and show that the variance of the fluctuations vanishes as $O(1/N)$ in the thermodynamic limit.Particle number conservation is also incorporated into the model, by which we further study the energy-shell eigenstate statistics and prove a factorization theorem of the eigenstate statistics. We further show that under a controlled eigenvector-eigenvalue correlation deformation, the diagonal energy-resolved slope and the off-diagonal eigenstate thermalization hypothesis spectral function acquire an energy dependence.Finally, we compute the fluctuations of correlation functions and compare the fluctuation scales with those of a fully chaotic system, revealing quantitative differences rooted in the Gaussian nature of the eigenstates.Our work establishes the random free fermion model as an analytically solvable realization of weak eigenstate thermalization hypothesis type self-averaging, and as a controllable setting in which eigenbasis chaos can be separated from spectral chaos.

Extending a fundamental concept of thermodynamics to the nonequilibrium realm of active matter, we derive an ideal gas law for a suspension of noninteracting active particles confined to a finite rectangular box. The law is exact for run-and-tumble particles (RTPs) in one dimension and established by a systematic analytical expansion of the steady-state probability density for active Ornstein-Uhlenbeck particles in any dimension. It also agrees well with numerical results for active Brownian particles and RTPs in higher dimensions and recovers previously known relations for the limit of large system sizes. Together, these results demonstrate the applicability of the ideal active gas law to the three most widely studied theoretical models of colloidal active matter. As an application, we analyze thermodynamic processes involving active matter on a macroscopic level, without recourse to microscopic particle trajectories or self-propulsion fluctuations.

We explore the fundamental limits on finite-time driving in quantum critical systems described by boundary conformal field theory. We show that stochastic work fluctuations arising from external driving are a resource for speedy control, and derive an exact, saturable fluctuation-based speed limit in weakly driven boundary conformal field theories at finite temperature. The bound and saturating protocol can be expressed entirely in terms of the universal scaling dimension, and the result interpolates between the Kibble–Zurek regime,where temporal correlations are strongly nonlocal, and an adiabatic regime where linear driving becomes optimal. For small scaling dimension, the enhanced temporal correlations produce pronounced departures from linear protocols and a larger optimization advantage. These results establish a universal work precision–time tradeoff for boundary-critical control, applicable to quantum impurity, fractional quantum Hall, and superconducting-circuit platforms.

Measuring part of a many-body wave function generates a projected ensemble of pure quantum states on the unmeasured subsystem. Recent advances in deep thermalization have shown that, in chaotic systems, this ensemble universally converges to the maximally random ensemble compatible with its average density matrix, known as the Scrooge ensemble. By contrast, free-fermion systems are nonchaotic, and their quantum states are constrained to remain Gaussian. Motivated by this distinction, we introduce the fermionic Gaussian Scrooge ensemble to describe deep thermalization in generic free-fermion systems. This ensemble is defined as a distortion of the Gaussian Haar ensemble by the average density matrix, and its moments reveal an enlarged symmetry of Gaussian states in the replicated Hilbert space. We demonstrate the emergence of the fermionic Gaussian Scrooge ensemble in two complementary settings: (1) we analytically prove that the projected ensemble of the SYK$_2$ model follows the fermionic Gaussian Scrooge ensemble at arbitrary evolution times; (2) we provide numerical evidence that it emerges at sufficiently long times in random Gaussian circuits with charge conservation. Our results establish the fermionic Gaussian Scrooge ensemble as a universal description of deep thermalization in free-fermion systems.

We prove that a quasi-local quantum Gibbs sampler rapidly mixes to the Gibbs state of any 1D finite-range Hamiltonian at all finite temperatures in $\mathcal{O}\left(\log (n/\varepsilon)\right)$ time. Each update traces out a contiguous block of constant length and reconstructs it using the Petz recovery map, following early proposals for quantum heat-bath Gibbs samplers by Kastoryano and Brandão~\cite{kastoryano2016quantum}. Our proof directly bounds the distance between the updated state and the target Gibbs state using quantum Wasserstein distance of order $1$. We further provide $\mathcal{O}(\text{polylog}(n/\varepsilon))$ depth of quantum circuits to prepare these Gibbs states. We hope these techniques will facilitate the analysis and design of other Gibbs samplers.

We study the dynamic critical behavior of the two-dimensional random-bond three-state Potts model using large-scale Monte Carlo simulations with the Wolff and Swendsen–Wang cluster algorithms. At the disorder-dependent critical temperature, we compute integrated and exponential autocorrelation times and extract the dynamic critical exponent $z$ via finite-size scaling. Critical slowing down is significantly weakened by bond randomness, with the dynamic exponent decreasing from $z \approx 0.54$ in the pure system to $z \approx 0.24$ at strong disorder. From the finite-size scaling of the Wolff cluster size, we obtain $\gamma/\nu \approx 1.73$, where $\gamma$ and $\nu$ are the susceptibility and correlation-length exponents, respectively, consistent with the universality class of the two-dimensional three-state Potts model. These results indicate that bond randomness strongly affects the critical dynamics but leaves the underlying static universality class unchanged. Furthermore, both static and dynamic observables, including the specific heat and the autocorrelation times, show a lack of self-averaging.

We discover a universal trade-off between the dissipation required to maintain a quantum state more sensitive than a thermal one and the sensitivity gain for a driven single-mode bosonic system under a thermal environment. Specifically, for Gaussian states, we rigorously derive a lower bound on the entropy production rate in the steady state in terms of the quantum Fisher information gain relative to a thermal reference state. Numerical investigations of Kerr nonlinearities further support that these bounds can hold beyond the Gaussian regime. Our results establish a new connection between steady-state thermodynamics and quantum metrological performance.

We conduct a numerical study of a generalization of the Blume-Capel model in which the crystal field $D_i$, which controls the local vacancy density, is site dependent rather than uniform. We employ Markov Chain Monte Carlo to compute the shifted phase transition line $T_c$ as a function of the width $\sigma$ of a gaussian distribution $P(D_i) \sim \exp( -(D_i - \bar{D})^2/2 \sigma^2)$ at fixed $\bar{D}$. We characterize how the presence of this on-site Gaussian disorder reduces $T_c$ across the second order transition line, and discuss how our results suggest that $T_c$ remains finite even at large values of $\sigma$. We also determine the effects of disorder on the tricritical point of the conventional, uniform, Blume-Capel model, finding that it significantly suppresses the first-order phase transition, eliminating it entirely at large values of $\sigma$.

Correlated oxides can switch to a low-resistance state when exposed to a voltage, making these insulator-to-metal transition materials promising candidates for memristor technology. Switching in materials such as VO2 occurs because of a thermal-runaway instability that leads to the abrupt formation of a hot current-carrying metallic filament within the insulator. We study, theoretically and experimentally, this bias-induced switching as a non-linear dynamics stability problem. We construct Landau free energy-like Lyapunov functions to show that both the on-state ("set") and the off-state ("reset") transitions can be described as separate saddle-node bifurcations. Starting from the reaction-diffusion equation for the heat transport, the abrupt snap-back (reset) to the insulating state is systematically formulated as a mean field Landau-like dynamics with the filament width playing the role of the order parameter. The formulation predicts an abrupt first-order phase transition with a break-off of a finite width filament across the current-controlled reset transition. The formulation is quantitatively compared against our electrical and optical microscopy experiments on VO2 thin film devices. Multi-cycle switching dynamics experiments further reveal the emergence of a stable stochastic regime following an initial electro-spatial forming phase. Beyond establishing a cross-disciplinary dynamical framework that may be readily compared to instabilities in various reaction-diffusion scenarios, the work also provides a predictive foundation for the rational design and optimization of Mott-transition-based technologies.

Understanding how macroscopic wealth distributions emerge from microscopic transaction rules among agents is a central problem in econophysics. While many traditional models restrict agents' wealth to non-negative values, debt is an essential feature of realistic economic systems. In this paper, we introduce a stochastic transaction mechanism into the agent-based model with a central-bank-mediated collective debt limit, as studied in [14]. In our model, each agent probabilistically determines whether to transfer a coin, depending on their current asset or debt level. From a probabilistic perspective, the resulting system can be formulated as a zero-range process with $\mathbb{Z}$-valued site occupation numbers, where negative values represent debt. We prove that, under an appropriate scaling, the wealth distribution in the stationary state converges to either a two-sided Gamma distribution or a Gamma distribution, depending on the asymptotic behavior of the function governing coin transfers. Our results rigorously identify these previously unconsidered limiting distributions and provide a mathematical framework for understanding how stochastic monetary exchanges give rise to macroscopic wealth distributions.

We investigate the relationship between the dissipation potential $S_{\mathrm{NB}}$ and information entropy in stochastic Nambu nonequilibrium thermodynamics (NNET). Starting from pure diffusion, gradient-flow systems, and systems with Hamiltonian rotational currents, we derive the stationary distribution of the Fokker–Planck equation including a Nambu flow. We show that, when the Nambu flow preserves the dissipation potential and an Einstein-type relation holds between the diffusion matrix and the transport tensor, the stationary distribution is governed by an exponential weight determined by $S_{\mathrm{NB}}$. Consequently, the local self-information is directly related to the dissipation potential, demonstrating that $S_{\mathrm{NB}}$ should not be identified with the Shannon entropy itself but instead serves as the stationary quasipotential governing the nonequilibrium steady-state distribution. Using the distinction between the thermodynamic entropy and the dissipation potential established for an open gas–piston system coupled to a thermal bath and an external-pressure reservoir, we further clarify the Massieu interpretation of $S_{\mathrm{NB}}$, introduce a Nambu canonical distribution, and derive the covariance of fluctuations within the saddle-point approximation. These results provide a statistical interpretation of the NNET dissipation potential by identifying it as the stationary quasipotential underlying nonequilibrium steady states.

In general, measurement error constrains the performance of information engines. However, this may not hold universally. In this work, we propose a class of two-reservoirs information engines (TRIEs) with a two-level system and demonstrate that the monotonic relationships between the work output, the efficiency, as well as the work fluctuations of the TRIEs and measurement error are determined by the demon's control parameters. Utilizing this, we establish the conditions that allow the TRIEs to generate useful work under any level of measurement error, and identify the regimes in which these performance parameters can be optimized simultaneously by the measurement error. Furthermore, we demonstrate that when the demon's energy cost is supplied solely by the cold reservoir, the efficiency that accounts for this cost can surpass the standard Carnot bound without violating the second law. Finally, we design a dual Otto cycles TRIE and provide an experimental scheme for its implementation based on a trapped $^{40}\mathrm{Ca}^+$ ion. Significantly, our results can be applied to the multi-level system information engines.

We study mixed-state entanglement in Gibbs states with strong $\mathrm{SU}(2)$ symmetry, focusing on locally interacting spin systems with ferromagnetic interactions. Our main result is to show that finite-temperature ordering transitions are associated with entanglement transitions, and therefore the steady state of strongly symmetric Lindbladians can exhibit entanglement transitions. While in the paramagnetic phase it is known that the distillable entanglement and logarithmic entanglement negativity between two halves of a large system grow logarithmically with the square root of the number of spins, we show that in ferromagnetic phases these quantities grow parametrically faster with system size. To arrive at this result we first establish relations between these mixed-state entanglement measures and spin correlations in states that are singlets under global $\rm{SU}(2)$ symmetry transformations. We then introduce a semiclassical theory for $\rm{SU}(2)$ singlet thermal states. While the global singlet constraint generally enters this theory as a complicated function of the full semiclassical spin configuration, we show that in large $S$ limit it simplifies drastically to a Gaussian suppression of total magnetization in disordered phases as well as in ordered phases in the vicinity of continuous thermal phase transitions. This leads us to a field theory describing spin correlations in the singlet sector. Using this we determine the behavior of various probes of mixed-state entanglement at low and at high temperatures, supporting our analytical results using numerical Monte Carlo simulations of a three-dimensional lattice realization of our semiclassical theory. We also use exact numerics in one-dimensional spin-$1/2$ systems to confirm our predictions for the scaling of mixed-state entanglement with correlation length and system size in the paramagnetic phase.

Here, I give a brief history of the theory, with twists and turns, and list possible predictions for the spectra of the direct cascade of gravity waves on the water. The description of long waves is straightforward within the weak-turbulence theory developed by Zakharov and his school. As the energy cascade proceeds to shorter scales, the mean surface steepness grows, and wave-breaking events appear with increasing frequency. Considering surface cusps, Phillips suggested a wavenumber spectrum (with a wrong magnitude, as I argue here) and a frequency spectrum whose whole form is incorrect. The right form for the frequency spectral slope due to breaking waves was suggested by Kuznetsov. Here we estimate the magnitude and argue that the frequency spectrum is expected to continue unchanged through the whole cascade. The transition from weak to strong turbulence in the wavenumber and spatio-temporal spectra is due to spectrally nonlocal interactions and happens earlier (at larger scales) than the dimensional estimate suggests. As a result, the magnitude of the strong-turbulence spectrum is not universal but depends on the pumping for a sufficiently long weak-turbulence cascade. The reason for nonlocality is likely that breaking of shorter waves is determined by the magnitude of the longest wave on whose crest they are running.

Strain offers a direct route to control electronic phases by altering bond lengths, hopping amplitudes, and lattice symmetries. These aspects make electron-phonon (e-ph) coupled systems a natural setting to study strain-induced effects. The Su-Schrieffer-Heeger (SSH) Hamiltonian describes the coupling between itinerant electrons and lattice degrees of freedom that modulate hopping and is thus expected to be strongly affected by strain fields. At half-filling and on a bipartite lattice, the SSH interactions drive dominant bond-order-wave (BOW) correlations at low- temperature in which short bonds with high kinetic energy alternate with long bonds with low kinetic energy along four possible patterns. We model uniaxial strain through anisotropic hopping, which breaks the $90^\circ$ rotational symmetry and reduces the BOW phase degeneracy to two. We also include an on-site Hubbard U that promotes antiferromagnetic correlations that are also (weakly) driven by the SSH interaction itself. We map out the half-filled phase diagram in the plane of the e-ph and Hubbard couplings, and determine the critical temperature of BOW formation. Using analytic continuation, we also evaluate the spectral function and demonstrate directionally dependent gap formation in the BOW phase

We construct an extensive model of bulk mutual information (MI) in anti-de Sitter spacetime and use it to describe the leading quantum corrections to the MI of certain holographic theories. The equivalence between bulk and boundary MI follows from the Faulkner–Lewkowycz–Maldacena prescription. We show that the extensivity of the bulk MI is sufficient for the quantum-corrected boundary entropy vector to satisfy monogamy of MI and all other holographic entropy cone inequalities. Our model is built from a covariantly conserved current-current kernel in AdS and is realized explicitly by a free massive Dirac fermion, whose boundary MI at long distances is that of a fermionic generalized free field (GFF). The construction also reproduces the expected short-distance divergence structure of a GFF, and the current-current correlator defines a positive and monotonically decreasing function along the renormalization-group flow. We illustrate this explicitly for disjoint half-disks at the conformal fixed point of the model in AdS$_3$, where we present the exact result.

We investigate fatigue failure in two-dimensional (2D) model glasses under cyclic shear deformation using atomistic simulations. We find that the number of cycles to failure diverges as a power law as the strain amplitude approaches the fatigue limit, with an exponent close to $-1$, in contrast to the exponent of $-2$ reported in three dimensions (3D). A failure exponent of $-1$ has also recently been observed in a 2D elastoplastic model, suggesting an interesting dependence on spatial dimensionality that needs to be rationalized. Measures of accumulated plastic activity, including dissipated work and non-affine displacements, exhibit scaling with the failure time that is consistent with results in 3D, and indicate a robust connection between damage accumulation and failure. To probe the origins of the variability of failure times, we perform isoconfigurational seeded simulations in which a localized soft region is introduced. While such seeding constrains the spatial location of failure, the distribution of failure times remains broad. These findings extend recent results in 3D concerning fatigue failure times to 2D glasses, including their relation to accumulated plasticity and apparent stochasticity, while also revealing a key difference, namely the exponent describing the divergence of the failure times.

We formulate the corner transfer matrix equations, and the corner transfer matrix renormalization group built on them, as a set of local equations on general planar graphs. These equations depend only on the local subgraphs of the planar graph and are glued together consistently to describe the whole graph. Solving them yields message tensors and corner matrices, which can be used to construct an MPS environment for any connected subgraph. We test the proposed equations on the ferromagnetic Ising model, on a variety of infinite lattices (including hyperbolic ones) and on finite graphs, and find systematic improvement over belief propagation.

We investigate the distributions of off-diagonal scattering matrix elements and cross-sections in the Ericson regime for time-reversal invariant systems with odd spin. Within the universal Heidelberg approach we prove that Gaussian and exponential behavior is found as the leading-order term of an asymptotic expansion of the aforementioned distributions. Furthermore, the subleading-order term is derived and compared with numerical simulations.

Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.

Open quantum systems can exhibit inherently mixed quantum orders, such as strong-to-weak spontaneous symmetry breaking (SW-SSB), which have no analogue in pure states. It is generally expected that a finite-depth local quantum channel cannot induce a phase transition to SW-SSB in one spatial dimension. We circumvent this obstruction by introducing a long-range quantum channel, which implements two-body dephasing on pairs of sites with probability falling off according to a power-law in the site separation. Applying this channel to a one-parameter family of matrix product states interpolating between trivial and symmetry-protected topological (SPT) phases, we construct a phase diagram that hosts trivial, mixed SPT, and SW-SSB phases with respect to Rényi-2 diagnostics. Notably, the mixed SPT phase is distinct from previously studied decohered SPT phases: it hosts two logical qubits and exhibits nonvanishing Rényi-2 string order, despite vanishing conventional string order. Through a series of mappings to a classical statistical mechanics model, we establish a direct connection between the loss of logical information and the onset of SW-SSB in this model. Finally, we consider the feasibility of experimental realization of the phenomena we have studied. We emphasize that our family of mixed states can be tuned to regimes of high purity, substantially reducing measurement overhead and enabling their experimental realization and detection on near-term quantum hardware.