In recent years, there has been growing interest in characterizing the complexity of quantum evolutions of interacting many-body systems. When a time-independent Hamiltonian governs the dynamics, Krylov complexity has emerged as a powerful tool. For unitary evolutions like kicked systems or Trotterized dynamics, a similar formulation based on the Arnoldi approach has been proposed yielding a new notion of quantum ergodicity [P. Suchsland, R. Moessner, and P. W. Claeys, Phys. Rev. B 111, 014309 (2025)]. In this work, we show that this formulation is robust for observing the transition from integrability to chaos in both autonomous and kicked systems. Examples from random matrix theory and spin chains are shown in this paper.

The quantum three-rotor problem concerns the dynamics of three equally massive particles moving on a circle subject to pairwise attractive cosine potentials and can model coupled Josephson junctions. Classically, it displays order-chaos-order behavior with increasing energy. The quantum system admits a dimensionless coupling with semiclassical behavior at strong coupling. We study stationary states with periodic ‘relative’ wave functions. Perturbative and harmonic approximations capture the spectrum at weak coupling and that of low-lying states at strong coupling. More generally, the cumulative distribution of energy levels obtained by numerical diagonalization is well-described by a Weyl-like semiclassical estimate. However, the system has an $S_3\times {\mathbb{Z}}_2$ symmetry that is obscured when working with relative angles. By exploiting a basis for invariant states, we obtain the spectrum restricted to the identity representation. To uncover universal quantum hallmarks of chaos, we partition the spectrum into energy windows where the classical motion is regular, mixed, or chaotic and unfold each separately. At strong coupling, we find striking signatures of transitions between regularity and chaos: spacing distributions morph from Poisson to Wigner-Dyson, while the number variance shifts from linear to logarithmic behavior at small lengths. Some nonuniversal features are also examined. For instance, for strong coupling, the number variance saturates and oscillates at large lengths, while the spectral form factor displays a nonuniversal peak at short times. Moreover, deviations from Poisson spacings at asymptotically low and high energies are well-explained by quantum harmonic and free-rotor spectra projected to the identity representation at strong and weak coupling. Interestingly, the degeneracy of free-rotor levels admits an elegant formula that we deduce using properties of Eisenstein primes.

We investigate the work function $U\left(T\right)$ for the Heider balance, driven by a thermal noise $T$, on several planar networks that contain separated triangles, pairs of triangles, chains of triangles, and complex structures of triangles. In simulations, the heat-bath algorithm is applied. Two schemes of link values updating are considered: synchronous and asynchronous (sequential). The latter results are compared with analytical calculations for small cliques. We argue that the actual shape of $U\left(T\right)$ is a consequence of a local topology rather than of a macroscopic ordering. Finally, we present the mathematical proof that for any planar lattice, perfect structural (Heider) balance is unreachable at $T>0$.

Diffusion-based generative models represent a forefront direction in generative artificial intelligence (AI) research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight motivates us to develop a diffusion-based generative model by reversing the momentum-space RG flow. We establish a framework that interprets RG flow as optimal transport gradient flow, which minimizes a functional analogous to the Kullback-Leibler divergence, thereby bridging statistical physics and information theory. Our model applies forward and reverse diffusion processes in Fourier space, exploiting the sparse representation of natural images in this domain to efficiently separate signal from noise and manage image features across scales. By introducing a scale-dependent noise schedule informed by a dispersion relation, the model optimizes denoising performance and image generation in Fourier space, taking advantage of the distinct separation of macro and microscale features. Experimental validations on standard datasets demonstrate the model's capability to generate high-quality images while significantly reducing training time compared to existing image-domain diffusion models. This approach not only enhances our understanding of the generative processes in images but also opens pathways for research in generative AI, leveraging the convergence of theoretical physics, optimal transport, and machine learning principles.

Soft films serve as the primary support materials for flexible devices. These films are frequently peeled perpendicularly during device preparation and application, resulting in large compression on the upper surface of the bending region and significant damage to the device's performance. Accurately assessing this damage is challenging because of the difficulties in calculating the compression in perpendicularly peeled large-deformation films. In this study, we propose a method to calculate the compressive strain on the upper surface of a bending soft film using only its thickness as the key parameter. Furthermore, we demonstrate that the length of the compressive region is directly proportional to the soft film thickness, whereas the maximum strain is inversely proportional to the thickness. These results provide theoretical guidance for applying soft films in flexible devices.

Discrete systems of coupled linear mechanical oscillators with nonreciprocal interaction are a model for a variety of physical systems. In general, the presence of nonreciprocal interactions renders their dynamics nonconservative, but under certain conditions it remains conservative. In this paper we show which thermodynamic properties induced by nonreciprocity can be observed in conservative systems and which are specific to nonconservative systems. To this end, we formulate a criterion for identifying conservative systems and construct a measure to quantify the deviation from conservativity.

Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the nonuniqueness of the quantum Fisher metric in Hilbert space, we exploit the fact that any quantum Fisher information (QFI) can be decomposed into a metric-independent incoherent part and a metric-dependent coherent contribution. We demonstrate that the incoherent component of any QFI can be directly linked to entropic acceleration, and for GKSL dynamics with local detailed balance, to the rate of change of generalized thermodynamic forces and entropic flow, paralleling the classical results. Furthermore, we tighten a classical uncertainty relation between the geometric uncertainty of a path in state space and the time-averaged rate of information change and demonstrate that it also holds for quantum systems. We generalize a classical geometric bound on the entropy rate for far-from-equilibrium processes by incorporating a nonnegative quantum contribution that arises from the geometric action due to coherent dynamics. Finally, we apply an information-geometric analysis to the recently proposed quantum-thermodynamic Mpemba effect, demonstrating this framework's ability to capture thermodynamic phenomena.

We explore how the disorder impacts the current fluctuations in the symmetric simple exclusion process (SSEP) within a heterogeneous environment. First, we analyze the SSEP with a defect site under the periodic boundary conditions. We derive the exact expression for the second moment of the current and observe deviations from that of the homogeneous system. Notably, the second moment of the current shows asymmetric density dependence around a density of $1/2$ and surpassing that of the homogeneous system in the low-density region. Furthermore, based on the finding from the SSEP with a defect site, we present an approximate derivation of the second moment of the current in the SSEP on a quenched random energy landscape using a partial-mean-field approach. The second moment of the current is heavily influenced by the energy landscape, revealing unique effects arising from the interplay between the heterogeneous environment and the many-body system. Our findings provide valuable insights that can be applied to control current fluctuations in systems involving the interactions of many particles, such as biological transport.

Understanding the characteristics of temporal correlations in a time series is crucial for developing accurate models in natural and social sciences. The burst-tree decomposition method was recently introduced to reveal temporal correlations in a time series in the form of an event sequence, in particular, the hierarchical structure of bursty trains of events for the entire range of timescales [Jo et al., Sci. Rep. 10, 12202 (2020)]. Such structure cannot be solely captured by the interevent time distribution but can show higher-order correlations beyond interevent times. It has been found to be simply characterized by the burst-merging kernel governing which bursts are merged together as the timescale for defining bursts increases. In this work, we study the effects of kernels on the higher-order temporal correlations in terms of burst-size distributions, memory coefficients for bursts, and the autocorrelation function. We employ several kernels, including the constant, sum, product, and diagonal kernels as well as those inspired by empirical results. We generically find that kernels with preferential merging lead to heavy-tailed burst-size distributions, while kernels with assortative merging lead to positive correlations between burst sizes. The decaying exponent of the autocorrelation function depends not only on the kernel but also on the power-law exponent of the interevent time distribution. In addition, thanks to the analogy to the coagulation process, analytical solutions of burst-size distributions for some kernels could be obtained. Our findings may shed light on the role of burst-merging kernels as underlying mechanisms of higher-order temporal correlations in a time series.

Higher-order interactions (HOIs) have the potential to greatly increase our understanding of ecological interaction networks beyond what is possible with established models that usually consider only pairwise interactions between organisms. While equilibrium values of such HOI-based models have been studied, the dynamics of these models and the stability of their equilibria remain underexplored. Here we present a novel investigation on the effect of the onset speed of a higher-order interaction. In particular, we study the stability of the equilibrium of all configurations of a three-species interaction network, including transitive as well as intransitive ones. We show that the HOI onset speed has a dramatic effect on the evolution and stability of the ecological network, with significant structural changes compared to commonly used HOI extensions or pairwise networks. Changes in the HOI onset speed from fast to slow can reverse the stability of the interaction network. The evolution of the system also affects the equilibrium that will be reached, influenced by the HOI onset speed. This implies that the HOI onset speed is an important determinant in the dynamics of ecological systems, and including it in models of ecological networks can improve our understanding thereof.

We computed the equation of state of iron using extended first-principles molecular dynamics simulations, ranging from $7.874\mathrm{g}/{\mathrm{cm}}^3$ and 5500 K up to $47.2\mathrm{g}/{\mathrm{cm}}^3$ and ${10}^9\mathrm{K}$. We compared the principal Hugoniot curve with semiempirical models, average atom-based model predictions, and shock experiment results. We derived the Helmholtz free energy and the entropy via thermodynamic integration along isochores. We explore the ionization processes at play along the Hugoniot curve by analyzing the evolution of the electronic densities of states in the gigabar regime.

Understanding crystal growth over arbitrary curved surfaces with arbitrary boundaries is a formidable challenge, stemming from the complexity of formulating nonlinear elasticity using geometric invariant quantities. Solutions are generally confined to systems exhibiting rotational symmetry. In this paper, we introduce a framework to address these challenges by numerically solving these equations without relying on inherent symmetries. We illustrate our approach by computing the minimum energy required for an elastic network containing a disclination at any point and by investigating surfaces that lack rotational symmetry. Our findings reveal that the transition from a defect-free structure to a stable state with a single fivefold or sevenfold disclination strongly depends on the shape of the domain, emphasizing the profound influence of edge geometry. We discuss the implications of our results for general experimental systems, particularly in elucidating the assembly pathways of virus capsids. This research enhances our understanding of crystal growth on complex surfaces and expands its applications across diverse scientific domains.

Developing methods to predict electromagnetic instabilities in cardiac dynamics is crucial. However, a comprehensive view of the heart's magnetic activity at a tissue scale is still needed. To address such a challenging problem, we present a theoretical framework to investigate thermoelectric cardiac dynamics from the magnetic field perspective. Our framework demonstrates that periodic stimulations of cardiac cell strands create an external magnetic field, revealing predictable features of nonlinear spatiotemporal cardiac dynamics. Magnetic restitution curves better discriminate instabilities and bifurcations through a thermo-electro-magnetic map analysis. This new approach lays the foundation for innovative, noninvasive diagnostic tools for cardiac arrhythmias.

Inspired by biological and artificial systems, the nonreciprocal $\mathit{XY}$ model with a vision cone interaction has been introduced. In this paper, we clarify that the model on the square lattice with the vision cone angle in a narrow regime, $\mathrm{\Theta }\in ({360}^{\circ },358.5^{\circ })$, undergoes two Kosterlitz-Thouless (KT) phase transitions, while it exhibits a single second-order phase transition with $\mathrm{\Theta }\in (358.5^{\circ },{305}^{\circ }]$. With the short-time dynamic approach, the phase-transition temperatures and critical exponents are accurately determined for both the second-order phase transition and two KT phase transitions.

We explore the hysteretic dynamics of spinor Bose-Einstein condensates of ultracold atoms loaded in static 2D ring geometries and subjected to varying synthetic magnetic fields. Electrically neutral, pseudo-spin-$1/2$ condensates are probed by one-component weak-link potentials that make available paths for the transit of vortices into and out of the ring in both components, and thus can control the number of flux quanta threading the ring hole. For perpendicular fields, domain walls that are dynamically generated in the relative phase of the spin components are shown to play a key role in driving the hysteretic behavior of the whole system through changes in the net magnetic flux. In the presence of spin-orbit coupling, hysteresis is exhibited around the phase transitions found by the metastable current states for varying fields.

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by random matrix theory (RMT). We propose and develop a complementary version of this conjecture: quantum chaotic systems display a Lanczos spectrum whose local means and covariances are well described by RMT. To support this proposal, we first demonstrate its validity in examples of chaotic and integrable systems. We then show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffice to produce the full long-time behavior of general survival probabilities including the spectral form factor, as well as the spread complexity. In addition, for initial states with continuous overlap with energy eigenstates, we analytically find the long-time averages of the probabilities of Krylov basis elements in terms of the mean Lanczos spectrum. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos. Finally, we clarify the relation between spread complexity and the universality classes of RMT by exploring various values of the Dyson index and Poisson distributed spectra.

The recently observed temperature-dependent quasiphase transition of the single-file water chain confined within a carbon nanotube in experiments has been validated by the simple lattice theory and molecular dynamics simulations. It has been pointed out that the atomic charges in water models are important, yet how the values will affect the structural details and thermodynamic properties of the quasiphase transition has not been fully revealed. In this work we perform orientational-biased replica exchange Monte Carlo simulations in the canonical ensemble to explore the effect of atomic charges in the SPC/E water model on the quasiphase transition of a single-file water chain. Based on the atomic charge values reported in literature, three distinct quasiphases are reproduced, comprising a fully hydrogen-bonded water chain at lower temperatures, a more ordered dipolar orientation along the tube axis at intermediate temperatures, and a completely disordered structure at higher temperatures. Then by increasing the atomic charge values, we find that the fragmentation of the entire water chain into shorter water segments, the orientational ordering of water dipoles along the tube axis, and the transition towards complete disorder are all inhibited. Consequently, the transition temperatures between three quasiphases have been shifted to higher temperatures. The thermodynamic analysis demonstrates that the increased atomic charge values enhance the hydrogen bonding between neighboring water molecules and also the electrostatic attraction within the water chain, leading to a longer water dipole correlation length even at higher temperatures. These findings highlight the vital role of atomic charges in water models and also the electrostatic interaction in regulating the orientational ordering of water molecules under nanoconfinement.

Friction-induced energy dissipation is one of the key factors contributing to the unique properties of granular materials, such as the preparation history dependence of the packing structure. However, it remains unclear whether or not more realistic systems that involve two or more types of friction possess unique properties distinct from those that are frictionless or with a single type of friction. Here, we use numerical simulations to investigate the packing structure of binary mixtures of particles with particle type–dependent friction coefficient. Taking single-component systems as reference, we use an effective friction coefficient ${\mu }_{\mathrm{e}}$ to represent the overall frictional strength in granular systems prepared via different protocols. Our results demonstrate that ${\mu }_{\mathrm{e}}$ exhibits a power-law dependence on the individual friction coefficients. Furthermore, we propose models that accurately predict the packing structure of frictional particle systems across a range of compositions, size ratios, and preparation protocols.

Liquid crystal elastomer (LCE) films deform under external stimuli showing significant potential in smart structures and flexible sensors. Due to the small out-of-plane stiffness of LCE films, wrinkling instability poses a critical challenge for the application of LCE films. Different from previous studies, we utilize the anisotropy constitutive model to investigate light-induced wrinkling instability in annulus LCE films with an internal hole. The degree of anisotropy in light-sensitive LCE is determined by two parameters: the anisotropic ratio (ratio of the elastic modulus) and the spontaneous strain ratio. Liquid crystal directors align radially, causing in-plane radial shrinkage and expansion in the other directions under light radiation. Using linear perturbation analysis, we study the critical conditions and wrinkle numbers for the onset of wrinkling instability. Our findings reveal that annulus LCE films with anisotropy exhibit a higher number of wrinkles upon instability. We present the phase diagrams of flat or wrinkled states illustrating the condition under which the film remains flat or transitions into a wrinkled state. This behavior depends on anisotropic parameters, light intensity, contraction coefficient, hole size, and film thickness. By adjusting the combination of these parameters, one can control the wrinkling instability of LCE films. Furthermore, we show that the critical time for the onset of wrinkling decreases as the light intensity and contraction coefficient increase. The findings from this work can provide references for the design of smart structures based on light-sensitive LCE films.

Traditional liquid crystal elastomer (LCE)-based machines are constrained by the need for complex controllers and large power supplies, which limits their applicability in microrobots and other small-scale machines. In this paper, we propose a light-powered self-scrolling LCE crane, which is capable of self-scrolling to lift weights under steady light. Based on a dynamic LCE model, we derive the lateral curvature of the LCE crane and the driving moment for steady scrolling. By numerically solving the equilibrium equations, we found that the driving moment for the self-scrolling is originated from the uneven distribution of the LCE rod in the horizontal direction caused by light. The angular velocity of the self-scrolling depends on five system parameters: heat flux, coefficient of heat transfer, support spacing, weight mass, and scrolling friction coefficient. Through experimental comparative analysis, the results are consistent with the numerical simulation. The light-powered self-scrolling LCE crane device proposed in this paper features a simple structure, consistent horizontal illumination, and a compact light irradiation area. It advances the understanding of self-sustaining structures utilizing active materials and offers valuable insight into the potential applications of light-responsive LCEs in self-driven devices, medical instruments, robotics, sensors, and the energy sector.