Papers

Lindbladian quantum master equations (LEs) are the most popular descriptions for quantum systems weakly coupled to baths. But, recent works have established that in many situations such Markovian descriptions are fundamentally limited: they cannot simultaneously capture populations and coherences even to the leading-order in system-bath couplings. This can cause violation of fundamental properties like thermalization and continuity equations associated with local conservation laws, even when such properties are expected in the actual setting. This begs the question: given a physical situation, how do we know if there exists an LE that describes it to a desired accuracy? Here we show that, for both equilibrium and non-equilibrium steady states (NESS), this question can be succinctly formulated as a semidefinite program (SDP), a convex optimization technique. If a solution to the SDP can be found to a desired accuracy, then an LE description is possible for the chosen setting. If not, no LE description is fundamentally attainable, showing that a consistent Markovian treatment is impossible even at weak system-bath coupling for that particular setting. Considering few qubit isotropic XXZ-type models coupled to multiple baths, we find that in most parameter regimes, LE description giving accurate populations and coherences to leading-order is unattainable, leading to rigorous no-go results. However, in some cases, LE description having correct populations but inaccurate coherences, and satisfying local conservation laws, is possible over some of the parameter regimes. Our work highlights the power of semidefinite programming in the analysis of physically consistent LEs, thereby, in understanding the limits of Markovian descriptions at weak system-bath couplings.

Hybrid systems consisting of metal-fullerene composites exhibit intriguing properties but often suffer from thermal instability. With proper control, such instability can be harnessed to enable the formation of sophisticated nanostructures with nanometric precision. These self-organization phenomena are not limited to thermal stimulation alone but can also be triggered by other external stimuli. In this work, we investigate the morphological evolution of thin films composed of evaporated C60 and sputtered nickel mixtures, focusing on how external stimuli influence both their structural and electrical properties. Thin films were prepared under controlled deposition conditions, and their surface morphology was analyzed using advanced characterization techniques. Progressive changes in film morphology were observed as a function of composition and external treatment, highlighting the interplay between metallic and molecular components. In particular, it was observed that, due to the annealing treatment, the sample undergoes strong phase separation, with the formation of structures tens of microns in diameter and an increase in electrical resistance, exhibiting insulating behavior. These findings provide insights into the mechanisms governing hybrid thin film formation and suggest potential applications in electronic, optoelectronic, and energy-related devices.

Understanding how the physical properties of a fluid influence bacterial behavior is essential for explaining how microorganisms interact with their environment and with animal hosts. Here, we examine how changes in fluid viscosity and rheological properties affect the locomotion of the marine bacterium Vibrio fischeri and its ability to produce luminescence through cell–cell communication. We track the three-dimensional motion of single cells in well-defined fluids with different physical properties and measure the luminescence emitted by cell populations. We find that fluids with higher viscosity cause V. fischeri to spend more time in a slower, turning-focused swimming mode, which reduces how effectively cells spread out and encounter the chemical signals required to activate luminescence. As a result, luminescence first increases and then decreases in Newtonian fluids, but decreases monotonically in fluids that exhibit non-Newtonian rheological behavior. Computer simulations based on our measurements confirm that the ability of cells to explore their surroundings plays a central role in determining when and how strongly they communicate. These findings reveal a direct link between the physical environment, bacterial movement, and collective behavior, and offer insight into how microorganisms adapt to complex fluid habitats, including those found inside animal hosts.

Muscle contraction is a prototypical multiscale chemomechanical process in which ATP hydrolysis at the molecular level drives force generation and mechanical work at larger scales. A central challenge is to incorporate the free energy supplied by ATP hydrolysis into a mechanical cross-bridge model in a way that is thermodynamically consistent and connects microscopic motor cycling to macroscopic force generation. Here we use the Energetic Variational Approach (EnVarA) to combine Hill's cycle-affinity viewpoint with Huxley's sliding-filament mechanics in a single thermodynamically consistent framework. We formulate a three-state Fokker–Planck–jump description for cross-bridge densities evolving on state-dependent free-energy landscapes, and treat ATP, ADP, and Pi as reacting and diffusing chemical species that share the same free-energy functional as the cross-bridge densities. ATP hydrolysis enters the model through local detailed balance, which biases the transition rates. Filament sliding velocity is incorporated as a convective transport term in the Fokker–Planck dynamics, so mechanical power output is defined directly from the energy balance law. Under chemostatted conditions and a fast-equilibration assumption for the two attached states, the model reduces to a closed two-state molecular motor description; in a further small-diffusion limit, this reduction recovers a Huxley-type transport-reaction equation whose effective attachment and detachment rates are derived from the underlying three-state cycle rather than prescribed phenomenologically, with their strain, ATP, and phosphate dependence fixed by the energy landscapes and local detailed balance. We calibrate the reduced model against cross-bridge-level observables and show that it reproduces key velocity-dependent trends and yields a Hill-like force–velocity relation comparable to established cross-bridge models.

BaAl$_2$O$_4$ is a ferroelectric material that exhibits structural quantum criticality through chemical composition tuning. Although theoretical calculations and several diffraction experiments have suggested the involvement of a soft mode in its ferroelectric structural phase transition, direct experimental verification is still lacking. In this study, we successfully observed two soft modes of BaAl$_2$O$_4$ using x-ray inelastic scattering, providing direct experimental evidence for their role in the structural phase transition. Furthermore, we reveal that the soft modes at the M and K points are nearly degenerate in energy, indicating a delicate balance in which either mode could potentially freeze. The K-point mode simultaneously softens toward the transition temperature ($T_{\rm C}$) in a manner nearly identical to the M-point mode. However, the phase transition condenses only at the M point, with the M-point mode stabilizing as an acoustic mode in the low-temperature structure and the K-point mode hardening as temperature decreases.

Phase transitions among Mg2SiO4 and its high-pressure polymorphs (wadsleyite and ringwoodite) are central to mantle dynamics and deep-mantle material cycling. However, the locations and Pressure-Temperature (P-T) dependences of these phase boundaries remain debated, largely due to experimental limitations at extreme conditions and the high computational cost of first-principles free-energy calculations. Here, a machine-learning-potential driven workflow combining non-equilibrium thermodynamic integration (NETI) and two-phase coexistence simulations is employed to enable large-scale, long-timescale molecular dynamics sampling. Within this workflow, the melting curve of forsterite is evaluated and a complete P-T phase diagram is constructed. Relative to conventional ab initio approaches, this strategy reduces computational expense while retaining thermodynamic consistency in phase-stability assessment. The workflow is applicable to efficient evaluation of phase stability and thermodynamic properties in deep-Earth silicate systems.

Semantic segmentation of microscopy images is a critical task for high-throughput materials characterisation, yet its automation is severely constrained by the prohibitive cost, subjectivity, and scarcity of expert-annotated data. While physics-based simulations offer a scalable alternative to manual labelling, models trained on such data historically fail to generalise due to a significant domain gap, lacking the complex textures, noise patterns, and imaging artefacts inherent to experimental data. This paper introduces a novel framework for labour-free segmentation that successfully bridges this simulation-to-reality gap. Our pipeline leverages phase-field simulations to generate an abundant source of microstructural morphologies with perfect, intrinsically-derived ground-truth masks. We then employ a Cycle-Consistent Generative Adversarial Network (CycleGAN) for unpaired image-to-image translation, transforming the clean simulations into a large-scale dataset of high-fidelity, realistic SEM images. A U-Net model, trained exclusively on this synthetic data, demonstrated remarkable generalisation when deployed on unseen experimental images, achieving a mean Boundary F1-Score of 0.90 and an Intersection over Union (IOU) of 0.88. Comprehensive validation using t-SNE feature-space projection and Shannon entropy analysis confirms that our synthetic images are statistically and featurally indistinguishable from the real data manifold. By completely decoupling model training from manual annotation, our generative framework transforms a data-scarce problem into one of data abundance, providing a robust and fully automated solution to accelerate materials discovery and analysis.

Realization of ferromagnetic ferroelectricity, combining two ferroic orders in a single phase, is the longstanding problem of great practical importance. One of the difficulties is that ferromagnetism alone cannot break inversion symmetry $\mathcal{I}$. Therefore, such a phase cannon be obtained by purely magnetic means. Here, we show how it can be designed by making orbital degrees of freedom active. The idea can be traced back to a basic principle of interatomic exchange, which states that an alternation of occupied orbitals along a bond (i.e., antiferro orbital order) favors ferromagnetic coupling. Moreover, the antiferro orbital order breaks $\mathcal{I}$, so that the bond becomes not simply ferromagnetic but also ferroelectric. Then, we formulate main principles governing the realization of such a state in solids, namely: (i) The magnetic atoms should not be located in inversion centers, as in the honeycomb lattice; (ii) The orbitals should be flexible enough to adjust they shape and minimize the energy of exchange interactions; (iii) This flexibility can be achieved by intraatomic interactions, which are responsible for Hund's second rule and compete with the crystal field splitting; (iv) For octahedrally coordinated transition-metal compounds, the most promising candidates appear to be iodides with a $d^{2}$ configuration and relatively weak $d$-$p$ hybridization. Such a situation is realized in the van der Walls compound VI$_3$, which we expect to be ferromagnetic ferroelectric.

We experimentally investigate the dynamics of a sphere rolling down a granular slope by varying the initial velocity, slope angle, and sphere density. The results show that the sphere rolls down with constant deceleration while sinking into the granular bed. $\delta/R$ (the sinking depth $\delta$ normalized to the sphere radius $R$) is scaled by the sphere density normalized by the bulk density of the granular layer. To evaluate the translational energy dissipation, we introduce an effective friction coefficient $\mu_\mathrm{d}$. We demonstrate that $\mu_\mathrm{d}$ decreases with increasing the slope angle and the slip ratio. Furthermore, systematic measurements over a wide range of sphere densities reveal that $\mu_\mathrm{d}$ increases linearly with $\delta/R$ : $\mu_\mathrm{d}=\beta(\delta/R)+\mu_0$. The value of $\mu_0$ is linearly decreasing with slip ratio and its coefficient $\beta(\simeq0.41)$ does not vary significantly. The results suggest that the normalized depth and slip ratio determine the effective friction of a rolling sphere.

Non-Hermitian systems have attracted significant theoretical interest due to their extreme properties. However, realizations have mostly been limited to classical applications or artificial setups. In this study, we focus on the quantum nature inherent in bosonic Bogoliubov-de Gennes (BdG) systems, which from the perspective of spectral theory corresponds to non-Hermiticity. Based on this insight, we propose a steady-state skin effect in quantum condensed matter utilizing such BdG non-Hermiticity. Specifically, we introduce BdG quantum terms arising from parametric pumping to the edge states of an underlying bosonic Hermitian Chern insulator, thereby realizing non-Hermiticity without dissipation. This system design has the advantage of being largely independent of microscopic model details. Through analysis using non-equilibrium Green's functions, we find that under open boundary conditions, a steady state exhibiting the non-Hermitian skin effect is realized. The pronounced corner particle accumulation observed in this steady state shows quadrature anisotropy, which manifests the bosonic quantum nature. Our results bridge the gap between the fascinating mathematics of non-Hermitian matrices and practical quantum physical systems.

We investigate the collective excitations of anisotropic dipolar supersolids in planar confinement, focusing on triangular and stripe phases in situations where the dipoles are titled to have a component in the plane. Using Bogoliubov-de Gennes calculations and hydrodynamic theory, we identify the elastic parameters that govern the long-wavelength dynamics, including two orientational coefficients that capture the broken rotational symmetry induced by dipole tilt. Analytical expressions for the speeds of sound are obtained along the principal axes for triangular supersolids and along any propagation direction for the stripe supersolid. Our results provide a unified framework for understanding sound propagation in anisotropic dipolar supersolids and establish connections to recent experiments on sound propagation in striped Bose-Einstein condensates.

The water-repellence properties of superhydrophobic surfaces make them promising for many applications. However, in some extreme environments, such as high humidities and low temperatures, condensation on the surface is inevitable, which induces the loss of surface superhydrophobicity. In this study, we propose a freezing-melting strategy to achieve the dewetting transition from the Wenzel state to the Cassie-Baxter state. It requires freezing the droplet by reducing the substrate temperature and then melting the droplet by heating the substrate. The condensation-induced wetting transition from the Cassie-Baxter state to the Wenzel state is analyzed first. Two kinds of superhydrophobic surfaces, i.e., single-scale nano-structured superhydrophobic surface and hierarchical-scale micro-nano-structured superhydrophobic surface, are compared and their effects on the static contact states and impact processes of droplets are analyzed. The mechanism for the dewetting transition is analyzed by exploring the differences in the micro/nano-structures of the surfaces and it is attributed to the unique structure and strength of the superhydrophobic surface. These findings will enrich our understanding of the droplet-surface interaction involving phase changes and have great application prospects for the design of superhydrophobic surfaces.

Topological states of matter are characterized by nonlocal structures that are naturally encoded in the quantum entanglement of many-body wavefunctions. Topological semimetals are short-range entangled states at weak coupling and their entanglement structure at strong coupling remains largely unexplored. In this work, we investigate the multipartite entanglement structure of strongly coupled holographic nodal line semimetals. Building on previous studies of entanglement entropy and the holographic c-function, we focus on multipartite entanglement measures, including the conditional mutual information, multi-entropy, and the Markov gap which is based on the entanglement wedge cross section. Our results demonstrate that while these multipartite measures vanish in the long-distance limit $l \to \infty$, which confirms that the holographic nodal line semimetal remains a short-range entangled state, their large $l$ scaling behavior remains highly sensitive to the underlying topology. The large $l$ power-law decay and scaling exponents serve as robust, non-local order parameters that exhibit sharp changes at the quantum critical point. This work establishes multi-partite entanglement as a powerful probe of quantum topological phase transitions in strongly coupled topological systems.

Spin relaxometry using solid-state spin defects, such as the diamond nitrogen-vacancy (NV) center, probes dynamical processes by measuring how environmental fluctuations enhance the spin relaxation rate. In the weak-coupling limit, relaxation rates sample the transverse magnetic-noise power spectral density through a sensor-specific filter function, turning the defect into a local, frequency-selective noise spectrometer. This review bridges theory and experiment, clarifying how measured relaxation rates map onto noise spectra and how near-field geometry shapes the response. We highlight representative applications across condensed-matter physics, chemical and biological sensing, and relaxometry-based magnetic-resonance spectroscopy. We conclude with emerging opportunities and key challenges.

Thermally actuated twisted and coiled polymer (TCP) artificial muscles exhibit exceptional specific work capacities but are limited by an inherent competition between load-bearing capacity and actuation stroke. To address this limitation, we investigate a hierarchical helical structure designed to decouple force generation from kinematic limits. We propose a coupled thermo-mechanical model incorporating inter-filamentary contact mechanics and geometric nonlinearities to predict the assembly's equilibrium response. The results indicate that this hierarchical topology significantly amplifies isometric actuation stress compared to monofilament baselines, while maintaining a biological-like contraction stroke of approximately 22%. A critical topological threshold governed by the balance between cooperative load-sharing and geometric confinement is identified. Beyond an optimal bundle complexity, the geometric jamming dominates, as excessive inter-filamentary friction hinders actuation. Furthermore, we elucidate a stiffness-stroke synergy in homochiral configurations, where high helical angles amplify the thermal untwisting torque to overcome increased structural rigidity. Crucially, the volumetric energy density exhibits scale invariance regarding the hierarchical radius, implying that absolute force output can be linearly scaled through geometric upsizing without compromising efficiency. These findings provide a mechanics-based rationale for the structural programming, demonstrating that soft actuator performance limits are dictated by topological order rather than intrinsic material properties.

We develop a statistical framework for wealth allocation in which equilibrium-like statistics follow from unbiased counting of admissible configurations rather than postulated exchange rules. Each agent is described by a value–wealth map $V_i(w)$, whose local resolution fixes the microscopic weight through a Jacobian relation. In a closed system, the microcanonical marginal and a reservoir expansion yield an emergent canonical distribution for the regular sector. Its partition sum gives a general condensation criterion: if this sector has finite wealth capacity, excess wealth concentrates on a small subset of agents. We extend the construction to open systems with variable wealth and agent number and to weak quasistatic driving. The global constraint determines an evolution equation for the common parameter $\lambda(t)$, while simultaneous changes in total wealth and value–wealth geometry produce a unified first-order response. The susceptibility $\chi_W=\sum_i\mathrm{Var}_i(w)$ equals the Fisher information of the joint canonical family, and Legendre duality gives $\mathrm{d}s^2=\chi_W\mathrm{d}\lambda^2=\chi_W^{-1}\mathrm{d}W^2=-\mathcal{S}''(W)\mathrm{d}W^2$. For power-law critical tails, finite capacity requires $p>2$; within this regime, $\chi_W$ diverges for $2<p\leq3$ and remains finite for $p>3$, while the critical boundary lies at finite Fisher–Rao distance. We also derive a qualified Cram'er–Rao duality and an open-system mixed-response relation. Contact-geometric, Airy-scaling, and stochastic-dynamical interpretations are identified only as conjectures or future work. The time-dependent results are quasistatic and do not determine microscopic relaxation times, while the information geometry describes the canonical family.

Probabilistic graphical models with frustration exhibit rugged energy landscapes that trap iterative optimization dynamics. These landscapes are shaped not only by local interactions, but crucially also by the global loop structure of the graph. The famous Bethe approximation treats the graph as a tree, effectively ignoring global structure, thereby limiting its effectiveness for optimization. Loop expansions capture such global structure in principle, but are often impractical due to combinatorial explosion. The $M$-layer construction provides an alternative: make $M$ copies of the graph and reconnect edges between them uniformly at random. This provides a controlled sequence of approximations from the original graph at $M=1$, to the Bethe approximation as $M \rightarrow \infty$. Here we generalize this construction by replacing uniform random rewiring with a structured mixing kernel $Q$ that sets the probability that any two layers are interconnected. As a result, the global loop structure can be shaped without modifying local interactions. We show that, after this copy-and-reconnect transformation, there exists a regime in which layer-to-layer fluctuations decay, increasing the probability of reaching the global minimum of the energy function of the original graph. This yields a highly general and practical tool for optimization. Using this approach, the computational cost required to reach these optimal solutions is reduced across sparse and dense Ising benchmarks, including spin glasses and planted instances. When combined with replica-exchange Monte Carlo, the same construction increases the polynomial-time algorithmic threshold for the maximum independent set problem. A cavity analysis shows that structured inter-layer coupling significantly smooths rugged energy landscapes by collapsing configurational complexity and suppressing many suboptimal metastable states.

It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits slow propagation of information (logarithmic light cone), a key signature of many-body localization (MBL), in any fixed energy interval at the bottom of the spectrum. The relevant parameter regime, which covers both weak interaction and strong disorder, is determined solely by the energy interval.

I study via Langevin dynamics simulations two opposite cases of systems of particles that alternate their identity according to density dependent motility (DDM) rules and interact via a soft repulsive potential. In the correlated case, dilute regions are passive and dense regions are active, while in the anti-correlated case, dilute regions are active and dense regions are passive. I classify the emerging steady states, explain the principal phase transitions, and finally suggest directions for further investigation.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

Self-accelerating Airy matter waves offer a clean setting to access the intrinsic cubic-in-time phase. Here we reconstruct the relative phase of simulated Airy-shaped Bose-Einstein condensates from interference fringes in free space, a regime approached in microgravity. The cubic phase dynamics are quantified via approximately debiased, windowed polynomial fits with systematics-aware uncertainty estimates that account for window-induced correlations. We compare two physically feasible phase-extraction methods, heterodyne-based and density-based, and show that an Airy-Gaussian geometry yields substantially improved robustness to fit-window selection relative to an Airy-Airy collision. In the weakly interacting regime, the extracted cubic coefficient responds linearly to leading order to the effective interaction strength, its shift from the noninteracting value providing a calibrated probe of weak mean-field nonlinearities in self-accelerating condensates.

We study a variant of the pseudo-inverse learning rule for Hopfield-like Neural Networks, which allows the network to infer archetypal concepts on the basis of a limited number of examples. The key novelty is that the new learning rule compensates for correlations between examples at the population level rather than at the level of the particular training set, reducing overfitting of the dataset and leading to generalization. The mean-field replica theory for this model reveals how this generalization ability is mediated by a multitude of thermodynamic states, with diverse thermodynamic properties, coexisting with the standard Hopfield ones. They appear and vanish through smooth transitions or discontinuous jumps and, interestingly, show much stronger Replica Symmetry Breaking (RSB) effects than the standard Hopfield model, as captured by our 1RSB analysis. Our results, in excellent agreement with numerical simulations, provide deeper insight into the interplay between memory storage and generalization in attractor neural networks.

Non-Hermitian degeneracies of Lindblad generators (Liouvillian exceptional points) can induce non-exponential relaxation and higher-order poles in dynamical response functions. A collective spin coupled to a polarized Markovian bath exhibits an exceptional spectral phase in which defective Liouvillian modes imprint super-Lorentzian features in frequency-resolved spectra. We compute the emission spectrum via the Liouvillian resolvent, identify symmetry-sector selection rules, and demonstrate that exceptional-point signatures are strongly state-dependent: they are suppressed in steady-state fluorescence yet become unambiguous for generic (infinite-temperature or random) initial states. Our results provide an experimentally accessible spectroscopic diagnostic of many-body Liouvillian exceptional phases and clarify when steady-state emission can (and cannot) reveal them.

Triadic percolation turns bond percolation into a dynamical problem governed by an effective one-dimensional unimodal map. We show that the geometry of superstable cycles provides a direct, map-agnostic probe of local nonlinearity: specifically, the distance from the map's maximum to a distinguished next-to-maximum point on the attracting $2^n$-cycle (which coincides with a preimage of the maximum at $2^n$-superstability) scales as $|\Delta p|^{\gamma}$ with $\gamma = 1/z$, where $z$ is the nonflat order of the maximum. This prediction is verified across canonical unimodal families and heterogeneous triadic ensembles, with Lyapunov spectra corroborating the one-dimensional reduction. A derivative condition on the activation kernel fixes the local nonlinearity order $z$ (and thus, under standard unimodal-map hypotheses, the associated $z$-logistic universality class) and gives conditions under which $z>2$ can be realized. The diagnostic operates directly on orbit data under standard regularity assumptions, providing a practical tool to classify universality in higher-order networks.

Mechanical and thermodynamic properties, including the influence of crystal defects, are critical for evaluating materials in engineering applications. Molecular dynamics simulations provide valuable insight into these mechanisms at the atomic scale. However, current practice often relies on fragmented scripts with inconsistent metadata and limited provenance, which hinders reproducibility, interoperability, and reuse. FAIR data principles and workflow-based approaches offer a path to address these limitations. We present reusable atomistic workflows that incorporate metadata annotation aligned with application ontologies, enabling automatic provenance capture and FAIR-compliant data outputs. The workflows cover key mechanical and thermodynamic quantities, including equation of state, elastic tensors, mechanical loading, thermal properties, defect formation energies, and nanoindentation. We demonstrate validation of structure-property relations such as the Hall-Petch effect and show that the workflows can be reused across different interatomic potentials and materials within a coherent semantic framework. The approach provides AI-ready simulation data, supports emerging agentic AI workflows, and establishes a generalizable blueprint for knowledge-based mechanical and thermodynamic simulations.

Our previous understanding of electronic transport in disordered systems was based on the assumption that there is a finite Fermi velocity for the relevant electrons. The Fermi velocity determines important length scales in disordered systems such as the diffusion length and the localization length. However, in disordered systems with vanishing or nearly vanishing Fermi velocity, it is uncertain what determines the important length scales in such systems. In this work, we use the 1D Lieb lattice with isolated flat bands as an example to show that the quantum metric length (QML) is a fundamental length scale in the ballistic, diffusive and localization regimes. The QML is defined through the Bloch state wave functions of the flat bands. In the ballistic regime with short junctions, the QML controls the finite energy transport properties. In the localization regime with long junctions, the localization length is determined by the QML and remarkably, independent of disorder strength over a wide range of disorder strength. We call this unconventional localization regime, the quantum metric localization regime. In the diffusive regime, we demonstrate that the diffusion coefficient is linearly proportional to the QML via the wave-packet dynamics numerically. Importantly, the numerical results are consistent with the analytical results obtained through the Bethe-Salpeter equation. We conclude that the QML is a fundamentally important length scale governing the properties of disordered flat band materials.

We present a comprehensive investigation of structural, magnetic and transport properties of Ni$_2$FeAl Heusler alloy nanoparticles (NPs) synthesized via template-less chemical route. The NPs exhibit high saturation magnetization of 3.02 $\mu_ {\rm B}$/f.u. at 5~K, large magnetic anisotropy of 0.238 MJ/m$^3$, and a Curie temperature of 874~K. Magnetocaloric analysis reveals a magnetic entropy change of 3.1 J.kg$^{-1}$K$^{-1}$ at 70 kOe. Low-temperature transport measurements show a weak resistivity upturn, following a $-T^{1/2}$ dependence, indicative of disorder-enhanced electron-electron interactions. First-principles calculations based on density functional theory yield a magneto-crystalline anisotropy energy of 0.987 MJ/m$^3$, consistent with experiment and demonstrate pronounced surface and finite-size effects through comparison of bulk and nanocluster geometries. The combination of high Curie temperature, sizable perpendicular magnetic anisotropy, and moderate spin polarization and magnetic entropy change make the Ni$_2$FeAl as promising candidate for various applications.

Determining the center-of-mass (COM) momentum of Cooper pairs in unconventional superconductors or superfluids is a topic of great interest in condensed matter physics and ultracold atomic gases. Theoretically, we investigate the dynamical excitations of a two-dimensional spin-polarized attractive Hubbard model on a square optical lattice under an effective Zeeman field by computing the density and spin dynamical structure factors, focusing on phase transition from a Bardeen-Cooper-Schrieffer (BCS) superfluid to an Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. In the FFLO superfluid, besides the phonon mode in the density channel, a low-energy bogolon mode emerges in the spin channel, which is associated with Bogoliubov quasiparticles on a Bogoliubov Fermi surface. Moreover, the dynamical excitations exhibit pronounced anisotropy in momentum space due to the finite COM momentum. At half filling, the roton mode around $[\pi,\pi]$ evolves from a point-like minimum into a ring structure shifted by the COM momentum across the BCS-FFLO transition, providing a roton-based protocol to extract the COM momentum. These predictions provide key insights for confirming the existence of FFLO superfluids and understanding their dynamical excitation spectra.

In this manuscript, we study the quench dynamics of a transverse-field XY model starting from coherent Gibbs states. The results reveal that the initial strength of magnetization plays a crucial role in the emergence of dynamical quantum phase transitions. In concrete terms, when quenching within the same phase, through the properties of observables such as Fisher zeros and magnetization, we show that the stronger the initial magnetization, the more difficult the emergence of dynamical quantum phase transitions. The underlying mechanism is that the strong initial magnetization provides a directional effect, which inhibits the spin flipping in the process of quantum quench, making the dynamical quantum phase transition difficult to emerge. Since dynamical quantum phase transitions can be experimentally realized in various artificial systems, we hope that the physics predicted here can be experimentally verified in tabletop platforms.

We study the splitting dynamics of a triply quantized vortex (TQV) confined in a ring-shaped Bose-Einstein condensate under a weakly elliptical harmonic trap. Using full 3D simulations in cylindrical coordinates, combined with a semi-analytical energy analysis, we show that the vortex preferentially splits along the long axis of the trap, a direction that minimizes the kinetic-energy cost relative to the initial TQV state. Systematic parameter scans reveal that initial quantum fluctuations increase the splitting time and suppress the transient three-core pattern observed in noise-free simulations, whereas stronger nonlinear interactions accelerate the splitting. When the trap is nearly isotropic, the unstable Bogoliubov modes are dominated by both azimuthal quantum number $l_q=3$ and $l_q=2$; this leads to a dynamical sequence where three daughter vortices first form a triangular arrangement, later evolving into a linear chain. For stronger anisotropy, geometric coupling selectively enhances the $l_q=2$ mode, making it the sole dominant channel and resulting directly in linear vortex alignment – a clear signature of geometry-induced mode competition explained through combined energy-based and Bogoliubov stability analysis. Our results provide a quantitative picture of how trap geometry can steer the instability pathway, splitting time, and final pattern of a multiply quantized vortex, offering a route toward geometry-controlled vortex engineering.